Establishing the distribution of cerebrovascular resistance using computational fluid dynamics and 4D flow MRI

Establishing the distribution of cerebrovascular resistance using computational fluid dynamics and 4D flow MRI | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Establishing the distribution of cerebrovascular resistance using computational fluid dynamics and 4D flow MRI Axel Vikström, Petter Holmlund, Madelene Holmgren, Anders Wåhlin, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3900174/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 11 You are reading this latest preprint version Abstract Cerebrovascular resistance (CVR) regulates blood flow in the brain, but little is known about the vascular resistances of the individual cerebral territories. We present a method to calculate these resistances and investigate how CVR varies in the hemodynamically disturbed brain. We included 48 patients with stroke/TIA (29 with symptomatic carotid stenosis). By combining flow rate (4D flow MRI) and structural computed tomography angiography (CTA) data, and using computational fluid dynamics (CFD) we computed the perfusion pressures out from the circle of Willis, with which CVR of the MCA, ACA, and PCA territories was estimated. 56 controls were included for comparison of total CVR. CVR were 33.8 ± 10.5, 59.0 ± 30.6, and 77.8 ± 21.3 mmHg·s/ml for the MCA, ACA, and PCA territories. We found no differences in total CVR between patients, 9.3 ± 1.9 mmHg·s/ml, and controls, 9.3 ± 2.0 mmHg·s/ml (p = 0.88), nor in territorial CVR in the carotid stenosis patients between ipsilateral and contralateral hemispheres. Territorial resistance associated inversely to territorial brain volume (p < 0.001). These resistances may work as reference values when modelling blood flow in the circle of Willis, and the method can be used when there is need for subject-specific analysis. Physical sciences/Physics/Fluid dynamics Health sciences/Diseases/Cardiovascular diseases/Vascular diseases/Carotid artery disease Health sciences/Diseases/Cardiovascular diseases Health sciences/Diseases/Cardiovascular diseases/Vascular diseases Health sciences/Diseases/Cardiovascular diseases/Vascular diseases/Cerebrovascular disorders/Stroke Carotid stenosis cerebrovascular resistance computational fluid dynamics peripheral cerebral territories stroke Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Introduction A balanced blood flow distribution throughout the brain is crucial for maintaining adequate cerebral function. Cerebral blood flow distribution is intimately connected to the blood pressure driving the flow (i.e., the perfusion pressure) and the flow resistance of the cerebral arteries, known as cerebrovascular resistance (CVR). The cerebral autoregulation regulates CVR by varying the size of the diameters of the cerebral small arteries and arterioles, ensuring stable flow during changes in perfusion pressure [ 1 ]. Simultaneously, variations in metabolic demands induce changes in CVR through neurovascular coupling to secure a sufficient blood flow [ 2 , 3 ]. Therefore, deviations in CVR may reflect disturbances or depletion of these regulatory processes. Additionally, impaired vascular structure and function has been found to be increasingly important in the development of cognitive diseases [ 4 – 8 ], making CVR and its distribution a potential screening tool in early cognitive decline [ 9 ]. Lastly, the vascular resistance of the different cerebral territories plays an essential role in the mathematical modelling and prediction of cerebral blood flow [ 10 , 11 ]. CVR is mostly estimated globally [ 12 , 13 ], usually due to the simplicity of measuring total cerebral inflow and mean arterial pressure, as opposed to the local flow rates and perfusion pressures needed to determine CVR of each vascular territory. Knowing these territorial resistances would not only improve our understanding of physiology and pathophysiology, but could also be used for predictions of blood flow and perfusion pressure during planned interventions such as medical or surgical treatments [ 14 ]. CVR can be computed from measurements of blood flow and perfusion pressure through an Ohm’s law equivalent [ 11 ]. The global measure of CVR, total CVR, represents the vascular resistance against the flow from the cervical arteries to the parenchyma. It can be determined by the difference in mean arterial pressure (MAP) and intracranial pressure (ICP) divided by total cerebral blood flow (tCBF) [ 15 ]. A majority of the total CVR comes from the peripheral vessels [ 16 ] in the territories supplied by the major cerebral arteries extending from the circle of Willis; the middle, anterior and posterior cerebral arteries (MCA, ACA, PCA) [ 17 ]. CVR of these territories, territorial CVR, can be determined through the difference in the perfusion pressure and ICP divided by the flow in each exiting artery of the circle of Willis. Previous estimations of territorial CVR have been made with assumptions on arterial pressure drops and flow distribution in the branches of the circle of Willis [ 18 , 19 ], in addition to often being reliant on literature data and thus not subject-specific data. Four-dimensional phase-contrast magnetic resonance imaging (4D flow MRI) [ 20 ] allows for simultaneous flow measurements in the vessels of the entire brain, eliminating the need for flow distribution assumptions. To accurately estimate the territorial resistance, the measured flow rates to each territory should be accompanied by their corresponding perfusion pressures, which can be determined with computational fluid dynamics (CFD) [ 21 ] modelling of the circle of Willis. Consequently, this allows for the assessment of each territorial resistance in a subject-specific manner while utilizing accurate flow rate measurements and accounting for pressure drops in the circle of Willis. In this study, we aim to establish the distribution of the CVR in a group of patients with a transient ischemic attack or stroke, with or without significant carotid stenoses. With this patient group we examine possible lateral differences in CVR from hemodynamic disturbances induced by carotid stenoses. A control group of elderly was included for comparison of total CVR. As a secondary analysis we examine the relationship between CVR and brain volume, in total as well as intra- and inter-territorially. Material and methods Overview of approach Vascular resistances of each cerebral arterial territory were computed on a subject-specific level (Fig. 1 ). The arterial tree of each patient was segmented from computed tomography angiography (CTA) data. The flow rate in each artery was acquired from the 4D flow MRI data. With the segmentation and flow rates, CFD computations estimate the perfusion pressure at each branch of the circle of Willis. The computed perfusion pressures together with the flow rate to each territory allowed for an assessment of CVR in the cerebral regions fed by the ACA, MCA, and PCA. Subjects The study population consisted of a patient group with two subgroups and a control group (Fig. 2 ). The patient subgroups originated from the stroke unit at Umeå University Hospital between 2012–2015. 29 patients were included in the stenotic group. They had a transient ischemic attack (TIA) or cerebral infarct and a symptomatic carotid stenosis ≥ 50%, with or without a non-symptomatic contralateral stenosis. The non-stenotic group consisted of 19 patients with TIA, without stenoses. North American Symptomatic Carotid Endarterectomy Trial (NASCET) method was used for grading the stenosis [ 22 ]. The side with the symptomatic stenosis was defined as the ipsilateral side, with the opposite being the contralateral side. A control group was recruited from the Swedish population registry (N = 61) [ 23 ]. It consisted of elderly, irrespective of previous disease, but those with previous TIA or stroke were excluded (N = 3). MRI was incomplete for two controls. Territorial CVR could not be estimated in the control group due to the lack of CTA but 4D flow data and mean arterial pressure (MAP) were available, allowing for computation of total CVR. Full characteristics are listed in Table 1 . Table 1 Characteristics of the patients and controls. Significant difference was tested with Student’s t-test for continuous variables and chi-squared test for categorical variables between the patient subgroups (†) as well as between all patients and the controls (*), where significance (p < 0.05) is highlighted in bold. mRS; modified Rankin Score. NIHSS; National Institutes of Health Stroke Scale. SBP; Systolic Blood Pressure. DBP, Diastolic Blood Pressure. MAP, Mean Arterial Pressure. Stenotic group (N = 29, 22 men) Non-stenotic group (N = 19, 13 men) All patients (N = 48, 35 men) Controls (N = 56, 36 men) Age (years) 73 ± 6 † 67 ± 7 † 71 ± 7 * 74 ± 4 * Stenosis degree (%) 75 ± 12 (ipsilateral) 67 ± 10 (contralateral, N = 9) N/A N/A N/A mRS score 0 (0–1) 0 (0–0) 0 (0–1) N/A NIHSS score 1 (0–6) 0 (0–3) 1 (0–6) N/A SBP (mmHg) 137 ± 17 132 ± 19 135 ± 18 * 142 ± 19 * DBP (mmHg) 70 ± 10 74 ± 12 72 ± 11 * 81 ± 10 * MAP (mmHg) 92 ± 11 94 ± 13 93 ± 12 * 102 ± 12 * Heart rate (bpm) 65 ± 11 69 ± 10 67 ± 11 68 ± 11 Hypertension (N) 22 (76%) 11 (58%) 33 (69%) 31 (55%) Hyperlipidemia (N) 16 (55%) 6 (32%) 22 (46%) * 12 (21%) * Diabetes mellitus (N) 7 (24%) 4 (21%) 11 (23%) 6 (11%) Ever smoker (N) 19 (66%) 9 (47%) 28 (58%) 36 (64%) The study was approved by the ethical review board of Umeå University (Dnr: 2011-440-31M) and the Swedish Ethical Review Authority (Dnr: 2019–05909) and was performed in accordance with the guidelines of the Declaration of Helsinki. All participants were given oral and written information about the study and written consent was obtained from all participants. Imaging For each patient, 4D flow MRI and CTA data with full brain coverage was available. A 3T scanner with a 32-channel head coil (GE Discovery MR 750, Milwaukee, WI, USA) was used for the MRI scans providing flow rates in the cerebral vessels, utilizing a balanced 5-point phase contrast vastly undersampled isotropic projection reconstruction (PC-VIPR) sequence [ 24 , 25 ]. The velocity encoding was 110 cm/s. Reconstructed MRI voxel size was 0.7×0.7×0.7 mm 3 . The CTA images used to segment patient-specific vessel geometries were obtained from different hospitals, with reconstructed slice thickness ranging between 0.3 to 0.625 mm. More information regarding settings for both imaging modes can be seen in the study of Holmgren et al [ 21 ]. Flow rates and vessel geometries The vessel geometries were semi-automatically segmented from the CTA, performed with Synopsys’ Simpleware™ software (ScanIP P-2019.09; Synopsys, Inc., Mountain View, USA). The segmentation included the complete circle of Willis with the internal carotid arteries (ICA), the basilar artery (BA), the middle cerebral arteries (MCA1), proximal and distal posterior cerebral arteries (PCA1/PCA2), proximal and distal anterior cerebral arteries (ACA1/ACA2), and the anterior and posterior communicating arteries (ACoA and PCoA). The segmentation process was carried out as previously described[ 21 ]. Average flow rates for each ICA, MCA1, ACA1, ACA2, BA, PCA1, PCA2 and PCoA were obtained with a post-processing method that averages consecutive flow waveforms [ 26 ]. The circle of Willis geometries were separated into an anterior and posterior part to ensure the correct flows in the subsequent simulations and to avoid possible underdetermination of the flow equations introduced by the circular structure of the circle of Willis. Examples of each type are shown in Fig. 3 A and Fig. 3 B. AV segmented all vascular trees of the non-stenotic group, as well as one complete and 20 posterior geometries from the stenotic group. MH segmented 28 anterior geometries from the stenotic group and the remaining 8 posterior geometries were segmented by PH. AV re-segmented 10 geometries from the stenotic group to examine inter-rater agreement through intraclass correlation. CFD simulations Stationary CFD models solving the Navier-Stokes equations were constructed using the CFD module in COMSOL Multiphysics® (COMSOL Multiphysics®, version 5.4, www.comsol.com , COMSOL AB, Stockholm, Sweden). Blood flow was assumed to be laminar with blood defined as an incompressible Newtonian fluid with a density and viscosity of \(\rho\) = 1060 kg/m 3 and \(\mu\) = 3.45 mPa·s. Rigidity and impermeability were assumed for the vessel walls. Meshes were automatically generated in ScanIP, with refinement in the circle of Willis as well as the closest segments of the cerebral arteries and ICAs. In the refinement area, the element size was set to equal the interpolated voxel size. Otherwise, the element size was increased by a factor of 1.5. The left and right ICA as well as the BA boundaries were defined as inlets, whereas the left and right MCA1, ACA2 and PCA2 boundaries were defined as outlets. Any possible PCoA boundary would be defined as an outlet or inlet depending on the direction of the flow. Consequently, flow through a PCoA from the anterior to the posterior circulation implied an outlet boundary in the anterior model and an inlet boundary in the corresponding posterior model, whereas a reversed flow direction would imply the opposite. COMSOL’s built-in boundary condition for fully developed flow was enabled for inlets and outlets, applying laminar parabolic flow rate profiles. The vessel walls were given a no-slip condition. To achieve mass conservation, in addition to correct flow through the circle of Willis, the inlet flow rates were based on summed flow rates of arteries in the circle of Willis. In anterior models, the inlets of the left and right ICA were set to the sum of each respective MCA1, ACA1, and possible PCoA flow rate. In posterior models, the BA inlet flow rate was set to the sum of all PCA2 and PCoA outflows. As an additional measure, an adjustment of the ACA2 outlets was applied such that the ACA1 flow rates were correct according to the 4D flow MRI measurements. See Fig. 3 C and 3 D for schematics of the boundary conditions. MAP was assumed as reference pressure in the contralateral ICA and the BA, and was applied as a pressure point at their boundaries. In the non-stenotic group, lacking significant stenoses, MAP was assumed in the ICA with the largest flow rate. For subjects in the stenotic group with a contralateral stenosis ≥ 50%, the pressure at the contralateral ICA was found by subtracting the pressure drop across the stenosis from the MAP, where the pressure drop was computed in a separate CFD simulation of the stenosis [ 14 ]. Computing the territorial resistance A finished simulation generated a steady state solution of the average pressure distribution in the geometry. The average perfusion pressures in the MCA1, ACA2 and PCA2 were obtained at cross-sectional cut planes placed perpendicular to the flow direction, positioned five millimeters from the bifurcations of the outflow arteries (of the circle of Willis, as seen in Fig. 3 A and 3 B). When PCoA was missing, the PCA cut plane was positioned five millimeters from the BA bifurcation. In case of double of any cerebral artery, e.g. two left MCA1, resistance was estimated as the parallel resistance between the two (two MCA1, N = 1; two ACA2, N = 4). Having determined the pressure P terr at the beginning of each major cerebral artery we computed the total downstream resistance, or territorial resistance, R as $$R=\frac{{P}_{terr}-ICP}{{Q}_{terr}}= \frac{\varDelta P}{{Q}_{terr}},$$ 1 where Q terr is the flow rate through the vessel and ICP the intracranial pressure which is the counter-pressure in the brain tissue (in line with the definition of cerebral perfusion pressure [ 27 ]). Similarly, total CVR (tCVR) was computed as $$tCVR=\frac{MAP-ICP}{{Q}_{total}}$$ 2 , where \({Q}_{total}\) is the total cerebral inflow, i.e. the sum of the ICA and BA flow rates. For ICP, we used a reference value in healthy elderly of 11.6 mmHg [ 28 ]. Computing brain volumes Brain volumes were computed with FreeSurfer 7.2.0 ( https://surfer.nmr.mgh.harvard.edu/ ) for comparisons against CVR. In FreeSurfer, the regions of the brain are automatically segmented from T1-weighted images into grey matter, white matter and cerebrospinal fluid [ 29 ]. Grey and white matter volumes of each territory were included as territorial brain volume. Which regions that belonged to each of the MCA, ACA and PCA territories was determined from the results of Tatu et al [ 30 ]. One subject lacked a T1 image, but the FreeSurfer algorithm successfully segmented the brain regions in all but one (where a consistent delineation was not possible) of the remaining subjects. Results were visually inspected for accuracy using FreeView (version 3.0, the General Hospital Corporation, Boston, MA). Statistical analysis Firstly, we wanted to compare tCVR of the controls and all patients to investigate relevance of the territorial CVR values as well as to assess global response of CVR in the event of hemodynamic disturbance. Secondly, territorial CVR within the patient group was compared between the clinically determined ipsilateral and contralateral hemispheres. Both ipsilateral and contralateral resistances were, in turn, compared to all territorial resistances of the non-stenotic group (averaged over hemispheres). A total of 279 territorial resistances were calculated. One patient lacked one PCA, another lacked one MCA, and 7 PCA territories were excluded due to posterior stenoses. Lastly, for a more perfusion-based comparison, an analysis was performed where hemispheres were separated by flow rates instead of stenosis degree, where an ICA flow rate below 160 ml/min was used to classify hemodynamic disturbance [ 31 ]. Territorial CVR of hemispheres classed as hemodynamically disturbed were compared pairwise to the corresponding territories of the patients’ opposite hemispheres. We also wanted to examine the correlation between CVR and brain volume, as territorial CVR previously have been estimated on flow rate assumptions such as distribution by brain volume. Both inter- and intra-territorial relationships between resistance and brain volume were investigated. Total and territorial brain volumes could be computed for 46 patients. As resistance is expected to relate inversely to volume it is appropriate to utilize the reciprocal of the vascular resistance, vascular conductance [ 32 ], when analyzing this relationship. All values are presented as mean with standard deviation. Lilliefors’ goodness-of-fit test was used for normality testing. For paired as well as unpaired tests of significance, Student’s t-test was used. Correlation between total conductance and volume was examined with Pearson correlation coefficient. Relations between territorial conductance and volume were examined with a linear mixed model based on restricted maximum likelihood, accounting for hemisphere as well as there being multiple samples from each subject. In the linear mixed model, parameters were set as; conductance as dependent variable, hemisphere (ipsilateral/contralateral/non-stenotic) as fixed factor, volume as covariate and subject ID as random effect. P < 0.05 was the threshold for statistical significance. The statistical analysis was carried out in MATLAB (R2022b, MathWorks, Natick, MA) and jamovi (2.3.28.0, The jamovi project, Sydney, Australia). Intraclass correlation coefficient analysis was performed to compare the segmentations between two different raters using two-way random effects, absolute agreement, single rater/measurement. All resistances for 10 subjects were used in the comparison. The resulting ICC result was r = 0.99, with CI = [0.980–0.994], p < 0.001, indicating excellent agreement. The corresponding CI for the MCA, ACA and PCA were all within [0.93–0.998]. Results Comparing tCVR among patients and controls The average tCVR was 9.3 ± 1.9 mmHg·s/ml for all patients (N = 48). It was 9.3 ± 1.7 mmHg·s/ml for the stenotic group (N = 29) versus 9.3 ± 2.1 mmHg·s/ml for the non-stenotic group (N = 19) (p = 0.91). The controls (N = 56) had a mean tCVR of 9.3 ± 2.0 mmHg·s/ml, which was not different compared to the patient group (p = 0.88). tCVR distribution among the patients and controls are given in Fig. 4 A and 4 B, respectively. Total cerebral inflow for the controls was 9.8 ± 1.4 ml/s, significantly higher (p < 0.01) compared to the patient group inflow of 9.0 ± 1.4 ml/s. Distribution of territorial CVR No differences in CVR were found within territories when comparing the ipsilateral and contralateral hemispheres of the stenotic group, nor when comparing each of them with the non-stenotic group’s averaged hemispheres (all p > 0.05, Fig. 5 ). Significant differences in CVR were observed between territories (p < 10 − 4 , Fig. 5 ), except between the contralateral ACA and PCA (p = 0.10) as well as ipsilateral ACA and PCA (p = 0.01, insignificant if Bonferroni-corrected by 18). Numerical values are given in Table 2 . Identifying hemispheres below a threshold ICA feeding flow rate of 160 ml/min and comparing the territories to the corresponding territories on the opposite hemisphere gave no significant difference in territorial CVR for any territory. Table 2 Mean resistances for the territories. No significant differences in CVR between the hemispheres were found. *Note that territories are averaged over the hemispheres for the non-stenotic group. All (mmHg·s/ml) Ipsilateral (mmHg·s/ml) Contralateral (mmHg·s/ml) Non-stenotic group* (mmHg·s/ml) MCA 33.8 ± 10.5 (N = 77) 34.0 ± 13.7 (N = 29) 32.3 ± 8.2 (N = 29) 35.9 ± 7.5 (N = 19) ACA 59.0 ± 30.6 (N = 77) 57.4 ± 26.9 (N = 29) 62.6 ± 38.8 (N = 29) 55.8 ± 21.1 (N = 19) PCA 77.8 ± 21.3 (N = 71) 74.6 ± 20.8 (N = 27) 76.8 ± 20.9 (N = 27) 84.4 ± 22.5 (N = 17) Relationship between resistance and brain volumes Average total brain volume was 1065 ± 108 ml and correlated significantly to total conductance with Pearson correlation coefficient (N = 46, r = 0.37, p = 0.01). When analyzing territorial resistances and volumes with our linear mixed model we found that when all territories are included, volume associates to conductance (p < 0.001). The model estimates the association with an intercept of 0.0224 ml/mmHg·s, 95% CI [0.0207, 0.0242], and volume-conductance slope of 1.84·10 − 4 1/mmHg·s, 95% CI [1.63·10 − 4 , 2.04·10 − 4 ]. However, applying the model to each respective territory yielded no association between volume and conductance (MCA, p = 0.44; ACA, p = 0.54; PCA, p = 0.49). Distribution of territorial conductance and volume is illustrated in Fig. 6 . Discussion We present the territorial distribution of CVR for stroke/TIA patients with and without symptomatic carotid stenoses. With arterial anatomy from CTA and blood flow from 4D flow MRI data in combination with CFD pressure estimation, we propose a subject-specific method for determining territorial CVR without relying on flow distribution assumptions. There were differences in CVR between most of the MCA, ACA and PCA territories. There was no difference between hemispheres in the stenotic group, nor any difference in total CVR between the patient and the control group. Our results suggest that CVR may be contained within fairly stable levels in these patients, despite significant carotid stenoses and diminished flow, i.e,. the expected regional autoregulatory control had an unexpectedly low impact. For future work these resistances may work as reference values when modelling blood flow in the circle of Willis, and the method can be used when there is need for subject-specific analysis. Distribution of CVR In the brain, regulatory systems such as autoregulation and neurovascular coupling utilize CVR to ensure a sufficient blood supply [ 1 – 3 ]. Thus, it is reasonable that hemodynamic disturbances such as carotid stenoses would impact CVR through e.g. dilation of arteries distal of a stenosis. Total CVR represents the relationship between the pressure drop from MAP in the cervical arteries to ICP in the parenchyma and the total blood supply feeding the brain. In our study, we found the patients to have a tCVR of 9.3 ± 1.7 mmHg·s/ml and the controls 9.3 ± 2.0 mmHg·s/ml, with comparable histograms (Fig. 4 ). This is slightly smaller compared to previous studies, where tCVR of patients with cerebrovascular disease has been reported as 9.8 ± 2.1 [ 13 ] and of healthy as 10.5 ± 2.1 mmHg·s/ml [ 12 ]. The difference can largely be explained by the inclusion of ICP in our computations, which is substantial in the supine position [ 28 ]. Interestingly, we found no difference in total CVR between controls and the hemodynamically affected patients. This could potentially be explained by the stage in the disease development at which the patients were examined. Previous studies have shown that regulatory processes in the brain are impaired by carotid stenoses and stroke [ 33 ]. In addition, MAP was lower among patients compared to controls, in contrast to reports of elevated blood pressure for such patients prior to medication [ 34 ]. Medication may play a role in further inhibiting regulation to relieve blood pressure and therefore bring cerebrovascular properties back to normal. We also did not find any differences in territorial CVR between patient hemispheres (Fig. 5 , Table 2 ), despite presence of carotid stenoses. Thus, there seems to be no difference in CVR between hospitalized patients (with limited amount of symptoms indicated by low mRS and NIHSS scores) compared to controls, nor between the patient hemispheres, suggesting that the presented distribution of CVR in patients (under treatment) reflects that of healthy elderly. It is possible that the CVR distribution may have differed at an earlier stage prior to the stroke/TIA event/treatment, where the previously discussed effects on autoregulation were not present. This was not possible to investigate in the current study, which motivates additional studies where the CVR distribution is assessed at different points in time over the cerebrovascular disease development. When comparing the resistances of different territories, the resistances differed significantly, with a distribution of 34:59:78 mmHg·s/ml for MCA:ACA:PCA (Table 2 ). An early and well referenced distribution of CVR was made by Hillen et al., in which the territorial resistances were estimated by assuming inverse proportion to the mass irrigated by the vessel [ 18 , 35 ]. They reported a distribution of 30:60:40 mmHg·s/ml. Stergiopulos et al. [ 36 ], reported CVR downstream of ICA which, by assuming proportionality to the initial cross-sectional area of the cerebral arteries [ 37 ], resulted in 45:64:83 mmHg·s/ml. Another approach to find territorial CVR is to apply outflow conditions containing estimates of territorial CVR and then updating them until the model re-creates a measured value, such as total cerebral blood flow and external carotid artery flow rate [ 19 ]. This verification-based approach has yielded a distribution of 26:93:69 mmHg·s/ml. A similar approach, where verification was made against arterial spin labeling data of perfusion amounts in the territories, yielded distributions 11:17:35 mmHg·s/ml and 24:53:82 mmHg·s/ml for two stenosis patients, as well as 9:24:47 mmHg·s/ml for a young, healthy control [ 38 ]. Notably, the distributions from these methods vary not only in size, but also in relation among territories. There could be several reasons for this, such as small subject groups or the reliance upon flow rate assumptions, or reference data built upon such assumptions. We offer values from a subject-specific method without flow rate assumptions in conjunction with local perfusion pressures in the circle of Willis. Additionally, results were acquired from a set of subjects much larger than most medical CFD studies, making for a more rigorous assessment than previously done. By determining total and territorial volumes of the patients, we were able to further investigate the relation between CVR and brain volume. The total and territorial brain volumes of our study are comparable to previous work [ 39 , 40 ]. Our results show a positive correlation between total conductance (i.e. negative correlation for total CVR) and total brain volume. Similarly, the linear mixed model showed that territorial conductance could be explained by territorial volume, which was expected but has not yet been shown. However, this could not be shown within the respective territories. We interpret these results as that the distribution of CVR over the territories can be assumed with brain volume or mass assumptions, but that a territorial volume cannot directly be converted into a territorial resistance due to larger inter-subject differences. Value of territorial resistances for modelling and predictions Computational modelling of cerebral blood flow has been developed to non-invasively estimate cerebral hemodynamics and assess clinical risks [ 11 ]. One example area where this type of modelling is of interest is cerebral pulsatility, since recent findings indicate a relation between increased downstream pulsatility and cognitive decline and dementia [ 41 – 43 ]. A common way to investigate cerebral arterial pulsatility is through Windkessel modelling [ 10 , 11 ], which is partly based on the downstream, territorial resistance distribution. Another, clinically relevant, modelling application are predictions of cerebral blood flow during surgeries where cerebral blood flow may be compromised. By estimating a patient’s hemodynamical properties prior to surgery, the risk of hypoperfusion can be assessed which could help guide intraoperative decision-making [ 14 ]. As blood flow is what is of interest for such predictions it is suitable to make assumptions on the surgical situation based on resistance. For both descriptive and predictive modelling it is therefore necessary that resistances are well determined and representative, which we offer with the presented method and CVR distribution. Limitations A limitation when studying hemodynamic effects of carotid stenoses is that patients typically are divided based upon stenosis degree, measured at the carotid bifurcation. The non-stenotic group was added to include less hemodynamically disturbed patients, as a type of controls, since CTA is needed for the territorial analysis. However, the lack of stenosis in the carotid bifurcations did not exclude the possibility for plaque further up the ICAs and we could not consider them as vascular healthy controls, but as a patient subgroup. A way to bypass this problem was to divide the hemispheres based on flow rate and consider it the threshold for hemodynamic disturbance. In our analysis this perfusion-based division did not yield any differences in CVR either. It is possible that this is an issue of statistical power, which also could explain the lacking inter-territorial difference between ACA and PCA for ipsilateral as well as contralateral hemispheres. However, we have a relatively large group of patients compared to other CFD studies and there were seemingly no other extreme differences. A strength of the study is that we base our boundary conditions on the very same flow rates that we measure, ensuring correct flow rates in the critical area, the circle of Willis. Some model assumptions should however be discussed. For example, MAP was measured prior to the acquisition of the flow rates and ICP was based on reference [ 28 ], which adds potential inaccuracies to the results. Additionally, we assumed MAP at the BA in the posterior models but we assumed this to be reasonable due to the exclusion of patients with posterior stenoses. Conclusion This study established the distribution of cerebrovascular resistance (CVR) among the major arterial territories of the brain of stroke/TIA patients with and without carotid stenoses, identifying values of 34:59:78 mmHg·s/ml between the MCA, ACA and PCA regions. The assessment was carried out with individual arterial trees and flow rates allowing for subject-specific analysis of CVR distribution. No difference in total CVR was found between patients and controls, nor for territorial CVR between hemispheres among patients, suggesting the presented distribution of territorial CVR may also be representative for the general age group. Declarations Data availability Data is available from the corresponding authors upon reasonable request. Acknowledgements We would like to acknowledge research nurse Hanna Ackelind for her contributions in describing the patients included in the study. Author contribution Concept and design by AV, MH, PH and AE. JM and AE contributed to the data acquisition. AV, PH, MH and AE performed the analysis. All authors interpreted the results. AV drafted the paper and created the figures. All authors critically edited and revised the manuscript. All authors approved the final version of the manuscript. Competing interests The author(s) declare(s) no competing interests. Funding This work was funded by the Swedish Research Council [2015-05616, 2017-04949]; the County Council of Västerbotten through Spjutspetsmedel and Centrala ALF; the Swedish Heart and Lung Foundation [20140592]; and the Swedish Foundation for Strategic Research. The funders had no role in study design, data collection and analysis. References Paulson, O. B., Strandgaard, S. & Edvinsson, L. Cerebral Autoregulation. Cerebrovascular and Brain Metabolism Reviews 2, 161–192 (1990). Attwell, D. et al. Glial and neuronal control of brain blood flow. Nature 468, 232–243 (2010). https://doi.org:10.1038/nature09613 Phillips, A. A., Chan, F. H., Zheng, M. M. Z., Krassioukov, A. V. & Ainslie, P. N. Neurovascular coupling in humans: Physiology, methodological advances and clinical implications. Journal of Cerebral Blood Flow & Metabolism 36, 647–664 (2016). https://doi.org:10.1177/0271678x15617954 de la Torre, J. C. 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Journal of Biomechanics 21, 807–814 (1988). https://doi.org:https://doi.org/10.1016/0021-9290(88)90013-9 Coogan, J. S., Humphrey, J. D. & Figueroa, C. A. Computational simulations of hemodynamic changes within thoracic, coronary, and cerebral arteries following early wall remodeling in response to distal aortic coarctation. Biomechanics and Modeling in Mechanobiology 12, 79–93 (2013). https://doi.org:10.1007/s10237-012-0383-x Markl, M., Frydrychowicz, A., Kozerke, S., Hope, M. & Wieben, O. 4D flow MRI. Journal of Magnetic Resonance Imaging 36, 1015–1036 (2012). https://doi.org:10.1002/jmri.23632 Holmgren, M. et al. Middle cerebral artery pressure laterality in patients with symptomatic ICA stenosis. PLOS ONE 16, e0245337 (2021). https://doi.org:10.1371/journal.pone.0245337 North America Symptomatic Carotid Endarterectomy Trial Steering, C. North America Symptomatic Carotid Endarterectomy Trial: methods, patient characteristics and progress. Stroke 22, 711–720 (1991). Vikner, T. Cerebral arterial pulsatility imaging using 4D flow MRI: methodological development and applications in brain aging , Umeå University, (2022). Tianliang, G. et al. PC VIPR: A High-Speed 3D Phase-Contrast Method for Flow Quantification and High-Resolution Angiography. American Journal of Neuroradiology 26, 743 (2005). Johnson, K. M. & Markl, M. Improved SNR in phase contrast velocimetry with five-point balanced flow encoding. Magnetic Resonance in Medicine 63, 349–355 (2010). https://doi.org:10.1002/mrm.22202 Holmgren, M., Wåhlin, A., Dunås, T., Malm, J. & Eklund, A. Assessment of Cerebral Blood Flow Pulsatility and Cerebral Arterial Compliance With 4D Flow MRI. Journal of Magnetic Resonance Imaging 51, 1516–1525 (2020). https://doi.org:10.1002/jmri.26978 Armstead, W. M. Cerebral Blood Flow Autoregulation and Dysautoregulation. Anesthesiology Clinics 34, 465–477 (2016). https://doi.org:https:// doi.org/10.1016/j.anclin.2016.04.002 Malm, J., Jacobsson, J., Birgander, R. & Eklund, A. Reference values for CSF outflow resistance and intracranial pressure in healthy elderly. Neurology 76, 903–909 (2011). https://doi.org:10.1212/wnl.0b013e31820f2dd0 Fischl, B. et al. Whole Brain Segmentation. Neuron 33, 341–355 (2002). https://doi.org:10.1016/s0896-6273(02)00569-x Tatu, L., Moulin, T., Vuillier, F. & Bogousslavsky, J. in Manifestations of Stroke Vol. 30 (eds M. Paciaroni, G. Agnelli, V. Caso, & J. Bogousslavsky) 99–110 (S.Karger AG, 2012). Zarrinkoob, L., Myrnäs, S., Wåhlin, A., Eklund, A. & Malm, J. Cerebral Blood Flow Patterns in Patients With Low-Flow Carotid Artery Stenosis, a 4D-PCMRI Assessment. Journal of Magnetic Resonance Imaging n/a (2024). https://doi.org:https://doi.org/10.1002/jmri.29216 Joyce, W., White, D. W., Raven, P. B. & Wang, T. Weighing the evidence for using vascular conductance, not resistance, in comparative cardiovascular physiology. Journal of Experimental Biology 222, jeb197426 (2019). https://doi.org:10.1242/jeb.197426 Castro, P., Azevedo, E. & Sorond, F. Cerebral Autoregulation in Stroke. Current Atherosclerosis Reports 20 (2018). https://doi.org:10.1007/s11883-018-0739-5 Fogelholm, R., Avikainen, S. & Murros, K. Prognostic Value and Determinants of First-Day Mean Arterial Pressure in Spontaneous Supratentorial Intracerebral Hemorrhage. Stroke 28, 1396–1400 (1997). https://doi.org:10.1161/01.STR.28.7.1396 Hillen, B., Hoogstraten, H. W. & Post, L. A mathematical model of the flow in the circle of Willis. Journal of Biomechanics 19, 187–194 (1986). https://doi.org: https://doi.org/10.1016/0021-9290(86)90151-X Stergiopulos, N., Young, D. F. & Rogge, T. R. Computer simulation of arterial flow with applications to arterial and aortic stenoses. Journal of Biomechanics 25, 1477–1488 (1992). https://doi.org:https://doi.org/10.1016/0021-9290(92)90060-E Alastruey, J., Parker, K. H., Peiró, J., Byrd, S. M. & Sherwin, S. J. Modelling the circle of Willis to assess the effects of anatomical variations and occlusions on cerebral flows. Journal of Biomechanics 40, 1794–1805 (2007). https://doi.org:https://doi.org/10.1016/j.jbiomech.2006.07.008 Schollenberger, J., Osborne, N. H., Hernandez-Garcia, L. & Figueroa, C. A. A Combined Computational Fluid Dynamics and Arterial Spin Labeling MRI Modeling Strategy to Quantify Patient-Specific Cerebral Hemodynamics in Cerebrovascular Occlusive Disease. Frontiers in Bioengineering and Biotechnology 9 (2021). https://doi.org:10.3389/fbioe.2021.722445 Van Der Zwan, A., Hillen, B., Tulleken, C. A. & Dujovny, M. A quantitative investigation of the variability of the major cerebral arterial territories. Stroke 24, 1951–1959 (1993). https://doi.org:10.1161/01.str.24.12.1951 Emilio, W. et al. Structural MRI markers of brain aging early after ischemic stroke. Neurology 89, 116 (2017). https://doi.org:10.1212/WNL.0000000000004086 Rivera-Rivera, L. A. et al. 4D flow MRI for intracranial hemodynamics assessment in Alzheimer's disease. J Cerebr Blood F Met 36, 1718–1730 (2016). https://doi.org:10.1177/0271678x15617171 Vikner, T. et al. Cerebral arterial pulsatility is linked to hippocampal microvascular function and episodic memory in healthy older adults. J Cerebr Blood F Met 41, 1778–1790 (2021). https://doi.org:10.1177/0271678x20980652 Pahlavian, S. H. et al. Cerebroarterial pulsatility and resistivity indices are associated with cognitive impairment and white matter hyperintensity in elderly subjects: A phase-contrast MRI study. Journal of Cerebral Blood Flow & Metabolism 41, 670–683 (2021). https://doi.org:10.1177/0271678x20927101 Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 22 May, 2024 Reviews received at journal 20 May, 2024 Reviewers agreed at journal 10 May, 2024 Reviews received at journal 29 Feb, 2024 Reviewers agreed at journal 27 Feb, 2024 Reviewers agreed at journal 12 Feb, 2024 Reviewers invited by journal 11 Feb, 2024 Editor assigned by journal 05 Feb, 2024 Editor invited by journal 02 Feb, 2024 Submission checks completed at journal 02 Feb, 2024 First submitted to journal 26 Jan, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3900174","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":270748096,"identity":"9959d4f6-d1b1-4d93-a8c5-f524982bf825","order_by":0,"name":"Axel Vikström","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA3klEQVRIiWNgGAWjYHACxgMMDBIGEHYFkXogWthAzDPEa2GAaGFsI0I5/4zkAwcY2yyM5ef3Pnx0c97haIMD7A8f4NMiceZYAlCLhJnBMXZj49xth3M3HOAxNsBrzfEegwMMZyRsDNjY2KShWtgk8OmQP8z/AaxFvg2kZQ5IC/vzH/i0GBzvAXq/QsKM4RhISwNIC4MZXncZnjlmcCChQsLY4Fgas3HOsfTcmYd5jPE6TO5G8sMHHwzqDOc3H2N8nFNjndt3vP3hB7zWgEACCo+ZoPpRMApGwSgYBYQAAF3TSdyzfnz4AAAAAElFTkSuQmCC","orcid":"","institution":"Department of Diagnostics and Intervention, Biomedical Engineering and Radiation Physics, Umeå University","correspondingAuthor":true,"prefix":"","firstName":"Axel","middleName":"","lastName":"Vikström","suffix":""},{"id":270748097,"identity":"3cf9ec09-7ccb-45c3-89c7-ca17e1376af7","order_by":1,"name":"Petter Holmlund","email":"","orcid":"","institution":"Department of Diagnostics and Intervention, Biomedical Engineering and Radiation Physics, Umeå University","correspondingAuthor":false,"prefix":"","firstName":"Petter","middleName":"","lastName":"Holmlund","suffix":""},{"id":270748098,"identity":"b9c39569-93dd-402f-aa85-68a09622ca73","order_by":2,"name":"Madelene Holmgren","email":"","orcid":"","institution":"Department of Diagnostics and Intervention, Biomedical Engineering and Radiation Physics, Umeå University","correspondingAuthor":false,"prefix":"","firstName":"Madelene","middleName":"","lastName":"Holmgren","suffix":""},{"id":270748099,"identity":"17ae28c1-79bc-47f7-8ef6-a4461bb93690","order_by":3,"name":"Anders Wåhlin","email":"","orcid":"","institution":"Department of Diagnostics and Intervention, Biomedical Engineering and Radiation Physics, Umeå University","correspondingAuthor":false,"prefix":"","firstName":"Anders","middleName":"","lastName":"Wåhlin","suffix":""},{"id":270748100,"identity":"bd9b6ba5-7e16-4606-94f8-71e8065ca2fb","order_by":4,"name":"Laleh Zarrinkoob","email":"","orcid":"","institution":"Department of Diagnostics and Intervention, Surgical and Perioperative Sciences, Umeå University","correspondingAuthor":false,"prefix":"","firstName":"Laleh","middleName":"","lastName":"Zarrinkoob","suffix":""},{"id":270748101,"identity":"4826717b-5142-4ea8-8a3a-563d29f88aa6","order_by":5,"name":"Jan Malm","email":"","orcid":"","institution":"Department of Clinical Science, Neurosciences, Umeå University","correspondingAuthor":false,"prefix":"","firstName":"Jan","middleName":"","lastName":"Malm","suffix":""},{"id":270748102,"identity":"85441039-d507-461d-8dcb-2dd17d29d804","order_by":6,"name":"Anders Eklund","email":"","orcid":"","institution":"Department of Diagnostics and Intervention, Biomedical Engineering and Radiation Physics, Umeå University","correspondingAuthor":false,"prefix":"","firstName":"Anders","middleName":"","lastName":"Eklund","suffix":""}],"badges":[],"createdAt":"2024-01-26 14:29:15","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3900174/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3900174/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":50683872,"identity":"c5dae5aa-b081-4673-bbf1-9d570212157a","added_by":"auto","created_at":"2024-02-05 17:47:09","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":117240,"visible":true,"origin":"","legend":"\u003cp\u003eOverview of our method for determining territorial CVR. Computational domains of the anterior and posterior parts of the circle of Willis are segmented from CTA data, and to them we apply the measured flow rates and MAP. This subject has a right posterior communicating artery, connecting the anterior and posterior parts of the circle of Willis (flow indicated by orange arrows). CFD is then used to compute the perfusion pressure in the circle of Willis given these conditions. The resulting perfusion pressure, in combination with the flow rates along each outflow branch (blue arrows), allows for computing territorial CVR, i.e. the lumped resistance downstream of each cerebral artery.\u003c/p\u003e","description":"","filename":"OnlineFigure1.png","url":"https://assets-eu.researchsquare.com/files/rs-3900174/v1/cb9da7714c0f84623557fc2c.png"},{"id":50683871,"identity":"fd3db704-9b14-4d00-8fa5-1efa6ad56858","added_by":"auto","created_at":"2024-02-05 17:47:09","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":48299,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic of the subject groups. CAS; carotid artery stenosis.\u003c/p\u003e","description":"","filename":"OnlineFigure2.png","url":"https://assets-eu.researchsquare.com/files/rs-3900174/v1/68af3434d05797429e754aee.png"},{"id":50683873,"identity":"6b8d2f4c-3527-4c10-a073-56fa87d7098d","added_by":"auto","created_at":"2024-02-05 17:47:09","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":161397,"visible":true,"origin":"","legend":"\u003cp\u003eExamples of (\u003cstrong\u003ea\u003c/strong\u003e) anterior and (\u003cstrong\u003eb\u003c/strong\u003e) posterior geometries (not to scale) from the same subject and cuts from which the computed pressure was read. In the bottom row are general schematic illustrations of the (\u003cstrong\u003ec\u003c/strong\u003e) anterior and (\u003cstrong\u003ed\u003c/strong\u003e) posterior boundary conditions used for the CFD. The flow rates were assessed by 4D flow MRI. Note the variability in sign for Q\u003csub\u003ePC0A\u003c/sub\u003e, introduced as an additional inlet require a reduction of the corresponding Q\u003csub\u003eICA\u003c/sub\u003e in anterior models and Q\u003csub\u003eBA\u003c/sub\u003e in posterior models to preserve mass conservation.\u003c/p\u003e","description":"","filename":"OnlineFigure3.png","url":"https://assets-eu.researchsquare.com/files/rs-3900174/v1/daaef9d22ae173bf379bfdd8.png"},{"id":50683870,"identity":"dd3feb4b-daee-4da1-813f-fa5f55fbdcbd","added_by":"auto","created_at":"2024-02-05 17:47:09","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":38721,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution of tCVR for (\u003cstrong\u003ea\u003c/strong\u003e) the patient group and (\u003cstrong\u003eb\u003c/strong\u003e) the controls with marked mean and standard deviation, between which no significant difference was found with unpaired Student’s t-test (p=0.88).\u003c/p\u003e","description":"","filename":"OnlineFigure4.png","url":"https://assets-eu.researchsquare.com/files/rs-3900174/v1/cbc54cf8cc5fb308ef48aaf2.png"},{"id":50683868,"identity":"6ea9f385-d190-49e7-8c93-626e1ec41c4c","added_by":"auto","created_at":"2024-02-05 17:47:09","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":33968,"visible":true,"origin":"","legend":"\u003cp\u003eDistributions and comparisons of territorial CVR within and between territories based on hemispheres. With Student’s t-test, there were no differences between hemispheres within each territory (all p\u0026gt;0.05) but significant difference between most territories except those highlighted (all p\u0026lt;10\u003csup\u003e-4\u003c/sup\u003e, p=0.01 insignificant if Bonferroni-corrected by 18).\u003c/p\u003e","description":"","filename":"Figure5.png","url":"https://assets-eu.researchsquare.com/files/rs-3900174/v1/b83ee887e321a72ae55831b4.png"},{"id":50684555,"identity":"dd60751c-d272-45ce-8038-6cc21efa7844","added_by":"auto","created_at":"2024-02-05 17:55:09","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":50014,"visible":true,"origin":"","legend":"\u003cp\u003eTerritorial conductance and volume for the patients (N=46). With the linear mixed model, there was an association between conductance and volume (p\u0026lt;0.001). This was not true for each respective territory (MCA, p=0.44; ACA, p=0.54; PCA, p=0.49). MCA outlier was mainly supplied by flow through the ACA1 and ACoA, resulting in a large drop in perfusion pressure and thus a low computed resistance.\u003c/p\u003e","description":"","filename":"Figure6.png","url":"https://assets-eu.researchsquare.com/files/rs-3900174/v1/6b4c4105f56dd5aaeca40443.png"},{"id":50685052,"identity":"451bf527-09c1-4167-a6ef-3f0a814f2abb","added_by":"auto","created_at":"2024-02-05 18:03:11","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1062421,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3900174/v1/90008d55-3719-447b-b696-c4dd7fe8bd61.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Establishing the distribution of cerebrovascular resistance using computational fluid dynamics and 4D flow MRI","fulltext":[{"header":"Introduction","content":"\u003cp\u003eA balanced blood flow distribution throughout the brain is crucial for maintaining adequate cerebral function. Cerebral blood flow distribution is intimately connected to the blood pressure driving the flow (i.e., the perfusion pressure) and the flow resistance of the cerebral arteries, known as cerebrovascular resistance (CVR). The cerebral autoregulation regulates CVR by varying the size of the diameters of the cerebral small arteries and arterioles, ensuring stable flow during changes in perfusion pressure [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. Simultaneously, variations in metabolic demands induce changes in CVR through neurovascular coupling to secure a sufficient blood flow [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Therefore, deviations in CVR may reflect disturbances or depletion of these regulatory processes. Additionally, impaired vascular structure and function has been found to be increasingly important in the development of cognitive diseases [\u003cspan additionalcitationids=\"CR5 CR6 CR7\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], making CVR and its distribution a potential screening tool in early cognitive decline [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. Lastly, the vascular resistance of the different cerebral territories plays an essential role in the mathematical modelling and prediction of cerebral blood flow [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. CVR is mostly estimated globally [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e], usually due to the simplicity of measuring total cerebral inflow and mean arterial pressure, as opposed to the local flow rates and perfusion pressures needed to determine CVR of each vascular territory. Knowing these territorial resistances would not only improve our understanding of physiology and pathophysiology, but could also be used for predictions of blood flow and perfusion pressure during planned interventions such as medical or surgical treatments [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eCVR can be computed from measurements of blood flow and perfusion pressure through an Ohm\u0026rsquo;s law equivalent [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. The global measure of CVR, total CVR, represents the vascular resistance against the flow from the cervical arteries to the parenchyma. It can be determined by the difference in mean arterial pressure (MAP) and intracranial pressure (ICP) divided by total cerebral blood flow (tCBF) [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. A majority of the total CVR comes from the peripheral vessels [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e] in the territories supplied by the major cerebral arteries extending from the circle of Willis; the middle, anterior and posterior cerebral arteries (MCA, ACA, PCA) [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. CVR of these territories, territorial CVR, can be determined through the difference in the perfusion pressure and ICP divided by the flow in each exiting artery of the circle of Willis. Previous estimations of territorial CVR have been made with assumptions on arterial pressure drops and flow distribution in the branches of the circle of Willis [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e], in addition to often being reliant on literature data and thus not subject-specific data. Four-dimensional phase-contrast magnetic resonance imaging (4D flow MRI) [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e] allows for \u003cem\u003esimultaneous\u003c/em\u003e flow measurements in the vessels of the entire brain, eliminating the need for flow distribution assumptions. To accurately estimate the territorial resistance, the measured flow rates to each territory should be accompanied by their corresponding perfusion pressures, which can be determined with computational fluid dynamics (CFD) [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e] modelling of the circle of Willis. Consequently, this allows for the assessment of each territorial resistance in a subject-specific manner while utilizing accurate flow rate measurements and accounting for pressure drops in the circle of Willis.\u003c/p\u003e \u003cp\u003eIn this study, we aim to establish the distribution of the CVR in a group of patients with a transient ischemic attack or stroke, with or without significant carotid stenoses. With this patient group we examine possible lateral differences in CVR from hemodynamic disturbances induced by carotid stenoses. A control group of elderly was included for comparison of total CVR. As a secondary analysis we examine the relationship between CVR and brain volume, in total as well as intra- and inter-territorially.\u003c/p\u003e"},{"header":"Material and methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eOverview of approach\u003c/h2\u003e \u003cp\u003eVascular resistances of each cerebral arterial territory were computed on a subject-specific level (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). The arterial tree of each patient was segmented from computed tomography angiography (CTA) data. The flow rate in each artery was acquired from the 4D flow MRI data. With the segmentation and flow rates, CFD computations estimate the perfusion pressure at each branch of the circle of Willis. The computed perfusion pressures together with the flow rate to each territory allowed for an assessment of CVR in the cerebral regions fed by the ACA, MCA, and PCA.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003eSubjects\u003c/h2\u003e \u003cp\u003eThe study population consisted of a patient group with two subgroups and a control group (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). The patient subgroups originated from the stroke unit at Ume\u0026aring; University Hospital between 2012\u0026ndash;2015. 29 patients were included in the stenotic group. They had a transient ischemic attack (TIA) or cerebral infarct and a symptomatic carotid stenosis\u0026thinsp;\u0026ge;\u0026thinsp;50%, with or without a non-symptomatic contralateral stenosis. The non-stenotic group consisted of 19 patients with TIA, without stenoses. North American Symptomatic Carotid Endarterectomy Trial (NASCET) method was used for grading the stenosis [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. The side with the symptomatic stenosis was defined as the ipsilateral side, with the opposite being the contralateral side. A control group was recruited from the Swedish population registry (N\u0026thinsp;=\u0026thinsp;61) [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. It consisted of elderly, irrespective of previous disease, but those with previous TIA or stroke were excluded (N\u0026thinsp;=\u0026thinsp;3). MRI was incomplete for two controls. Territorial CVR could not be estimated in the control group due to the lack of CTA but 4D flow data and mean arterial pressure (MAP) were available, allowing for computation of total CVR. Full characteristics are listed in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eCharacteristics of the patients and controls. Significant difference was tested with Student\u0026rsquo;s t-test for continuous variables and chi-squared test for categorical variables between the patient subgroups (\u0026dagger;) as well as between all patients and the controls (*), where significance (p\u0026thinsp;\u0026lt;\u0026thinsp;0.05) is highlighted in bold. mRS; modified Rankin Score. NIHSS; National Institutes of Health Stroke Scale. SBP; Systolic Blood Pressure. DBP, Diastolic Blood Pressure. MAP, Mean Arterial Pressure.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eStenotic group\u003c/p\u003e \u003cp\u003e(N\u0026thinsp;=\u0026thinsp;29, 22 men)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNon-stenotic group\u003c/p\u003e \u003cp\u003e(N\u0026thinsp;=\u0026thinsp;19, 13 men)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAll patients\u003c/p\u003e \u003cp\u003e(N\u0026thinsp;=\u0026thinsp;48, 35 men)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eControls\u003c/p\u003e \u003cp\u003e(N\u0026thinsp;=\u0026thinsp;56, 36 men)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAge (years)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e73\u0026thinsp;\u0026plusmn;\u0026thinsp;6\u003c/b\u003e\u003csup\u003e\u003cb\u003e\u0026dagger;\u003c/b\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e67\u0026thinsp;\u0026plusmn;\u0026thinsp;7\u003c/b\u003e\u003csup\u003e\u003cb\u003e\u0026dagger;\u003c/b\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e71\u0026thinsp;\u0026plusmn;\u0026thinsp;7\u003c/b\u003e\u003csup\u003e\u003cb\u003e*\u003c/b\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e74\u0026thinsp;\u0026plusmn;\u0026thinsp;4\u003c/b\u003e\u003csup\u003e\u003cb\u003e*\u003c/b\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStenosis degree (%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e75\u0026thinsp;\u0026plusmn;\u0026thinsp;12 (ipsilateral)\u003c/p\u003e \u003cp\u003e67\u0026thinsp;\u0026plusmn;\u0026thinsp;10 (contralateral, N\u0026thinsp;=\u0026thinsp;9)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eN/A\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eN/A\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eN/A\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003emRS score\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0 (0\u0026ndash;1)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0 (0\u0026ndash;0)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0 (0\u0026ndash;1)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eN/A\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNIHSS score\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1 (0\u0026ndash;6)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0 (0\u0026ndash;3)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1 (0\u0026ndash;6)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eN/A\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSBP (mmHg)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e137\u0026thinsp;\u0026plusmn;\u0026thinsp;17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e132\u0026thinsp;\u0026plusmn;\u0026thinsp;19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e135\u0026thinsp;\u0026plusmn;\u0026thinsp;18\u003c/b\u003e\u003csup\u003e\u003cb\u003e*\u003c/b\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e142\u0026thinsp;\u0026plusmn;\u0026thinsp;19\u003c/b\u003e\u003csup\u003e\u003cb\u003e*\u003c/b\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDBP (mmHg)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e70\u0026thinsp;\u0026plusmn;\u0026thinsp;10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e74\u0026thinsp;\u0026plusmn;\u0026thinsp;12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e72\u0026thinsp;\u0026plusmn;\u0026thinsp;11\u003c/b\u003e\u003csup\u003e\u003cb\u003e*\u003c/b\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e81\u0026thinsp;\u0026plusmn;\u0026thinsp;10\u003c/b\u003e\u003csup\u003e\u003cb\u003e*\u003c/b\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMAP (mmHg)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e92\u0026thinsp;\u0026plusmn;\u0026thinsp;11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e94\u0026thinsp;\u0026plusmn;\u0026thinsp;13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e93\u0026thinsp;\u0026plusmn;\u0026thinsp;12\u003c/b\u003e\u003csup\u003e\u003cb\u003e*\u003c/b\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e102\u0026thinsp;\u0026plusmn;\u0026thinsp;12\u003c/b\u003e\u003csup\u003e\u003cb\u003e*\u003c/b\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHeart rate (bpm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e65\u0026thinsp;\u0026plusmn;\u0026thinsp;11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e69\u0026thinsp;\u0026plusmn;\u0026thinsp;10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e67\u0026thinsp;\u0026plusmn;\u0026thinsp;11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e68\u0026thinsp;\u0026plusmn;\u0026thinsp;11\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHypertension (N)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e22 (76%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e11 (58%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e33 (69%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e31 (55%)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHyperlipidemia (N)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e16 (55%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e6 (32%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e22 (46%)\u003c/b\u003e\u003csup\u003e\u003cb\u003e*\u003c/b\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e12 (21%)\u003c/b\u003e\u003csup\u003e\u003cb\u003e*\u003c/b\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDiabetes mellitus (N)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e7 (24%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4 (21%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e11 (23%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e6 (11%)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEver smoker (N)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e19 (66%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e9 (47%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e28 (58%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e36 (64%)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e The study was approved by the ethical review board of Ume\u0026aring; University (Dnr: 2011-440-31M) and the Swedish Ethical Review Authority (Dnr: 2019\u0026ndash;05909) and was performed in accordance with the guidelines of the Declaration of Helsinki. All participants were given oral and written information about the study and written consent was obtained from all participants.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003eImaging\u003c/h2\u003e \u003cp\u003eFor each patient, 4D flow MRI and CTA data with full brain coverage was available. A 3T scanner with a 32-channel head coil (GE Discovery MR 750, Milwaukee, WI, USA) was used for the MRI scans providing flow rates in the cerebral vessels, utilizing a balanced 5-point phase contrast vastly undersampled isotropic projection reconstruction (PC-VIPR) sequence [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. The velocity encoding was 110 cm/s. Reconstructed MRI voxel size was 0.7\u0026times;0.7\u0026times;0.7 mm\u003csup\u003e3\u003c/sup\u003e. The CTA images used to segment patient-specific vessel geometries were obtained from different hospitals, with reconstructed slice thickness ranging between 0.3 to 0.625 mm. More information regarding settings for both imaging modes can be seen in the study of Holmgren et al [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003eFlow rates and vessel geometries\u003c/h2\u003e \u003cp\u003eThe vessel geometries were semi-automatically segmented from the CTA, performed with Synopsys\u0026rsquo; Simpleware\u0026trade; software (ScanIP P-2019.09; Synopsys, Inc., Mountain View, USA). The segmentation included the complete circle of Willis with the internal carotid arteries (ICA), the basilar artery (BA), the middle cerebral arteries (MCA1), proximal and distal posterior cerebral arteries (PCA1/PCA2), proximal and distal anterior cerebral arteries (ACA1/ACA2), and the anterior and posterior communicating arteries (ACoA and PCoA). The segmentation process was carried out as previously described[\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. Average flow rates for each ICA, MCA1, ACA1, ACA2, BA, PCA1, PCA2 and PCoA were obtained with a post-processing method that averages consecutive flow waveforms [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. The circle of Willis geometries were separated into an anterior and posterior part to ensure the correct flows in the subsequent simulations and to avoid possible underdetermination of the flow equations introduced by the circular structure of the circle of Willis. Examples of each type are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eA and Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eB.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAV segmented all vascular trees of the non-stenotic group, as well as one complete and 20 posterior geometries from the stenotic group. MH segmented 28 anterior geometries from the stenotic group and the remaining 8 posterior geometries were segmented by PH. AV re-segmented 10 geometries from the stenotic group to examine inter-rater agreement through intraclass correlation.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003eCFD simulations\u003c/h2\u003e \u003cp\u003eStationary CFD models solving the Navier-Stokes equations were constructed using the CFD module in COMSOL Multiphysics\u0026reg; (COMSOL Multiphysics\u0026reg;, version 5.4, \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ewww.comsol.com\u003c/a\u003e\u003c/span\u003e\u003cspan address=\"http://www.comsol.com\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e, COMSOL AB, Stockholm, Sweden). Blood flow was assumed to be laminar with blood defined as an incompressible Newtonian fluid with a density and viscosity of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\rho\\)\u003c/span\u003e\u003c/span\u003e = 1060 kg/m\u003csup\u003e3\u003c/sup\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\mu\\)\u003c/span\u003e\u003c/span\u003e = 3.45 mPa\u0026middot;s. Rigidity and impermeability were assumed for the vessel walls. Meshes were automatically generated in ScanIP, with refinement in the circle of Willis as well as the closest segments of the cerebral arteries and ICAs. In the refinement area, the element size was set to equal the interpolated voxel size. Otherwise, the element size was increased by a factor of 1.5.\u003c/p\u003e \u003cp\u003eThe left and right ICA as well as the BA boundaries were defined as inlets, whereas the left and right MCA1, ACA2 and PCA2 boundaries were defined as outlets. Any possible PCoA boundary would be defined as an outlet or inlet depending on the direction of the flow. Consequently, flow through a PCoA from the anterior to the posterior circulation implied an outlet boundary in the anterior model and an inlet boundary in the corresponding posterior model, whereas a reversed flow direction would imply the opposite. COMSOL\u0026rsquo;s built-in boundary condition for fully developed flow was enabled for inlets and outlets, applying laminar parabolic flow rate profiles. The vessel walls were given a no-slip condition.\u003c/p\u003e \u003cp\u003eTo achieve mass conservation, in addition to correct flow through the circle of Willis, the inlet flow rates were based on summed flow rates of arteries in the circle of Willis. In anterior models, the inlets of the left and right ICA were set to the sum of each respective MCA1, ACA1, and possible PCoA flow rate. In posterior models, the BA inlet flow rate was set to the sum of all PCA2 and PCoA outflows. As an additional measure, an adjustment of the ACA2 outlets was applied such that the ACA1 flow rates were correct according to the 4D flow MRI measurements. See Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eC and \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eD for schematics of the boundary conditions.\u003c/p\u003e \u003cp\u003eMAP was assumed as reference pressure in the contralateral ICA and the BA, and was applied as a pressure point at their boundaries. In the non-stenotic group, lacking significant stenoses, MAP was assumed in the ICA with the largest flow rate. For subjects in the stenotic group with a contralateral stenosis\u0026thinsp;\u0026ge;\u0026thinsp;50%, the pressure at the contralateral ICA was found by subtracting the pressure drop across the stenosis from the MAP, where the pressure drop was computed in a separate CFD simulation of the stenosis [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eComputing the territorial resistance\u003c/h2\u003e \u003cp\u003eA finished simulation generated a steady state solution of the average pressure distribution in the geometry. The average perfusion pressures in the MCA1, ACA2 and PCA2 were obtained at cross-sectional cut planes placed perpendicular to the flow direction, positioned five millimeters from the bifurcations of the outflow arteries (of the circle of Willis, as seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eA and \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eB). When PCoA was missing, the PCA cut plane was positioned five millimeters from the BA bifurcation. In case of double of any cerebral artery, e.g. two left MCA1, resistance was estimated as the parallel resistance between the two (two MCA1, N\u0026thinsp;=\u0026thinsp;1; two ACA2, N\u0026thinsp;=\u0026thinsp;4).\u003c/p\u003e \u003cp\u003eHaving determined the pressure \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003eterr\u003c/em\u003e\u003c/sub\u003e at the beginning of each major cerebral artery we computed the total downstream resistance, or territorial resistance, \u003cem\u003eR\u003c/em\u003e as\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$R=\\frac{{P}_{terr}-ICP}{{Q}_{terr}}= \\frac{\\varDelta P}{{Q}_{terr}},$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003eQ\u003c/em\u003e\u003csub\u003e\u003cem\u003eterr\u003c/em\u003e\u003c/sub\u003e is the flow rate through the vessel and \u003cem\u003eICP\u003c/em\u003e the intracranial pressure which is the counter-pressure in the brain tissue (in line with the definition of cerebral perfusion pressure [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]). Similarly, total CVR (tCVR) was computed as\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$tCVR=\\frac{MAP-ICP}{{Q}_{total}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e,\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({Q}_{total}\\)\u003c/span\u003e\u003c/span\u003e is the total cerebral inflow, i.e. the sum of the ICA and BA flow rates. For ICP, we used a reference value in healthy elderly of 11.6 mmHg [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003eComputing brain volumes\u003c/h2\u003e \u003cp\u003eBrain volumes were computed with FreeSurfer 7.2.0 (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://surfer.nmr.mgh.harvard.edu/\u003c/span\u003e\u003cspan address=\"https://surfer.nmr.mgh.harvard.edu/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e) for comparisons against CVR. In FreeSurfer, the regions of the brain are automatically segmented from T1-weighted images into grey matter, white matter and cerebrospinal fluid [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. Grey and white matter volumes of each territory were included as territorial brain volume. Which regions that belonged to each of the MCA, ACA and PCA territories was determined from the results of Tatu et al [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. One subject lacked a T1 image, but the FreeSurfer algorithm successfully segmented the brain regions in all but one (where a consistent delineation was not possible) of the remaining subjects. Results were visually inspected for accuracy using FreeView (version 3.0, the General Hospital Corporation, Boston, MA).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003eStatistical analysis\u003c/h2\u003e \u003cp\u003eFirstly, we wanted to compare tCVR of the controls and all patients to investigate relevance of the territorial CVR values as well as to assess global response of CVR in the event of hemodynamic disturbance. Secondly, territorial CVR within the patient group was compared between the clinically determined ipsilateral and contralateral hemispheres. Both ipsilateral and contralateral resistances were, in turn, compared to all territorial resistances of the non-stenotic group (averaged over hemispheres). A total of 279 territorial resistances were calculated. One patient lacked one PCA, another lacked one MCA, and 7 PCA territories were excluded due to posterior stenoses. Lastly, for a more perfusion-based comparison, an analysis was performed where hemispheres were separated by flow rates instead of stenosis degree, where an ICA flow rate below 160 ml/min was used to classify hemodynamic disturbance [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. Territorial CVR of hemispheres classed as hemodynamically disturbed were compared pairwise to the corresponding territories of the patients\u0026rsquo; opposite hemispheres.\u003c/p\u003e \u003cp\u003eWe also wanted to examine the correlation between CVR and brain volume, as territorial CVR previously have been estimated on flow rate assumptions such as distribution by brain volume. Both inter- and intra-territorial relationships between resistance and brain volume were investigated. Total and territorial brain volumes could be computed for 46 patients. As resistance is expected to relate inversely to volume it is appropriate to utilize the reciprocal of the vascular resistance, vascular conductance [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e], when analyzing this relationship.\u003c/p\u003e \u003cp\u003eAll values are presented as mean with standard deviation. Lilliefors\u0026rsquo; goodness-of-fit test was used for normality testing. For paired as well as unpaired tests of significance, Student\u0026rsquo;s t-test was used. Correlation between total conductance and volume was examined with Pearson correlation coefficient. Relations between territorial conductance and volume were examined with a linear mixed model based on restricted maximum likelihood, accounting for hemisphere as well as there being multiple samples from each subject. In the linear mixed model, parameters were set as; conductance as dependent variable, hemisphere (ipsilateral/contralateral/non-stenotic) as fixed factor, volume as covariate and subject ID as random effect. P\u0026thinsp;\u0026lt;\u0026thinsp;0.05 was the threshold for statistical significance. The statistical analysis was carried out in MATLAB (R2022b, MathWorks, Natick, MA) and jamovi (2.3.28.0, The jamovi project, Sydney, Australia). Intraclass correlation coefficient analysis was performed to compare the segmentations between two different raters using two-way random effects, absolute agreement, single rater/measurement. All resistances for 10 subjects were used in the comparison. The resulting ICC result was r\u0026thinsp;=\u0026thinsp;0.99, with CI = [0.980\u0026ndash;0.994], p\u0026thinsp;\u0026lt;\u0026thinsp;0.001, indicating excellent agreement. The corresponding CI for the MCA, ACA and PCA were all within [0.93\u0026ndash;0.998].\u003c/p\u003e \u003c/div\u003e"},{"header":"Results","content":"\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003eComparing tCVR among patients and controls\u003c/h2\u003e \u003cp\u003eThe average tCVR was 9.3\u0026thinsp;\u0026plusmn;\u0026thinsp;1.9 mmHg\u0026middot;s/ml for all patients (N\u0026thinsp;=\u0026thinsp;48). It was 9.3\u0026thinsp;\u0026plusmn;\u0026thinsp;1.7 mmHg\u0026middot;s/ml for the stenotic group (N\u0026thinsp;=\u0026thinsp;29) versus 9.3\u0026thinsp;\u0026plusmn;\u0026thinsp;2.1 mmHg\u0026middot;s/ml for the non-stenotic group (N\u0026thinsp;=\u0026thinsp;19) (p\u0026thinsp;=\u0026thinsp;0.91). The controls (N\u0026thinsp;=\u0026thinsp;56) had a mean tCVR of 9.3\u0026thinsp;\u0026plusmn;\u0026thinsp;2.0 mmHg\u0026middot;s/ml, which was not different compared to the patient group (p\u0026thinsp;=\u0026thinsp;0.88). tCVR distribution among the patients and controls are given in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eA and \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eB, respectively. Total cerebral inflow for the controls was 9.8\u0026thinsp;\u0026plusmn;\u0026thinsp;1.4 ml/s, significantly higher (p\u0026thinsp;\u0026lt;\u0026thinsp;0.01) compared to the patient group inflow of 9.0\u0026thinsp;\u0026plusmn;\u0026thinsp;1.4 ml/s.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003eDistribution of territorial CVR\u003c/h2\u003e \u003cp\u003eNo differences in CVR were found within territories when comparing the ipsilateral and contralateral hemispheres of the stenotic group, nor when comparing each of them with the non-stenotic group\u0026rsquo;s averaged hemispheres (all p\u0026thinsp;\u0026gt;\u0026thinsp;0.05, Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e). Significant differences in CVR were observed between territories (p\u0026thinsp;\u0026lt;\u0026thinsp;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e, Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e), except between the contralateral ACA and PCA (p\u0026thinsp;=\u0026thinsp;0.10) as well as ipsilateral ACA and PCA (p\u0026thinsp;=\u0026thinsp;0.01, insignificant if Bonferroni-corrected by 18). Numerical values are given in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. Identifying hemispheres below a threshold ICA feeding flow rate of 160 ml/min and comparing the territories to the corresponding territories on the opposite hemisphere gave no significant difference in territorial CVR for any territory.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eMean resistances for the territories. No significant differences in CVR between the hemispheres were found. *Note that territories are averaged over the hemispheres for the non-stenotic group.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAll\u003c/p\u003e \u003cp\u003e(mmHg\u0026middot;s/ml)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eIpsilateral\u003c/p\u003e \u003cp\u003e(mmHg\u0026middot;s/ml)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eContralateral\u003c/p\u003e \u003cp\u003e(mmHg\u0026middot;s/ml)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNon-stenotic group*\u003c/p\u003e \u003cp\u003e(mmHg\u0026middot;s/ml)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMCA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e33.8\u0026thinsp;\u0026plusmn;\u0026thinsp;10.5\u003c/p\u003e \u003cp\u003e(N\u0026thinsp;=\u0026thinsp;77)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e34.0\u0026thinsp;\u0026plusmn;\u0026thinsp;13.7\u003c/p\u003e \u003cp\u003e(N\u0026thinsp;=\u0026thinsp;29)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e32.3\u0026thinsp;\u0026plusmn;\u0026thinsp;8.2\u003c/p\u003e \u003cp\u003e(N\u0026thinsp;=\u0026thinsp;29)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e35.9\u0026thinsp;\u0026plusmn;\u0026thinsp;7.5\u003c/p\u003e \u003cp\u003e(N\u0026thinsp;=\u0026thinsp;19)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eACA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e59.0\u0026thinsp;\u0026plusmn;\u0026thinsp;30.6\u003c/p\u003e \u003cp\u003e(N\u0026thinsp;=\u0026thinsp;77)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e57.4\u0026thinsp;\u0026plusmn;\u0026thinsp;26.9\u003c/p\u003e \u003cp\u003e(N\u0026thinsp;=\u0026thinsp;29)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e62.6\u0026thinsp;\u0026plusmn;\u0026thinsp;38.8\u003c/p\u003e \u003cp\u003e(N\u0026thinsp;=\u0026thinsp;29)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e55.8\u0026thinsp;\u0026plusmn;\u0026thinsp;21.1\u003c/p\u003e \u003cp\u003e(N\u0026thinsp;=\u0026thinsp;19)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePCA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e77.8\u0026thinsp;\u0026plusmn;\u0026thinsp;21.3\u003c/p\u003e \u003cp\u003e(N\u0026thinsp;=\u0026thinsp;71)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e74.6\u0026thinsp;\u0026plusmn;\u0026thinsp;20.8\u003c/p\u003e \u003cp\u003e(N\u0026thinsp;=\u0026thinsp;27)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e76.8\u0026thinsp;\u0026plusmn;\u0026thinsp;20.9\u003c/p\u003e \u003cp\u003e(N\u0026thinsp;=\u0026thinsp;27)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e84.4\u0026thinsp;\u0026plusmn;\u0026thinsp;22.5\u003c/p\u003e \u003cp\u003e(N\u0026thinsp;=\u0026thinsp;17)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003eRelationship between resistance and brain volumes\u003c/h2\u003e \u003cp\u003eAverage total brain volume was 1065\u0026thinsp;\u0026plusmn;\u0026thinsp;108 ml and correlated significantly to total conductance with Pearson correlation coefficient (N\u0026thinsp;=\u0026thinsp;46, r\u0026thinsp;=\u0026thinsp;0.37, p\u0026thinsp;=\u0026thinsp;0.01). When analyzing territorial resistances and volumes with our linear mixed model we found that when all territories are included, volume associates to conductance (p\u0026thinsp;\u0026lt;\u0026thinsp;0.001). The model estimates the association with an intercept of 0.0224 ml/mmHg\u0026middot;s, 95% CI [0.0207, 0.0242], and volume-conductance slope of 1.84\u0026middot;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e 1/mmHg\u0026middot;s, 95% CI [1.63\u0026middot;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e, 2.04\u0026middot;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e]. However, applying the model to each respective territory yielded no association between volume and conductance (MCA, p\u0026thinsp;=\u0026thinsp;0.44; ACA, p\u0026thinsp;=\u0026thinsp;0.54; PCA, p\u0026thinsp;=\u0026thinsp;0.49). Distribution of territorial conductance and volume is illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"Discussion","content":"\u003cp\u003eWe present the territorial distribution of CVR for stroke/TIA patients with and without symptomatic carotid stenoses. With arterial anatomy from CTA and blood flow from 4D flow MRI data in combination with CFD pressure estimation, we propose a subject-specific method for determining territorial CVR without relying on flow distribution assumptions. There were differences in CVR between most of the MCA, ACA and PCA territories. There was no difference between hemispheres in the stenotic group, nor any difference in total CVR between the patient and the control group. Our results suggest that CVR may be contained within fairly stable levels in these patients, despite significant carotid stenoses and diminished flow, i.e,. the expected regional autoregulatory control had an unexpectedly low impact. For future work these resistances may work as reference values when modelling blood flow in the circle of Willis, and the method can be used when there is need for subject-specific analysis.\u003c/p\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003eDistribution of CVR\u003c/h2\u003e \u003cp\u003eIn the brain, regulatory systems such as autoregulation and neurovascular coupling utilize CVR to ensure a sufficient blood supply [\u003cspan additionalcitationids=\"CR2\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Thus, it is reasonable that hemodynamic disturbances such as carotid stenoses would impact CVR through e.g. dilation of arteries distal of a stenosis. Total CVR represents the relationship between the pressure drop from MAP in the cervical arteries to ICP in the parenchyma and the total blood supply feeding the brain. In our study, we found the patients to have a tCVR of 9.3\u0026thinsp;\u0026plusmn;\u0026thinsp;1.7 mmHg\u0026middot;s/ml and the controls 9.3\u0026thinsp;\u0026plusmn;\u0026thinsp;2.0 mmHg\u0026middot;s/ml, with comparable histograms (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). This is slightly smaller compared to previous studies, where tCVR of patients with cerebrovascular disease has been reported as 9.8\u0026thinsp;\u0026plusmn;\u0026thinsp;2.1 [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e] and of healthy as 10.5\u0026thinsp;\u0026plusmn;\u0026thinsp;2.1 mmHg\u0026middot;s/ml [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. The difference can largely be explained by the inclusion of ICP in our computations, which is substantial in the supine position [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. Interestingly, we found no difference in total CVR between controls and the hemodynamically affected patients. This could potentially be explained by the stage in the disease development at which the patients were examined. Previous studies have shown that regulatory processes in the brain are impaired by carotid stenoses and stroke [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. In addition, MAP was lower among patients compared to controls, in contrast to reports of elevated blood pressure for such patients prior to medication [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e]. Medication may play a role in further inhibiting regulation to relieve blood pressure and therefore bring cerebrovascular properties back to normal.\u003c/p\u003e \u003cp\u003eWe also did not find any differences in territorial CVR between patient hemispheres (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e), despite presence of carotid stenoses. Thus, there seems to be no difference in CVR between hospitalized patients (with limited amount of symptoms indicated by low mRS and NIHSS scores) compared to controls, nor between the patient hemispheres, suggesting that the presented distribution of CVR in patients (under treatment) reflects that of healthy elderly. It is possible that the CVR distribution may have differed at an earlier stage prior to the stroke/TIA event/treatment, where the previously discussed effects on autoregulation were not present. This was not possible to investigate in the current study, which motivates additional studies where the CVR distribution is assessed at different points in time over the cerebrovascular disease development.\u003c/p\u003e \u003cp\u003eWhen comparing the resistances of different territories, the resistances differed significantly, with a distribution of 34:59:78 mmHg\u0026middot;s/ml for MCA:ACA:PCA (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). An early and well referenced distribution of CVR was made by Hillen et al., in which the territorial resistances were estimated by assuming inverse proportion to the mass irrigated by the vessel [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e, \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]. They reported a distribution of 30:60:40 mmHg\u0026middot;s/ml. Stergiopulos et al. [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e], reported CVR downstream of ICA which, by assuming proportionality to the initial cross-sectional area of the cerebral arteries [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e], resulted in 45:64:83 mmHg\u0026middot;s/ml. Another approach to find territorial CVR is to apply outflow conditions containing estimates of territorial CVR and then updating them until the model re-creates a measured value, such as total cerebral blood flow and external carotid artery flow rate [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. This verification-based approach has yielded a distribution of 26:93:69 mmHg\u0026middot;s/ml. A similar approach, where verification was made against arterial spin labeling data of perfusion amounts in the territories, yielded distributions 11:17:35 mmHg\u0026middot;s/ml and 24:53:82 mmHg\u0026middot;s/ml for two stenosis patients, as well as 9:24:47 mmHg\u0026middot;s/ml for a young, healthy control [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e]. Notably, the distributions from these methods vary not only in size, but also in relation among territories. There could be several reasons for this, such as small subject groups or the reliance upon flow rate assumptions, or reference data built upon such assumptions. We offer values from a subject-specific method without flow rate assumptions in conjunction with local perfusion pressures in the circle of Willis. Additionally, results were acquired from a set of subjects much larger than most medical CFD studies, making for a more rigorous assessment than previously done.\u003c/p\u003e \u003cp\u003eBy determining total and territorial volumes of the patients, we were able to further investigate the relation between CVR and brain volume. The total and territorial brain volumes of our study are comparable to previous work [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e]. Our results show a positive correlation between total conductance (i.e. negative correlation for total CVR) and total brain volume. Similarly, the linear mixed model showed that territorial conductance could be explained by territorial volume, which was expected but has not yet been shown. However, this could not be shown within the respective territories. We interpret these results as that the \u003cem\u003edistribution\u003c/em\u003e of CVR over the territories can be assumed with brain volume or mass assumptions, but that a territorial volume cannot directly be converted into a territorial resistance due to larger inter-subject differences.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec17\" class=\"Section2\"\u003e \u003ch2\u003eValue of territorial resistances for modelling and predictions\u003c/h2\u003e \u003cp\u003eComputational modelling of cerebral blood flow has been developed to non-invasively estimate cerebral hemodynamics and assess clinical risks [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. One example area where this type of modelling is of interest is cerebral pulsatility, since recent findings indicate a relation between increased downstream pulsatility and cognitive decline and dementia [\u003cspan additionalcitationids=\"CR42\" citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e]. A common way to investigate cerebral arterial pulsatility is through Windkessel modelling [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e], which is partly based on the downstream, territorial resistance distribution. Another, clinically relevant, modelling application are predictions of cerebral blood flow during surgeries where cerebral blood flow may be compromised. By estimating a patient\u0026rsquo;s hemodynamical properties prior to surgery, the risk of hypoperfusion can be assessed which could help guide intraoperative decision-making [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. As blood flow is what is of interest for such predictions it is suitable to make assumptions on the surgical situation based on resistance. For both descriptive and predictive modelling it is therefore necessary that resistances are well determined and representative, which we offer with the presented method and CVR distribution.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section2\"\u003e \u003ch2\u003eLimitations\u003c/h2\u003e \u003cp\u003eA limitation when studying hemodynamic effects of carotid stenoses is that patients typically are divided based upon stenosis degree, measured at the carotid bifurcation. The non-stenotic group was added to include less hemodynamically disturbed patients, as a type of controls, since CTA is needed for the territorial analysis. However, the lack of stenosis in the carotid bifurcations did not exclude the possibility for plaque further up the ICAs and we could not consider them as vascular healthy controls, but as a patient subgroup. A way to bypass this problem was to divide the hemispheres based on flow rate and consider it the threshold for hemodynamic disturbance. In our analysis this perfusion-based division did not yield any differences in CVR either. It is possible that this is an issue of statistical power, which also could explain the lacking inter-territorial difference between ACA and PCA for ipsilateral as well as contralateral hemispheres. However, we have a relatively large group of patients compared to other CFD studies and there were seemingly no other extreme differences.\u003c/p\u003e \u003cp\u003eA strength of the study is that we base our boundary conditions on the very same flow rates that we measure, ensuring correct flow rates in the critical area, the circle of Willis. Some model assumptions should however be discussed. For example, MAP was measured prior to the acquisition of the flow rates and ICP was based on reference [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e], which adds potential inaccuracies to the results. Additionally, we assumed MAP at the BA in the posterior models but we assumed this to be reasonable due to the exclusion of patients with posterior stenoses.\u003c/p\u003e \u003c/div\u003e"},{"header":"Conclusion","content":"\u003cp\u003eThis study established the distribution of cerebrovascular resistance (CVR) among the major arterial territories of the brain of stroke/TIA patients with and without carotid stenoses, identifying values of 34:59:78 mmHg\u0026middot;s/ml between the MCA, ACA and PCA regions. The assessment was carried out with individual arterial trees and flow rates allowing for subject-specific analysis of CVR distribution. No difference in total CVR was found between patients and controls, nor for territorial CVR between hemispheres among patients, suggesting the presented distribution of territorial CVR may also be representative for the general age group.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003e\u003cem\u003eData availability\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eData is available from the corresponding authors upon reasonable request.\u003c/p\u003e\n\u003ch2\u003eAcknowledgements\u0026nbsp;\u003c/h2\u003e\n\u003cp\u003eWe would like to acknowledge research nurse Hanna Ackelind for her contributions in describing the patients included in the study.\u003c/p\u003e\n\u003ch3\u003e\u003cem\u003eAuthor contribution\u003c/em\u003e\u003c/h3\u003e\n\u003cp\u003eConcept and design by AV, MH, PH and AE. JM and AE contributed to the data acquisition. AV, PH, MH and AE performed the analysis. All authors interpreted the results. AV drafted the paper and created the figures. All authors critically edited and revised the manuscript. All authors approved the final version of the manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eCompeting interests\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe author(s) declare(s) no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eFunding\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work was funded by the Swedish Research Council [2015-05616, 2017-04949]; the County Council of V\u0026auml;sterbotten through Spjutspetsmedel and Centrala ALF; the Swedish Heart and Lung Foundation [20140592]; and the Swedish Foundation for Strategic Research. The funders had no role in study design, data collection and analysis.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003ePaulson, O. B., Strandgaard, S. \u0026amp; Edvinsson, L. Cerebral Autoregulation. 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H. \u003cem\u003eet al.\u003c/em\u003e Cerebroarterial pulsatility and resistivity indices are associated with cognitive impairment and white matter hyperintensity in elderly subjects: A phase-contrast MRI study. Journal of Cerebral Blood Flow \u0026amp; Metabolism 41, 670\u0026ndash;683 (2021). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org:10.1177/0271678x20927101\u003c/span\u003e\u003cspan address=\"https://doi.org:10.1177/0271678x20927101\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Carotid stenosis, cerebrovascular resistance, computational fluid dynamics, peripheral cerebral territories, stroke","lastPublishedDoi":"10.21203/rs.3.rs-3900174/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3900174/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eCerebrovascular resistance (CVR) regulates blood flow in the brain, but little is known about the vascular resistances of the individual cerebral territories. We present a method to calculate these resistances and investigate how CVR varies in the hemodynamically disturbed brain. We included 48 patients with stroke/TIA (29 with symptomatic carotid stenosis). By combining flow rate (4D flow MRI) and structural computed tomography angiography (CTA) data, and using computational fluid dynamics (CFD) we computed the perfusion pressures out from the circle of Willis, with which CVR of the MCA, ACA, and PCA territories was estimated. 56 controls were included for comparison of total CVR. CVR were 33.8\u0026thinsp;\u0026plusmn;\u0026thinsp;10.5, 59.0\u0026thinsp;\u0026plusmn;\u0026thinsp;30.6, and 77.8\u0026thinsp;\u0026plusmn;\u0026thinsp;21.3 mmHg\u0026middot;s/ml for the MCA, ACA, and PCA territories. We found no differences in total CVR between patients, 9.3\u0026thinsp;\u0026plusmn;\u0026thinsp;1.9 mmHg\u0026middot;s/ml, and controls, 9.3\u0026thinsp;\u0026plusmn;\u0026thinsp;2.0 mmHg\u0026middot;s/ml (p\u0026thinsp;=\u0026thinsp;0.88), nor in territorial CVR in the carotid stenosis patients between ipsilateral and contralateral hemispheres. Territorial resistance associated inversely to territorial brain volume (p\u0026thinsp;\u0026lt;\u0026thinsp;0.001). These resistances may work as reference values when modelling blood flow in the circle of Willis, and the method can be used when there is need for subject-specific analysis.\u003c/p\u003e","manuscriptTitle":"Establishing the distribution of cerebrovascular resistance using computational fluid dynamics and 4D flow MRI","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-02-05 17:47:04","doi":"10.21203/rs.3.rs-3900174/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-05-22T05:29:19+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-05-20T20:18:33+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"114328350069909779077987579487371135329","date":"2024-05-10T05:30:03+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-02-29T09:03:25+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"0864fa83-23d8-4fcd-a6db-c4625aefae87","date":"2024-02-28T02:32:00+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"e12eafab-bc56-4c6f-9566-9e5b2c6e99be","date":"2024-02-12T17:43:35+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-02-11T06:25:31+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-02-06T03:39:21+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2024-02-02T13:16:43+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-02-02T13:13:53+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2024-01-26T14:26:58+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"a7bed6c0-c057-464f-ab00-39e8a4385b24","owner":[],"postedDate":"February 5th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":28545580,"name":"Physical sciences/Physics/Fluid dynamics"},{"id":28545581,"name":"Health sciences/Diseases/Cardiovascular diseases/Vascular diseases/Carotid artery disease"},{"id":28545582,"name":"Health sciences/Diseases/Cardiovascular diseases"},{"id":28545583,"name":"Health sciences/Diseases/Cardiovascular diseases/Vascular diseases"},{"id":28545584,"name":"Health sciences/Diseases/Cardiovascular diseases/Vascular diseases/Cerebrovascular disorders/Stroke"}],"tags":[],"updatedAt":"2024-06-20T04:25:09+00:00","versionOfRecord":[],"versionCreatedAt":"2024-02-05 17:47:04","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-3900174","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3900174","identity":"rs-3900174","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}