Calibration and validation strategy for electromechanical cardiac digital twins

State-of-the-art cardiac electromechanical modelling and simulation form the basis for recent developments in cardiac Digital Twin technologies. However, a comprehensive evaluation of electromechanical models at cellular, tissue, and organ level has yet to be performed that addresses both ECG and pressure-volume biomarkers. Such an evaluation would build credibility for applications of cardiac Digital Twins in clinical research and therapy development. We aimed to follow ASME V&V40 standards to develop a strategy for calibration, validation, and uncertainty quantification of ventricular electromechanical Digital Twins under healthy conditions. We performed a multi-scaled review of ventricular electromechanics to compile a dataset for calibration and validation incorporating ECG, pressure-volume, displacement, and strain biomarkers. When applied to a biventricular multiscale model, we achieved healthy calibrated values for the QRS duration (89 ms), QT interval (360 ms), left ventricular ejection fraction (LVEF) (51 %), peak systolic pressure (14 kPa), end diastolic (110 mL) and end systolic volumes (50 mL), peak ejection flow rate (180 mL/ms). Model validation was performed by comparison to displacement and strain biomarkers including systolic atrioventricular plane displacement (1.5 cm), systolic fibre strain (-0.18) and longitudinal strain (-0.15). Sensitivity analysis of model parameters at cellular and ventricular scales was also performed. We quantified the effects of variability in ionic conductance, mechanical stiffness, cross-bridge cycling dynamics, and systemic circulation on action potential and active tension dynamics at the cellular scale, and on ECG, pressure-volume, displacement, and strain biomarkers at the ventricular scale. Simulations showed that the relationship between healthy LVEF and T wave biomarkers was primarily underpinned by variability in L-type calcium channel conductance and SERCA activity through multi-scale effects. In this study, we pave the way towards credible cardiac electromechanical Digital Twins by setting the basis for a strategy for calibration and validation based on both ECG and mechanical biomarkers. 2 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint

Digital Twins are playing an increasingly important role in healthcare to enable tailored therapy design for precision medicine. The importance of this emerging technology was attested to by recent regulatory attention and the publication of the ASME V&V40 Standard in 20181. The Standard provided a risk-based framework for evaluating their credibility for biomedical applications. At the core of the cardiac Digital Twin are realistic mechanistic models that can coherently assimilate multi-modal and multi-scale data and can explain disease mechanisms and predict therapy outcomes2–4. An important aspect of cardiac function is the coupling of electrophysiology and mechanics in the ventricles5–7. To describe electromechanical function, Digital Twin models are built on mathematical descriptions of electromechanical coupling at cellular, tissue, and organ scales. The biophysical detail gives the model the advantage of high explainability and predictive power over statistical or machine learning approaches. Electromechanical cardiac Digital Twins have had broad applicability in cardiology, such as in unravelling the relationship between the electrocardiogram (ECG) and mechanical deformation8, the ECG and ejection fraction in post-myocardial infarction9, demonstrate how mechanical deformation provides triggers and substrate for arrhythmia10 and affects re-entrant wave stability11, and predicting therapy outcomes in hypertrophic cardiomyopathy12 and heart failure13. Recent developments have enabled increasingly personalised cardiac Digital Twins through assimilation of omics, imaging, blood pressure, and electrocardiogram (ECG) data6,14–16 and promises to deliver patient-specific therapy planning17 in the near future. Despite significant developments, a lack of thorough reviews of model credibility considering both electrophysiological and mechanical properties from cell to organ scales hinders wider acceptance of cardiac Digital Twin technologies. Thus far, cardiac applications of the ASME V&V40 standards have focused on device optimisation using fluid-structure interaction models for left ventricular assistive devices18 and for artificial heart valves19, but this has yet to be applied to ventricular electromechanical simulations. Examples of rigorous model 3 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint evaluation at cellular scale20–22 highlight the importance of strictly separating calibration and validation data20 and consideration of both electrophysiological and mechanical biomarkers23. At the ventricular scale, most studies focused either on the ECG8 or pressure-volume biomarkers24–27 18 28 but not on both, and deformation and strain biomarkers are rarely considered. Simulation studies have investigated how model parameters relate to specific aspects of cardiac electromechanical function, such as the atrioventricular plane displacement28, and how model deformations relate to ECG morphologies8, but not in a comprehensive manner. Large scale global sensitivity analyses studies of pressure and volume biomarkers have analysed effects from anatomical variations25 and contractility and haemodynamic parameter variations29, without any analysis of concurrent ECG biomarker effects. Furthermore, the strategies and data used for calibration and validation in these studies were typically not discussed5,6,25. Therefore, in this study we aim to propose a calibration and validation strategy based on a thorough review of the literature for model parameters and considering both ECG and mechanical biomarkers for evaluating ventricular electromechanical Digital Twins, following ASME V&V40 principles. We apply this to a multiscale, biventricular model with the aim to 1) reproduce healthy pressure-volume, ECG, deformation, and strain dynamics, and 2) investigate multi-scale mechanisms that underpin the relationship between ECG and pressure-volume biomarkers.

Multi-scale human biventricular electromechanics Human electrophysiological model Simulation of the electrical excitation and relaxation through the ventricles was through the monodomain model with orthotropic diffusion along the fibre, sheet, and sheet-normal directions. Ionic current dynamics and calcium handling dynamics were modelled using the human ventricular electrophysiological cell ToR_ORd model 20, with extensive validation on 4 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint experimental action potential morphology and calcium dynamics, as well as responses to multi-channel drug block. Purkinje-myocardial junctions were modelled using a fast endocardial activation layer with isotropic conduction velocity σ endo on the left and right ventricular endocardial surfaces. Standard 12-lead electrode positions were manually mapped from the heart and torso geometry of a previous study to the current geometry, and the 12-lead ECG was simulated at these electrode positions using the pseudo-ECG method15. Mechanical model The mechanical behaviour was characterised by the balance of linear momentum in a total Lagrangian formulation, considering inertial contributions but ignoring volumetric forces. The reference configuration was the scaled down version of the biventricular mesh (diastasis) Ω0 ⊂ R 3 , at t=0. The constitutive law for the passive mechanical behaviour of the ventricular tissue was a nearly incompressible version of Holzapfel and Ogden which was orthotropic in mechanical behaviour7. The strain energy density function defining this hyper-elastic continuum is: ψ ( C) = K ct 2 ( J −1) 2 + a 2 b ( e b ( I 1−3)−1)+ ∑ i=f , s ai 2b i ( e bi ( I 4 i−1 ) 2 −1)+ a fs 2 bfs ( e bfs I 8 fs 2 −1) where J=det ( F ), C=F T F, bar notation indicates that  x=J −2 3 x, f 0 and s0 indicate fibre and sheet directions, respectively, in the reference configuration such that I 1=trC, I 4 f =f 0∙ C f 0, I 4 s=s0∙ C s0, I 8 fs= 1 2 ( f 0∙ C s0+ s0∙ C f 0), and Kct controls the compressibility of the material. The reader is directed elsewhere7 for the precise form of the passive contribution to the second Piola-Kirchhoff stress tensor. 5 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint Boundaries were defined as: epicardium Γ epi, left ventricular endocardium Γ LV endo, right ventricular endocardium Γ RV endo, and the non-endocardial surfaces of the valvular plugs Γ valv e epi, FS n0−J P LV endoF −T n0=0 , on Γ LV endo×( 0 , T ] , FS n0−J P RV endoF −T n0=0 , on Γ RV endo×( 0 , T ] , FS n0−( K epi ( uv cl) u ∙ n0) n0=0 , on Γepi × where n 0 was the outward normal defined on the whole material boundary ∂ Ω0, and K epi ( uv cl) was the stiffness corresponding to an elastic spring boundary condition applied to the endocardium and was described as a step function of the longitudinal coordinate l with magnitude of K epi at values of 0<uv cl<0.85 (i.e. applied for 85% of the longitudinal dimension of the heart from the apex). This was a simplified version of the method28, which uses an exponential decay formulation at the ‘edge’ of the pericardial constraint rather than a step function. P LV endo and P RV endo were the pressures applied to the left and right endocardial surfaces, respectively, and was prescribed by two independent piece-wise functions that describe the five-phases (not including initiation) of the cardiac cycle:  Phase 0: Initiation. Endocardial pressures were linearly increased to reach diastasis values P RVDS and P LVDS.  Phase 1: Active diastolic filling. Endocardial pressures were linearly increased over time t EDP to end diastolic values EDP LV and ED P RV to mimic the effect of atrial contraction.  Phase 2: Isovolumetric contraction. Electrical activation ensues and active contraction develops. During this, the ventricular pressure was controlled such that the volume was maintained to be constant via: d PLV endo= −1 C PLV d V LV endo− 1 C V LV d V LV endo dt 6 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint d PRV endo= −1 C PRV d V RV endo− 1 CV RV d V RV endo dt Where C pLV, C pRV, C V LV, C V RV, were the inverse of penalty terms for volume difference and volume rates for the left and right ventricles, respectively. The volume rate term was used as stabilisation against spurious oscillations of the ventricular pressure, which might occur due to inertial effects.  Phase 3: Ejection. When the ventricular pressure surpasses the aortic P AO and pulmonary artery P P A pressures, the ejection phase begins. To model the blood pressure of the systemic circulation system during the ejection phase, the following two element Windkessel model was used: C AO d P AO dt + P AO R AO =−d V LV endo dt C P A d P P A dt + PP A RP A =−d V RV endo dt Where C AO and C P A were the compliance of the aortic and pulmonary arteries, respectively, and R AO and R P A were the resistance of the aortic and pulmonary circuits, respectively. During the ejection phase, the ventricular pressures P LV endo and P RV endo were modelled as equal to the arterial pressures P AO and P P A respectively, disregarding negligible pressure gradients across the arterial valves.  Phase 4: Isovolumetric relaxation. This phase was triggered when the ventricular flow reverses   ˙V LV endo>0, and ˙V RV endo>0, and it follows the same formulation as the isovolumetric contraction Phase 2.  Phase 5: Passive filling. This phase begins when the endocardial pressure drops below the left and right atrial pressures P_LA, P_RA. The pressure was prescribed so that the two ventricular volumes were returned to its diastasis value (DSV_LV, DSV_RV). 7 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint d PLV endo= −1 C pLAV ( V LV endo−DS V LV)− 1 C vLAV d V LV endo dt , d PRV endo= −1 C pRAV ( V RV endo−DS V RV ) − 1 C vRAV d V LV endo dt Where C pLAV , C pRAV ,C vLAV , C vRAV were the inverse of penalty terms for volume different to DSVs and volume rates, for the left and right ventricles, respectively. The two ventricular volumes V LV endo and V RV endo were calculated and updated throughout the cardiac cycle by using the divergence theorem and the assumption that the volume was constrained by a flat lid located on the aortic and pulmonary valvular planes, for right and left ventricles respectively, leading to: V LV endo= ∫ ∂ Ω0L V endo J ( x ∙ eAO) ( eAO ∙ F −T n 0) d ∂ Ω0, V RV endo= ∫ ∂ Ω 0RV endo J ( x ∙ eP A) ( eP A∙ F −T n0) d ∂ Ω0 , Where e AO and eP A were defined so that e AO∙ n 0=0 on the aortic valve plane, and eP A∙ n0=0 on the pulmonary valve plane. Electromechanical coupling Electrophysiological activation begins at Phase 2 of the cardiac cycle and drives the active tension generation. This is modelled at the cellular level by coupling of the Land active force generation21 with intracellular calcium dynamics from the human cellular electrophysiology ToRORd model20, henceforth referred to as the human cellular electromechanical ToRORd- Land model. In order to couple the ToRORd to the Land model, the Hill coefficient of calcium cooperativity and tropomyosin rate constant of the Land model were re-fitted in a previous study23 so that physiological active 8 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint tension could be produced in response to the calcium transient dynamics of the ToRORd model, which were different to the calcium transient to which the original Land model was fitted. In the Land model, active force generation is modelled using four cross- bridge cycling states (blocked, unbound, pre-power stroke and the force- generating state) and the transition rates between each were calibrated to human skinned myocyte data21. The ToRORd-Land coupling is bidirectional, where calcium from the ToRORd binds to troponin C and drives the transition between the blocked and unbound states of the crossbridge system, while the binding of calcium from the Land model acts as a buffer for the ToRORd calcium transient. Furthermore, the length-dependence of troponin calcium affinity/sensitivity in the Land model means that calcium buffering in the ToRORd is dynamically affected by tissue deformation. The Land model was first constructed using skinned myocyte data, then several of the parameters were re-fitted to enable sufficient ejection at the ventricular scale, including the transition rate from the pre-power stroke to force-generating state of the cross bridge (kws), the sensitivity of troponin to calcium binding (Cal50)21. At the tissue level, the active tension was then added to the stress tensor to drive mechanical contraction7. Literature-informed parameter initialisation 9 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint A review of the literature produced a list of initial model parameter values as compiled in Table 1, including also reported parameter variability. Passive mechanical properties were extracted from the non-viscoelastic version of the model fitted to human ex vivo stress-strain measurements30. Ionic time constants and conductance values were set to baseline values of the human membrane kinetics ToR_ORd model, which had been calibrated to patch clamp, action potential and calcium transient data20. The active tension Land model parameters were as previous calibrated to achieve a physiological calcium transient23. Table 1 Initial parameter values and literature basis for the choice of uncertainty ranges for the model inputs. Unless stated explicitly, quoted values from the literature have come from previous modelling choices. Group Parameters Initial value Literature ranges Passive mechanics parameters a, af, as, afs 0.61 kPa, 1.56 kPa, 0.70 kPa, 0.46 kPa 0.61, 1.56, 0.70, 0.46 (fitted to human data shear and axial data)30 0.057, 21.503, 6.841, - (fitted to partial shear pig data)31 0.059, 18.472, 2.481, 0.216 (fitted to full shear pig data)31 2.28, 1.685, -, - (fitted to biaxial dog data)31 0.333, 18.535, 2.564, 0.417 32 b, bf, bs, bfs 7.5, 35.31, 33.24, 5.09 7.5, 35.31, 33.24, 5.09 (fitted to human data shear and axial data)30 8.094, 15.819, 6.959, - (fitted to partial shear pig data)31 8.023, 16.026, 11.12, 11.436 (fitted to full shear pig data)31; 9.726, 15.779, -, - (fitted to biaxial dog data)31 9.242, 15.972, 10.446, 11.602 32 Kct 5000 kPa 333332, 10 - 1000 33 Active tension parameters Tref 120 kPa * 10 120 (fitted to human contraction data)21 Cross-fibre contraction 30% of Tref 0 – 60% 7, 46% (rabbit heart tissue measurements) 34 Pressure volume control parameters R_LV 10 kPa ms/mL 75 – 750 mmHg ms/mL 7 , 750 mmHg ms /mL32, 852 mmHg ms/mL 21 R_RV 33.3 kPa ms/mL A third of left ventricular value 21, 2.0 +- 0.8 mmHg min/L (control patient measurements) 35 C_LV 1.5 mL/kPa 0.2 mL/ mmHg32, 2.73 mL/mmHg21 10 218 219 220 221 222 223 224 225 226 227 228 229 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint C_RV 4.5 mL/kPa Threefold of left ventricular value21 P ejection LV 10 kPa 73 -78 mmHg (human measurements)36, 9 kPa21 P ejection RV 2.3 kPa 17.5 +- 7.5 mmHg (control patient measurements)35, 3 kPa21 P diastolic cut-off LV 1.3 kPa 10 [7-13] mmHg (control patient measurements)37, 0.1 kPa21 P diastolic cut-off RV 1.5 kPa 14.4 ± 5.8 mmHg, pulmonary diastolic pressure35 Atrial filling duration LV 150 ms ~150 ms at resting cycle length 1000 ms (human exercise measurements)38 EDP_LV 1.3 kPa 10 ± 1 mmHg (control patient measurements)39, ~7.5 mmHg(control patient measurements)40, 7.5 mmHg21. EDP_RV 1.0 kPa 11.0 ± 6.3 mmHg35, A third of left ventricular value21 Pericardial constraint K_epi 500 kPa/cm 20 kPa/cm with 5e-2 kPa*s/cm for viscous term41, 500 kPa/cm28, 0 – 100 kPa/cm (20 kPa/cm specifically for baseline)7 Microstructure Transmural fibre angle endo to epi -60 to 60 in LV, 90 to – 25 in RV, 0 to 90 at outflow tract -60 to 60 in LV, 90 to –25 in RV, 0 to 90 at outflow tract42 Transmural sheet angle to radial axis 0 degrees -45 endocardium to 45 epicardium (canine measurements) 43, 45 endocardium to 0 epicardium (canine measurements) 44, ~45 degrees at diastole, ~0 degrees at systole (swine DTI measurements)45 Heart rate Cycle length 1000 ms 63+-2 beats/min46, 72 +- 13 beats/min47 Model assessment strategy Following examples of the ASME V&V 40-based analysis applied in the context of cardiovascular science 18,48, we devised a calibration and validation 11 230 231 232 233 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint strategy for human ventricular electromechanical modelling and simulation frameworks by considering the following: Question of interest Can the modelling and simulation framework produce healthy physiological electromechanical function at cellular, tissue, and organ levels including both ECG and pressure-volume loop biomarkers? Context of use Human ventricular electromechanics models provide mechanistic explanations for various disease conditions and evaluate therapeutic interventions. Here we focused on model evaluation under healthy conditions to build the foundations of model credibility for disease and therapy investigations in the future. Quantities of interest To ensure model relevance to its context of use, the quantities of interest were chosen to be biomarkers with known links to key cardiac diseases, including Torsade de Pointes, myocardial infarction, hypertrophic cardiomyopathy, dilated cardiomyopathy, heart failure, and pulmonary hypertension. Therefore we selected the following biomarkers from the 12- lead ECG (QRS duration, QT dispersion, T wave amplitude, T peak to T end duration, and JT interval), the pressure-volume relationship (left and right end diastolic and end systolic volumes and end systolic pressures, and left ejection fraction, left pressure upstroke velocity, left peak ejection and peak filling flow rate), and from measurements of displacement (end diastolic and end systolic wall thicknesses, atrioventricular plane displacements, systolic percentage volume change, and apical displacement) and strain (systolic global longitudinal strain, radial strain, circumferential strain, and fibre stretch ratio). The relevance of each biomarker to cardiac diseases was summarised in Table 3. 12 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint Cellular biomarkers including action potential duration (APD90), active tension peak (Tamax), active tension duration (TaD50) and peak upstroke of active tension (dTa/dtmax) were not explicitly included in the biomarker list since they have already been used to calibrate and validation the cellular electromechanical model previously20,23. However, these properties were evaluated in uncertainty quantification (see below) to inform ventricular simulations. Compilation of biomarker data The healthy ranges for each quantity of interest (biomarker) were compiled from the literature. Reports from larger datasets were preferred for better estimates of population variability. For this reason, values were preferentially included from the UK Biobank, which is a large-scale biomedical database with health information from half a million UK participants, with more than 40,000 cardiac magnetic resonance recordings available49–51. This is then supplemented by smaller studies as needed. The use of gold standard magnetic resonance imaging data was preferentially included over other imaging modalities such as echocardiography for volumetric and deformation biomarkers. Separation of calibration vs validation data The quantities of interest were separated into a calibration and a validation dataset20. The calibration dataset consisted of ECG and pressure-volume biomarkers that clinically defined healthy electromechanical function, while the validation dataset included displacement and strain biomarkers that explored the model’s capabilities for providing mechanistic explanations. Sensitivity analyses strategy The model was further validated through sensitivity analyses. To showcase versatility, a wider set of parameters were included in the analyses than has explicitly been linked to any disease or therapeutic target. 13 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint The following model parameters were included from the cellular electrophysiology (conductances of the fast sodium current GNa, late sodium current GNaL, L-type calcium current GCaL, transient outward potassium current Gto, rapid delayed rectifier potassium current GKr, slow delayed rectifier potassium current GKs, sodium calcium exchanger GNCX, inward rectifier current GK1, sodium-potassium pump current GNaK, peak calcium release Jrel, peak calcium re-uptake SERCA, and magnitude of the stimulus current Istim), the cellular active tension generation (peak active tension Tref, calcium sensitivity Cal50, cross bridge transition rates from unbound to pre- powerstroke kuw and from pre- to post-powerstroke kws), passive mechanical properties (bulk stiffness a, fibre stiffness af, sheet stiffness as, fibre-sheet shear stiffness afs, compressibility coefficient Kct, pericardial constraint stiffness Kepi), and circulatory haemodynamics (aortic resistance RLV, aortic compliance CLV, aortic ejection threshold pressure PejectionLV). Model parameter ranges were informed by variabilities in literature reports (summarised in Table 2). Cellular conductances were uniformly varied from 50 to 200% to cover the experimentally measured ranges as done in previous studies22. For passive mechanics, only the parameters carrying units of stiffness were included in the exploration and their ranges come directly from the literature. The compressibility parameter (Kct), pericardial constraint stiffness (Kepi), and the active tension coefficient (Tref) parameters were allowed greater ranges of variation since they do not correspond to experimental measurements and their physical meanings were model-dependent. Similarly, the resistance and compliance parameters and the ejection threshold pressure were allowed a large uncertainty range since they were part of a lumped parameter model and do not directly map to experimental measurements. Table 2 Variability ranges for mechanical and haemodynamic parameters explored in ventricular sensitivity analysis. Mechanical and haemodynamic parameters Literature ranges Variability ranges 14 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint a, af, as, afs (kPa) 0.61, 1.56, 0.70, 0.46 (fitted to human data shear and axial data)30 0.057, 21.503, 6.841, - (fitted to partial shear pig data)31 0.059, 18.472, 2.481, 0.216 (fitted to full shear pig data)31 2.28, 1.685, -, - (fitted to biaxial dog data)31 0.333, 18.535, 2.564, 0.417 32 [0.057, 0.61] [1.56, 2.15] [0.7, 6.8410] [0.216, 0.46] Kct (kPa) 333332, 10 - 1000 33 [10, 500] Tref (kPa) 120 (fitted to human contraction data)21 [1200, 2400] Arterial resistance 75 – 750 mmHg ms/mL 7 , 750 mmHg ms /mL32, 852 mmHg ms/mL 21 [500, 999] Arterial compliance 0.2 mL/ mmHg32, 2.73 mL/mmHg21 [0.1, 0.2] P ejection LV (kPa) 73 -78 mmHg (human measurements)36, 9 kPa21 [5, 10] K_epi (kPa) 20 kPa/cm with 5e-2 kPa*s/cm for viscous term41, 500 kPa/cm28, 0 – 100 kPa/cm (20 kPa/cm specifically for baseline)7 [20, 500] A specific example of model calibration, validation and sensitivity analysis Input data To demonstrate our strategy we selected a patient-specific (female, age 49, weight 90 kg) biventricular tetrahedral mesh with valvular plugs from four-chamber meshes available from a published database25. Since the mesh was constructed based on imaging data at end diastole, the mesh was scaled down isotropically to achieve a diastasis volume of 80 mL39 to mimic the process of unloading to diastasis. Fibre f 0, sheet s0, and sheet-normal n 0 vectors at resting were generated using a rule-based method designed for biventricular geometry with outflow tracts42. Ventricular coordinates were taken from the published database25, and consisted of the longitudinal coordinate (uv cl) where uv ct=1 at the apex and 0 at the base, a 15 319 320 321 322 323 324 325 326 327 328 329 330 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint transmural coordinate (uv ct), where endocardium was uv ct=1 and epicardium was uv ct=0, and a rotational coordinate (uv cr), where uv cr=0 was in the middle of the left ventricular lateral wall. Calibration to ECG and pressure-volume biomarkers The 12-lead ECG signals of a female healthy volunteer with similar myocardial mass (108 g) as the biventricular mesh (96 g) was extracted and beat-averaged15 for calibration of electrophysiological activation and repolarisation characteristics. The conduction velocities along the fibre and sheet-normal directions were extracted from surgical measurements52. The root nodes of earliest activation on the endocardial surface as well as the conduction velocities on the endocardial surface and transmurally were calibrated using the QRS segment of the ECG signal, while spatial heterogeneity in the slow rectifier potassium current (IKs) was calibrated to the ST-T segment of the ECG signal, using a Bayesian-based inference method15,53. The calibrated model had a transmural conduction velocity of 48 cm/s, and the fibre and sheet-normal conduction velocities were set to 67 cm/s and 44 cm/s as measured using plunge needle in control subjects52. When the initialised parameter values were used in a preliminary electromechanical simulation, the results undershot healthy values of left ventricular peak systolic pressure by 2 kPa, ejection fraction by 32%, stroke volume by 29 mL, and peak ejection rate by 142 mL/ms, and peak filling rate by 207 mL/ms, and overshot the end systolic volume by 18 mL, and the peak pressure upstroke velocity by 70 kPa/ms. This demonstrated the need for model calibration and explorations of model uncertainties. Due to the high computational cost of ventricular electromechanics simulations, calibration methods that require high volume of evaluations were infeasible. In this study, we designed a sequential calibration strategy based on knowledge of model sensitivities (described in detail in Appendix 1). This involves a series of sampling and parameter selections as follows, 16 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint where single parameters were uniformly sampled and multiple parameters were sampled using Latin Hypercube Sampling: 1. Sample ejection pressure threshold, Kct, Cal50 and kws and select parameter set that gives highest LVEF. 2. Sample arterial resistance RLV and select value that gives best peak systolic pressure. 3. Sample GCaL and select value that gives highest LVEF. 4. Sample kws and select value that gives best peak ejection rate, dP/dtmax and LVEF. 5. Sample diastolic volume change parameter and select value that gives best peak filling rate. Validation by comparison to deformation and strain biomarkers The calibrated model was evaluated against displacement and strain biomarkers as listed in Table 3 and not used for model calibration. Atrioventricular plane displacement was calculated by tracking the longitudinal displacement of the top 10% of the geometry using the apex-to- base ventricular coordinate. Wall thickness was calculated using perpendicular projections of the endocardial and epicardial surfaces. Myocardial strains were evaluated at a mid-ventricular short axis slice and at a four-chamber longitudinal, to match DENSE measurements. Circumferential, radial, and fibre strains were evaluated using the short axis slice, while the longitudinal strain was evaluated using the long axis slice. The strain transients were then time- shifted to begin at the end of diastolic filling (Phase 1) and offset by the end diastolic strain, to match DENSE measurements. Sensitivity analysis at cellular and ventricular scales A global sensitivity analysis was first performed at the cellular scale using the human cellular electromechanical ToR_ORd-Land model23 to identify the key parameters that affect active tension and action potential duration. The conductances of all ionic currents as well as troponin calcium sensitivity and 17 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint the cross-bridge power stroke rate and myosin head attachment rates (kws and kuw) were varied from 50% to 200%. The key parameters that affect active tension dynamics and action potential duration were identified through ranking the parameters using the total Sobol index. This analysis showed that the key parameters which affected active tension amplitude, duration, and upstroke were GCaL, SERCA, calcium sensitivity Cal50, the cross-bridge cycling rate (kws) and GNaL (Appendix Figure 1). At the ventricular scale, the mechanical and haemodynamic parameters listed in Table 2 along with the cellular parameters GCaL, SERCA, Cal50, kws, and GNaL were included one-at-a-time sensitivity analyses, varying each parameter uniformly in a total of eight simulations each over the ranges as specified in Table 2 for mechanical and haemodynamic parameters and over 50% and 200% for cellular parameters. Each biomarker as listed in Table 3 were evaluated, and linear regression was performed. Parameter-biomarker relationships that had p-values less than 0.05 and absolute r-values larger than 0.6 were considered significant and linear relationships. The magnitudes of biomarker effects were normalised by the maximum magnitude for each biomarker. To visualise the relative importance of model parameter on simulated biomarker, a summary diagram was generated with lines linking each parameter to each biomarker. The colour of each line indicated a positive (red) or a negative (blue) relationship. The thickness of each line was scaled by the normalised magnitude of the effect. The transparency of each line was scaled by the r- value as measure of the linearity of relationship (Results Figure 3). 18 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint Computations and software Cellular electrophysiological simulations and Latin Hypercube Sampling were performed using bespoke MATLAB codes. Coupled cellular electromechanics, as well as biventricular electromechanics simulations, were performed using the high-performance numerical software, Alya for complex coupled multi- physics and multi-scale problems54 on the JURECA pre-exascale module supercomputer operated by Juelich Supercomputing Centre, Germany, through a PRACE-ICEI (project, as well as on the ARCHER2 supercomputer provided by the UK National Supercomputing Service through the CompBioMedX project (Computational Biomedicine a the Exascale) funded by EPSRC under grant agreement EP/X019446/1. Code for the generation of simulation files for multi-scale sensitivity analysis, calibration and validation, as well as scripts for evaluation of ECG, PV, deformation and strain biomarkers from ventricular simulations can be found at: https://github.com/jennyhelyanwe/Alya_input_setup/

Experimental and clinical dataset for model calibration and validation Table 3 presents the experimental and clinical dataset for healthy human ventricular electromechanics. For pressure-volume biomarkers and ECG biomarkers, reported values from the UK Biobank1 were used, where the number of samples reaches the tens of thousands. Catheter measurements of intraventricular pressure dynamics were rare in the literature and have small dataset sizes. Mechanical displacement and strain biomarkers came from MRI studies with specialised sequences (e.g. DENSE strain imaging). 19 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint Table 3 Experimental and clinical datasets for calibration and validation of healthy ventricular electromechanical models, with summary of why each biomarker was important due to their implications in cardiac diseases. Data were presented in the forms: [x, y]95% were 95% confidence intervals, x±ystd were mean and standard deviations, x±zsem were mean and standard error of the mean, [x, y]range were the minimum (x) and maximum (y), x [y, z]IQR were median (x) and first (y) and third (z) quartiles , x (y)IQR were median (x) and interquartile range (y). UKBB indicates values extracted from the UK Biobank. Unit conversions from original source has been done where appropriate to preserve consistency across the entire table. SCD: sudden cardiac death, HCM: hypertrophic cardiomyopathy, DCM: dilated cardiomyopathy, CAD: coronary artery disease, HF: heart failure, HFpEF: HF with preserved ejection fraction, PAH: pulmonary artery hypertension, MI: myocardial infarction, HHD: hypertensive heart disease. Group Biomarker Ranges Data info Implication for cardiac diseases Calibration dataset 12-lead ECG JT interval (ms) 313 [294, 335]IQR 55 mixed sex, UKBB CMR, n=76,266 In patients with QRS > 120 ms, risk of Torsade de Pointes56,57 Tpe (ms) 62 (12)IQR 58 mixed sex, UKBB without life threatening arrhythmias, n=51,574 Risk of SCD59 T wave amplitude (Tpeak) (mV) 0.15 [0.11, 0.19]IQR 4 mixed sex, UKBB normal ventricular mass, n=36,956 Risk of SCD in HCM60 QT dispersion (ms) 56.6 [37.0, 84.0]IQR 4 mixed sex, UKBB normal ventricular mass, n=36,956 Severity of CAD61 QRS duration (ms) 89 [81, 97]IQR 4 mixed sex, UKBB normal ventricular mass, n=36,956 Poor prognosis in DCM62 and risk stratification for HFpEF62 Pressure volume LVEDV (mL) [88, 161]95% 49 female UKBB CMR, n=804 Predictor of exercise capacity in HFpEF63 LVESV (mL) [31, 68]95% 49 female UKBB CMR, n=804 Predictor of HFpEF64 RVEDV (mL) [85, 166]95% 49 female UKBB CMR, n=804 Predictor of functional class in PAH65 RVESV (mL) [27, 77]95% 49 female UKBB CMR, n=804 Stratifies PAH66,67 SVL (mL) [49, 100]95% 49 female UKBB CMR, n=804 Incident rate of HF44 LVESP (kPa) 16.7 ± 2.2std 68 mixed sex, UKBB, Associated with 20 437 438 439 440 441 442 443 444 445 446 447 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint n=150 hypertrophy68,69 RVESP (kPa) 3.2 ±0.4std 70 male, radionuclide ventriculography, n=12 Stratifies PAH66,67 LVEF (%) [51, 70]95% 49 female UKBB CMR, n=804 Stratifies HF, MI, and SCD risk71 dP/dtmax (kPa/s) 150 ±30std 72 catheter measurement in successful CRT, n=17 Surrogate measure of ventricular contractility in HF73 Peak ejection rate (PER) (mL/s) 410 ± 102std 74 mixed sex, 3D echocardiography, n=15 Valvular regurgitation75 and peak systolic velocity associated with CHD76 Peak early filling rate (PFR) (mL/s) 361 ± 110std 74 mixed sex, 3D echocardiography, n=15 Points to relaxation dysfunction in CHF77 Validation dataset Displaceme nts and strains ED wall thickness (cm) [0.57, 1.38]range 78 mixed sex, range of mean values over 17 AHA regions, UKBB CMR, n=4620 Increased in HCM or HHD79,80 ES wall thickness (cm) [1.07, 1.749]range 78 mixed sex, range of mean values of 17 AHA regions, UKBB CMR, n=4620 Fractional thickening reduced in HCM80 Atrioventricular plane displacement (AVPD) (ES – ED) (cm) [1.4, 1.9]range 46 mixed sex, CMR, healthy subjects n=12 Reduced in DCM46 Systolic percentage volume loss 13 ± 4 %std Mixed sex, CMR, healthy subjects, n=115 Less compressibility in HFrEF81 Apical displacement (AD) (ES – ED) (cm) [-0.1, 5.1]range 46 mixed sex, CMR, n=12, with positive meaning apex shifted towards the base during systole Predicts CRT outcomes in ischaemic cardiomyopathy82 Systolic global longitudinal strain −0.16 [−0.16, −0.16]IQR 47 four chamber slice, mixed sex, cDTI + Major predictor of LV dysfunction and HF, 21 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint (Ell) DENSE, n=30 greater accuracy than LVEF83,84 Systolic radial strain (Err) 0.27 [0.22, 0.29]IQR 47 Short axis slices, mixed sex, cDTI + DENSE, n=30 Associated with chronic HF85 Systolic circumferential strain (Ecc) -0.10 [-0.14, - 0.08]IQR 47 Short axis slices, mixed sex, cDTI + DENSE, n=30 Associated with chronic HF85 Biventricular electromechanics model calibration to ECG and pressure-volume biomarkers  Following model calibration, the simulated ECG showed good R wave progression from V1 to V6 and QRS duration that fell within the ranges shown in Table 1 (Figure 1A) as well as simulated left ventricular ejection fraction of 51% and peak systolic pressure of 14 kPa, with end diastolic and end systolic volumes of 110 mL and 50 mL (Figure 1B), and a peak filling rate of 310 mL/ms (Figure 1C), all falling within 95% interval of physiological biomarker ranges as listed in Table 1. The right ventricular end diastolic and end systolic volumes also fell within physiological ranges, though the right ventricular ejection fraction did not, as this was not a key target for calibration. The calibrated model overshot the peak pressure upstroke by 30 kPa/ms and peak ejection rate by 180 mL/ms (Figure 1D). However, the importance of matching to these two biomarkers is lower compared with other haemodynamic markers due to the relative paucity of reported data: n=17 for peak pressure upstroke and n=15 for peak ejection rate, compared with n=804 for ejection fraction and n=150 for peak systolic pressure (Table 3), It is also possible that the calibration could be improved by including some additional model parameters, such as those relating to stretch-rate dependent force generation, even though they did not show a strong effect on single cell active tension upstroke (Appendix Figure A1). These additional parameters might have a stronger effect on the upstroke at ventricular scale 22 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint than at single cell scale because the single cell simulations were performed under isometric conditions. The calibrated model parameters are listed in Figure 1E. Figure 1 Comparison of (A) simulated ECG, (B) pressure-volume, (C) flow rate, and (D) pressure upstroke biomarkers of the calibrated baseline electromechanical model with healthy population data ranges shown in green, except for (B) where the left ventricular ranges were shown in blue and the right ventricular ranges in orange. The calibrated model parameters were show in the table (E). 23 471 472 473 474 475 476 477 478 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint Validation by comparison to deformation and strain biomarkers, not used in calibration Simulation showed broad agreement with the trend and magnitude of in vivo strain measurements from DENSE+cDTI images47 for fibre strain, circumferential, radial, and longitudinal strain in mid-ventricular and four- chamber view slices. Simulated strain traces (n=5004 for short axis, n=9282 for long axis) showed higher variability than in vivo traces (n=30). Simulated fibre strain (Eff, Figure 2A) showed agreement in terms of transmural homogeneity when compared with in vivo measurements, and the magnitude of fibre shortening was similar to in vivo (compare with red line at -0.15 strain). Peak circumferential (Ecc), radial (Err), and longitudinal strains (Ell) in the simulations (Figure 2B) showed good agreement in magnitude with in vivo measurements (compare with red line at ±0.15 strain). The timing of simulated peak strains occurred earlier than that in vivo. However, this is partially because the model was not calibrated to the cardiac cycle timings of the single individual in the DENSE+cDTI dataset. 24 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint Figure 2 Comparison of simulated baseline left ventricular strains with non-invasive DENSE+cDTI MRI (in vivo) measurements. (A) Comparison of strain along the myofiber direction measured in the mid- short-axis of the ventricles. (B) Comparison of strains in the circumferential and radial directions measured in a mid-short-axis slice and longitudinal strains measured in a four-chamber long axis slice. In terms of deformations, the simulated systolic vs diastolic atrioventricular plane displacement of the calibrated biventricular (1.5 cm) showed good agreement with ranges reported in the literature (1.4 to 1.9 cm, Table 1). When compared with literature reports of wall thickness changes, simulations showed thickening in systole in agreement with literature. The simulated end diastolic wall thickness (0.5 cm) was lower than the report range [0.57, 1.38] cm (Table 1, n=4620), and the end systolic wall thickness (0.7 cm) was also lower than the report range of [1.07, 1.75] cm (Table 1, 25 494 495 496 497 498 499 500 501 502 503 504 505 506 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint 4620). The low wall thickness in both diastole and systole were consistent with the small heart size of the example used (96 g ventricular mass), and a larger and thicker heart would have greater wall thickening and fall better within the population ranges. One-at-a-time sensitivity analysis Figure 3 summarises how variability in single model parameters relate to simulated ECG (Figure 3A), pressure-volume (Figure 3B), displacement (Figure 3C), and strain (Figure 3D) biomarkers. Positive relationships between parameter and biomarker were shown in red and the negative were shown in blue. 26 507 508 509 510 511 512 513 514 515 516 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint Figure 3 The effect of variability in single model parameters in cellular ionic conductances (red), passive and active biomechanical parameters (green), and circulatory model parameters (yellow) on simulated biomarkers of the ECG (A), pressure-volume (B), deformations (C), and strains (D). Only relationships with p-value <0.05 were plotted. Positive correlations are shown in red, and negative correlations shown in blue. The thickness of each line indicates the normalised magnitude of effect and the transparency of each line indicates the r-value of the relationship. ECG biomarkers (Figure 3A) were mostly affected by variabilities in ionic conductances (red block), with some small effects from the mechanical parameters (green block). QRS effects were very minimal, since conduction velocities were not altered in the analysis. QRS duration altered by SERCA 27 517 518 519 520 521 522 523 524 525 526 527 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint (magnitude of change: 2.8 ms), GCaL (1 ms), GKr (1.8 ms), and GNaL (1.3 ms), while normalised QRS amplitude in lead V3 was very weakly affected by calcium sensitivity Cal50 (magnitude of change: 0.04), pericardial stiffness kepi (0.01), and the passive stiffness parameter af (0.02) (Appendix Figure A1.A). The ST and T wave segments were much more sensitive to model parameters. The QT interval was strongly affected by GKr (magnitude of change: 173 ms), GNaL (92 ms), GNaK (72 ms), GCaL (69 ms), and SERCA (49 ms), with weak effects from calcium sensitivity (Cal50) (1.7 ms). Normalised T wave amplitude was affected by GKr (magnitude of change: 0.1), GNaK (0.06), GNaL (0.06), and SERCA (0.04), GCaL (0.03), with very minor (<0.01) amplitude changes in select precordial leads for Tref (lead V4), Cal50 (lead V4), pericardial stiffness (lead V3) and Kct (lead V2) (Appendix Figure A1.B). Pressure volume biomarkers (Figure 3B) were mostly affected by the mechanical (green block) and circulatory parameters (yellow block), alongside ionic currents (red block) that affect the calcium signaling system (GCaL and SERCA). Appendix Figure A2 illustrates in detail the parameter effects on the pressure-volume loops. The ejection fraction was predominantly affected by cross-bridge power-stroke rate (kws) (magnitude of change in ejection fraction: 32 %), compressibility (Kct) (16 %), GCaL (15 %), peak active tension (Tref) (12 %), SERCA activity (10 %). There were also some effects on LVEF from GNaL (9%), arterial resistance (6 %), calcium sensitivity (Cal50) (8 %), and very weak effects from pericardial stiffness (4 %), passive mechanical parameters a (3 %), af (2 %), as (4 %), and GNaK (2 %), and GKr (2 %). The peak systolic pressure was affected by the same parameters as the ejection fraction, except for GNaK, GNaL and GKr, and with the addition of arterial compliance (magnitude change: 1.1 kPa) and ejection pressure threshold (1.9 kPa). The peak rate of rise of ventricular pressure (dPdtmax) was strongly influenced by only the cross-bridge power-stroke rate (kws) 28 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint (magnitude of change: 1 kPa/s), with weak effects from calcium sensitivity (Cal50) (0.6 kPa/s) (Appendix Figure A3.A). The peak ejection flow rate (PER) was influenced by Cal50, Tref, k_ws, while the peak filling rate (PFR) was influenced by a larger group of parameters including Tref, Cal50, Kct, GCaL, SERCA, and the bulk parameter controlling the diastolic filling rate (Appendix Figure A3.B). Mechanical displacement biomarkers (Figure 3C) were predominantly affected by active mechanics (green block) and calcium system conductances (red block), with very minor effects from passive mechanical parameters. Systolic AVPD (Appendix Figure A4.A) was strongly influenced by Cal50 (magnitude of effect: 0.54 cm), GCaL (0.36 cm), Tref (0.33 cm), Kct (0.41 cm), SERCA (0.31 cm), with weaker effect from kws (0.15 cm), arterial resistance (0.09 cm), and pericardial stiffness (0.08 cm). Systolic wall thickness was predominantly affected by the same parameters as systolic AVPD, except for Kct, which had only a weak effect. Systolic percentage volume change (Appendix Figure A4.C) was strongly affected by the compressibility parameter (Kct) (magnitude of change: 12 %), as was expected, but also strongly affected by GCaL (9 %), Tref (8 %), SERCA (6 %), and kws (3 %). An increase in SERCA and Cal50 shifted the timing of peak volume reduction to earlier during systole. Simulated strain biomarkers (Figure 3D) were predominantly affected by passive mechanical parameters (green block) and circulatory parameters (yellow block). The influence of parameters on the radial, circumferential and longitudinal strain patterns (Appendix Figure A5) followed broadly that of the AVPD and wall thickness. Of note was that at high values of the ejection pressure, the mid-ventricular circumference expands rather than contracts during systole and fails to return to the reference condition even after relaxation, pointing to failure of proper pumping function (Appendix Figure A5.A). 29 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint Multi-scale mechanisms underpinning ECG and LVEF relationship Simulation results indicated that the link between ECG biomarkers and LVEF was chiefly underpinned by GCaL and SERCA, which had strong effects on both T wave biomarkers and the pressure-volume loop (Figure 3). Mechanical parameters Tref, calcium sensitivity (Cal50), compressibility (Kct), and fibre stiffness (af) had much stronger effects on LVEF than on ECG signatures. On the other hand, ionic conductance parameters GNaL, GKr, GNaK had much stronger effects on the T wave than on LVEF. Figure 4 illustrates the multi-scale mechanisms of GCaL’s effect on both LVEF and ECG. A four- fold increase in GCaL caused an eight-fold increase in cellular active tension peak and a 200 ms prolongation of active tension duration (Figure 4A), which resulted in a 15 mL decrease in end systolic volume and 2.5 kPa higher peak systolic pressure at the ventricular scale (Figure 4C). GCaL’s dramatic effect on end systolic volume was facilitated by 10 % higher systolic myocardial volume compression, 4.5 % higher systolic longitudinal contraction, 3.5 % higher systolic circumferential contraction, and 0.4 cm lower (towards apex) systolic position of the atrioventricular plane (Figure 4B). The increase in GCaL caused an increase of 60 ms in cellular action potential duration (Figure 4A), which prolonged the global repolarisation time (Figure 4D) and led to the prolongation of the QT interval (Figure 4C). GCaL did not have a significant effect on the activation pattern and conduction velocity in our simulations (Figure 4D) or on the QRS complex of the ECG (not shown). 30 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint Figure 4 Multi-scale effect of GCaL on active tension, action potential duration (A), ventricular deformation and strains (B), the pressure-volume loop (C) and precordial ECG leads (D). ECG characteristics were explained by the activation and repolarization maps (E). Figure 5 illustrates how a four-fold increase in SERCA activity caused a 12% decrease in LVEF, with non-monotonic effects on the QT interval. The increase in SERCA conductance increased diastolic residual active tension (Figure 5A), which was sufficient to cause 3 mL reduction in end diastolic volume (Figure 5C). Even though increasing SERCA increased peak active 31 606 607 608 609 610 611 612 613 614 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint tension at the cellular scale by 9 kPa (Figure 5A), it reduced peak systolic pressure and LVEF at the ventricular scale (Figure 5C). This was because increasing SERCA hastened the arrival of peak active tension by 50 ms and reduced its duration by 100 ms (Figure 5A), which meant that the mechanical contractions were not given enough time to developed, resulting in earlier and weaker systolic contractions (Figure 5B). On the electrophysiological side, while SERCA did not elicit strong APD changes at the single cell simulation, when combined with non-isometric conditions in ventricular simulations, it caused action potential prolongation at values higher than 1.5-fold and resulted in prolonged repolarization (Figure 5E). 32 615 616 617 618 619 620 621 622 623 624 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint Figure 5 Multi-scale effect of SERCA conductance on active tension, calcium transient, action potential duration (A), ventricular deformation and strains (B), the pressure-volume loop (C) and precordial ECG leads (D). ECG characteristics were explained by the activation and repolarization maps (E).

In this study we presented the calibration, validation and sensitivity analysis of human healthy ventricular electromechanical modelling and simulation, 33 625 626 627 628 629 630 631 632 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint following the ASME V&V40-based assessment guidelines. The first step was compiling biomarkers values from multi-modal data characterizing pressure- volume, ECG, displacement, and strain behavior of human healthy ventricles, and separated the data for calibration and validation. The calibration was informed by unravelling the interlinking relationships between simulated biomarkers and model parameters, especially highlighting the plethora of model parameters that affect the ejection fraction. We demonstrated multi- scale mechanistic explanations of the relationship between LVEF and ECG underpinned by variability in L-type calcium channel conductance and SERCA activity. Previous examples of applying the ASME V&V40 framework for cardiac model credibility assessment have focused primarily on evaluating computational models of medical devices such as the left ventricular assist device18 and artificial heart valves19, where model validation was performed by comparing to experimental recordings specifically designed for this purpose. These studies, as well as other examples of model validation without explicit

to the ASME Standard, commonly have narrow focuses on specific diseases and/or therapies, and the biomarkers used for model evaluation were similarly limited in scope. In the case of disease models, calibrations were commonly performed at the cellular or tissue scale and validation was performed at the ventricular scale through comparisons with known ECG or ejection fraction phenotypes9,12. While these studies have been valuable for providing model credibility in their specific disease/therapeutic contexts of use, they have not been designed to give credibility to the underlying computational electromechanics framework. In this study, we instead focused on building a comprehensive calibration and validation strategy for baseline healthy biventricular electromechanics. Through considering biomarkers at multiple scales and across both electrophysiology and mechanics, we hoped to establish a firm foundation of credibility for computational electromechanics that can be refined in future studies. 34 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint We showed in this study that literature values for model parameters do not automatically provide good baseline simulations. We proposed a sequential calibration strategy based on knowledge of model sensitivities, as detailed in the methods. This approach can be adapted for more sophisticated numerical techniques involving the use of emulators and Bayesian statistics to enable faster and more comprehensive explorations of the parameter space24,26,86. Our sensitivity analysis results showed that in the simulated ECGs, the T wave was far more sensitive to electrophysiological parameters than to mechanical ones, within the ranges of uncertainty expected from literature reports of each parameter. In our simulations, the ionic conductances GNaK and GNaL primarily affected the T wave through altering the action potential duration (Appendix Figure A1) while having minimal effect on mechanical deformation or strain. GCaL and SERCA strongly affected the repolarization pattern and deformation and strain patterns during systole (Figures 4 and 5). However, other parameters that had a strong effect on deformation and strain, such as Tref, Cal50, pericardial stiffness and Kct had only a minor effect on the T wave (Appendix Figure A2). Previous studies on this question focused on comparing either end diastolic versus end systolic geometry8 or a static versus dynamic geometry87 when simulating the T wave. These simulations involved a much larger perturbation in deformation than relevant to physiological situations and showed a larger effect on the T wave amplitude than our simulations. Within the context of physiological systolic deformations, however, our results showed that deformation uncertainties had only minor effects on T wave amplitude. Our simulations showed only minor changes to QRS amplitudes in response to variation in those parameters that influenced the end diastolic geometry: calcium sensitivity, through altering diastolic residual active tension, pericardial stiffness, through restricting diastolic inflation, and the passive mechanical parameters a and af, through altering bulk stiffness and stiffness along the myofibre direction. However, it is possible that the magnitude of changes to the QRS was underestimated in our simulations, because the local activation times on the endocardial surface in our simulations were fixed. This meant that our simulations did not 35 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint explore the effect of variations in end diastolic geometry on the conduction velocity of the fast endocardial activation layer or on Purkinje conductivity. It should also be noted that other parameters that affect the activation pattern, such as GNa and conduction velocities, were not included in this analysis. The fact that the initialised literature values of model parameters failed to achieve LVEF above 50 % pointed to limitations in using ex vivo tissue measurements to represent in vivo function. In our simulations, we saw that the LVEF was strongly sensitive to changes in the incompressibility of the tissue (Kct), such that an increase in compressibility of the myocardial tissue helped to increase LVEF. The systolic volume has been reported to change up to 13%81, pointing to limitations of assumptions of incompressibility in the modelling of the myocardial tissue. Additionally, our model did not achieve a high amount of wall thickening in validation, which meant that the high compressibility required in our model to achieve LVEF could be compensating for a lack of sufficient wall thickening, in addition to anatomical effects. Previous experimental and simulations studies have shown how wall thickening is related to sliding of sheetlets88,89. However, in our simulations we did not see a significant effect of the sheer stiffness parameter afs on wall thickness or LVEF. One possible avenue of exploration would be the effect of sheet and fibre orientations on the thickening effect, as explored in a previous simulation study89. Displacement and strain biomarkers (Figure 2D) were far more sensitive to calcium handling dynamics, cross-bridge cycling rate, and contractility than to passive stiffness parameters, which indicates they would be better indicators of systolic rather than diastolic dysfunctions in HF. The sensitivity of strains and displacements to the pericardial stiffness parameter was unsurprising due to the association of reduced strains in diseases affecting the pericardial sack90. The sensitivity of longitudinal and radial strain to the incompressibility of the myocardium (Kct) mirrors the sensitivity of the LVEF 36 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint to that parameter, which was in accordance with the fact that those two strains were surrogate markers of LVEF and show better predictive power83,84.

In this study, we show the importance of applying vigorous VVUQ evaluations of ventricular electromechanics for achieving physiological simulations. We set the basis for a strategy for calibrating and validating baseline electromechanical modelling and simulation frameworks for cardiac Digital Twins. We compiled a comprehensive list of biomarkers for evaluating healthy electromechanical function, and grouped the dataset into non- overlapping calibration and validation sets. We provide evidence of credibility through calibration to haemodynamic and ECG biomarkers and validation by comparison to strain and deformation biomarkers and uncertainty quantification. Furthermore, our analyses highlighted the interplay between cellular, tissue, and haemodynamic parameters on the LVEF and provided multi-scale explanations of its link with ECG biomarkers. Taken together, the study paves the way towards credible electromechanical cardiac Digital Twins.

This work was funded in whole, or in part, by the Wellcome Trust (214290/Z/18/Z). For the purpose of Open Access, the author has applied a CC BY public copyright licence to any Author Accepted Manuscript version arising from this submission. This work was supported by a Wellcome Trust Fellowship in Basic Biomedical Sciences to B.R. (214290/Z/18/Z), the Personalised In-Silico Cardiology (PIC) project, the CompBioMed 1 and 2 Centre of Excellence in Computational Biomedicine (European Commission Horizon 2020 research and innovation programme, grant agreements No. 675451 and No. 823712), the Oxford BHF 37 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint Centre of Research Excellence (RE/13/1/30181), PRACE-ICEI funding projects icp005, icp013, icp019.

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Imaging 22, e14 (2021). 50 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint Appendix 1. Pressure volume calibration strategy design The goal of the calibration of the initialised set of parameters was to increase LVEF, increase systolic pressure, increase peak filling rate, but decrease peak ejection rate and lower dP/dtmax. The LVEF and peak systolic pressure had the highest degree of importance for calibration, since they were implicated in a variety of diseases and was well established. The filling rates and dPdtmax took a secondary role, since the data came from much smaller sample sizes, and the filling rates were measured using echocardiography techniques, which were not as reliable as volume measurements in CMR (Table 1). From the uncertainty quantification, we saw that a handful of parameters can increase both LVEF and peak systolic pressure simultaneously: Tref, kws, GCaL, SERCA, Cal50, Kct (Figure 3). However, Tref and kws effects saturate at high values, large changes in SERCA and GCaL can become arrhythmic substrates, Cal50 has a non-monotonic effect on LVEF due to its effect on the diastolic function, and dramatic reductions in Kct brings unrealistic amounts of systolic volume change. A combination of changes in these parameters was needed to dramatically improve LVEF and peak systolic pressure, and in practice, was insufficient by themselves. Decreasing arterial resistance was also needed to help increase LVEF. However, this comes at the cost of reducing peak systolic pressure, which needed to be counterbalanced by increasing the ejection pressure threshold. An increase in ejection pressure increased time spent in isovolumic contraction and isometric force development, and thereby increased the peak systolic pressure. An additional challenge was that there was not a single parameter in our analysis that could decrease peak ejection flow rate (Tref, kws, Kct) and dPdtmax (kws) without also decreasing LVEF at the same time. This meant 51 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint that we needed to achieve higher than healthy LVEF first. With all this in mind, the calibration strategy was as detailed in the Methods section. 2. Cellular global sensitivity analysis Figure A1: Global sensitivity analysis (C) using cellular model of ventricular electromechanics show the effect of the top five model parameters on active tension (A) and action potential duration (A and B) biomarkers. 52 1062 1063 1064 1065 1066 1067 1068 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint 3. Additional ventricular sensitivity analysis results Figure A2 Uncertainties in simulated pressure volume dynamics were influenced by uncertainties in mechanical (green), circulatory (yellow) and ionic conductance (red) parameters of the model. 53 1069 1070 1071 1072 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint Figure A3: Of the parameters included in the analysis, the QRS section of the ECG showed minor sensitivity to uncertainty in mechanical parameters (green labels) (A) while the ST and T wave segments of the ECG were strongly sensitivity to uncertainties in ionic conductances (red labels), and only showed minor sensitivity to some mechanical parameters (green labels) (B). 54 1073 1074 1075 1076 1077 1078 1079 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint Figure A4: Pressure (A) and volume (B) transients in response to parameter uncertainties in mechanical properties(green), circulation (yellow), ionic conductances (red). 55 1080 1081 1082 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint Figure A5: Key aspects of the ventricular deformation, including atrioventricular plane displacement, wall thickness changes, and myocardium volume changes were affected predominantly by mechanical parameters (green) and ionic conductance parameters (red), with weaker effects from circulatory parameters (yellow). 1083 1084 1085 1086 2 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint Figure A6: Uncertainty in simulated strain transients were influenced by uncertainties in mechanical (green), circulatory (yellow), and ionic conductance (red) parameters. 57 1087 1088 1089 1090 1091 .CC-BY-NC 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.06.638897doi: bioRxiv preprint