In vivo palpation of anisotropic human brain tissue using MRI

In vivo palpation of anisotropic human brain tissue using MRI | bioRxiv /* */ /* */ <!-- <!-- /*! * yepnope1.5.4 * (c) WTFPL, GPLv2 */ (function(a,b,c){function d(a){return"[object Function]"==o.call(a)}function e(a){return"string"==typeof a}function f(){}function g(a){return!a||"loaded"==a||"complete"==a||"uninitialized"==a}function h(){var a=p.shift();q=1,a?a.t?m(function(){("c"==a.t?B.injectCss:B.injectJs)(a.s,0,a.a,a.x,a.e,1)},0):(a(),h()):q=0}function i(a,c,d,e,f,i,j){function k(b){if(!o&&g(l.readyState)&&(u.r=o=1,!q&&h(),l.onload=l.onreadystatechange=null,b)){"img"!=a&&m(function(){t.removeChild(l)},50);for(var d in y[c])y[c].hasOwnProperty(d)&&y[c][d].onload()}}var j=j||B.errorTimeout,l=b.createElement(a),o=0,r=0,u={t:d,s:c,e:f,a:i,x:j};1===y[c]&&(r=1,y[c]=[]),"object"==a?l.data=c:(l.src=c,l.type=a),l.width=l.height="0",l.onerror=l.onload=l.onreadystatechange=function(){k.call(this,r)},p.splice(e,0,u),"img"!=a&&(r||2===y[c]?(t.insertBefore(l,s?null:n),m(k,j)):y[c].push(l))}function j(a,b,c,d,f){return q=0,b=b||"j",e(a)?i("c"==b?v:u,a,b,this.i++,c,d,f):(p.splice(this.i++,0,a),1==p.length&&h()),this}function k(){var a=B;return a.loader={load:j,i:0},a}var l=b.documentElement,m=a.setTimeout,n=b.getElementsByTagName("script")[0],o={}.toString,p=[],q=0,r="MozAppearance"in l.style,s=r&&!!b.createRange().compareNode,t=s?l:n.parentNode,l=a.opera&&"[object Opera]"==o.call(a.opera),l=!!b.attachEvent&&!l,u=r?"object":l?"script":"img",v=l?"script":u,w=Array.isArray||function(a){return"[object Array]"==o.call(a)},x=[],y={},z={timeout:function(a,b){return b.length&&(a.timeout=b[0]),a}},A,B;B=function(a){function b(a){var a=a.split("!"),b=x.length,c=a.pop(),d=a.length,c={url:c,origUrl:c,prefixes:a},e,f,g;for(f=0;f<d;f++)g=a[f].split("="),(e=z[g.shift()])&&(c=e(c,g));for(f=0;f<b;f++)c=x[f](c);return c}function g(a,e,f,g,h){var i=b(a),j=i.autoCallback;i.url.split(".").pop().split("?").shift(),i.bypass||(e&&(e=d(e)?e:e[a]||e[g]||e[a.split("/").pop().split("?")[0]]),i.instead?i.instead(a,e,f,g,h):(y[i.url]?i.noexec=!0:y[i.url]=1,f.load(i.url,i.forceCSS||!i.forceJS&&"css"==i.url.split(".").pop().split("?").shift()?"c":c,i.noexec,i.attrs,i.timeout),(d(e)||d(j))&&f.load(function(){k(),e&&e(i.origUrl,h,g),j&&j(i.origUrl,h,g),y[i.url]=2})))}function h(a,b){function c(a,c){if(a){if(e(a))c||(j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}),g(a,j,b,0,h);else if(Object(a)===a)for(n in m=function(){var b=0,c;for(c in a)a.hasOwnProperty(c)&&b++;return b}(),a)a.hasOwnProperty(n)&&(!c&&!--m&&(d(j)?j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}:j[n]=function(a){return function(){var b=[].slice.call(arguments);a&&a.apply(this,b),l()}}(k[n])),g(a[n],j,b,n,h))}else!c&&l()}var h=!!a.test,i=a.load||a.both,j=a.callback||f,k=j,l=a.complete||f,m,n;c(h?a.yep:a.nope,!!i),i&&c(i)}var i,j,l=this.yepnope.loader;if(e(a))g(a,0,l,0);else if(w(a))for(i=0;i (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];var j=d.createElement(s);var dl=l!='dataLayer'?'&l='+l:'';j.src='//www.googletagmanager.com/gtm.js?id='+i+dl;j.type='text/javascript';j.async=true;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-M677548'); Skip to main content Home About Submit ALERTS / RSS Search for this keyword Advanced Search New Results In vivo palpation of anisotropic human brain tissue using MRI Kulam Najmudeen Magdoom , View ORCID Profile Alexandru V. Avram , Joelle E. Sarlls , Peter J. Basser doi: https://doi.org/10.1101/2025.06.20.660588 Kulam Najmudeen Magdoom 1 Eunice Kennedy Shriver National Institute of Child Health and Human Development (NICHD), National Institutes of Health , Bethesda, MD, USA 2 Military Traumatic Brain Injury Initiative (MTBI2) , Bethesda, MD, USA 3 Uniformed Services University of the Health Sciences (USUHS) , Bethesda, MD, USA 4 The Henry M. Jackson Foundation for the Advancement of Military Medicine (HJF) Inc. , Bethesda, MD, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site Alexandru V. Avram 1 Eunice Kennedy Shriver National Institute of Child Health and Human Development (NICHD), National Institutes of Health , Bethesda, MD, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Alexandru V. Avram Joelle E. Sarlls 5 National Institute of Neurological Disorders and Stroke (NINDS), National Institutes of Health , Bethesda, MD, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site Peter J. Basser 1 Eunice Kennedy Shriver National Institute of Child Health and Human Development (NICHD), National Institutes of Health , Bethesda, MD, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site For correspondence: pjbasser{at}helix.nih.gov Abstract Full Text Info/History Metrics Supplementary material Preview PDF Abstract The mechanical stiffness of brain parenchyma varies across physiological states and pathophysiological conditions, such as during normal and abnormal development, in degenerative diseases and disorders, like Alzheimer’s disease and traumatic brain injury (TBI), neuronal activation, and sleep via the glymphatic brain waste clearance mechanism. Despite its biological and clinical importance, relatively few techniques exist to measure and map mechanical properties of brain tissue non-invasively and in vivo . MR elastography (MRE) is an established method that has been widely used to estimate tissue stiffness in the liver by applying mechanical waves using an external tamper and measuring their resulting deformations. However, applying MRE in the brain is more challenging due to the skull and cerebrospinal fluid (CSF), which impede mechanical wave propagation, and tissue mechanical anisotropy, which requires a 4 th -order tensor description. In this study, we propose using the intrinsic deformation of brain tissue caused by periodic cardiac pulsation to measure the 4 th -order stiffness tensor throughout the brain while simultaneously estimating the 2 nd -order diffusion tensor in each voxel throughout the cardiac cycle, which we use as a priori information in the reconstruction of the stiffness tensor. While the DTI-derived mean diffusivity (MD) appears uniform throughout brain parenchyma, stiffness maps obtained at about 1 Hz (i.e., at the fundamental cardiac frequency) show contrast within gray matter, and within white matter pathways such as along the corpus callosum, internal capsule, corona radiata, etc. Generally, stiffness differences at internal tissue boundaries are expected to lead to local stress concentration, which may predispose tissues to damage in TBI. Therefore, our novel tamperless MRE method has the potential to not only identify such interfaces, but assess changes in tissue stiffness there that might occur following injury. Introduction Understanding structure-function relationships in the human brain remains a desideratum with profound scientific implications and wide-ranging potential clinical applications. While it is currently not feasible to image whole brain structures in vivo at micro/nanometer length and nanosecond time scales, it is possible to measure and map various physical properties, such as magnetic susceptibility, water diffusivity, viscosity, bulk and shear moduli, hydraulic permeability, electrical conductivity, etc., at a larger continuum or mesoscopic length scale using Magnetic Resonance Imaging (MRI) methods. These physical parameters are valuable as potential quantitative imaging biomarkers as they are intrinsic to the tissue, and appear in equations governing the transport of fundamental physical quantities, such as magnetization, mass, momentum, energy, and charge, which underlie and constrain basic physiological phenomena and processes. Two such physical quantities are the shear modulus, which quantifies the resistance of a material to shear deformations, affecting the transport of momentum; and the diffusivity which quantifies how thermally induced random tissue water motions result in molecular mixing. The shear modulus has been reported to vary by orders of magnitude among tissue types compared to other properties such as magnetization relaxation rates and bulk moduli [ 1 , 2 ]. Water diffusivity on the other hand does not have a large dynamic range in tissue but is sensitive to tissue water content. The diffusivity does not directly contribute to the shear modulus (as Newtonian fluids like water cannot support static shear stresses) thus providing complementary information about the tissue milieu. However, both properties are sensitive to the structural alignments of tissue components, such as axons, neurofilaments, and microtubules, which are ubiquitous in the brain [ 3 , 4 ], and are expected to lead to orientational biases in transport processes. Based upon effective medium theory as discussed in [ 5 ] one expects fundamental connections between the anisotropic stiffness and anisotropic diffusion properties in tissue. In particular, effective medium theory would predict that the stiffness and diffusion tensors share the same principal axes, but their corresponding principal values arise from different physical processes: diffusivity - from transport of momentum or mixing via thermal collisions, and shear modulus - from the transport of momentum via adjacent mechanical linkages [ 5 ]. Partial differential equations describing these transport processes often have a similar form, but possess different parameter values with different units and often different internal boundary conditions. Nevertheless, the microstructure of the medium helps dictate similarities in their respective anisotropic behaviors. These transport parameters are sensitive to features of material structure, composition, and organization in different ways. Moreover, these properties may have very different time dependencies. The shear modulus in the brain changes by orders of magnitude for time scales between 1 ms and 1 sec [ 6 , 7 ] while diffusivity changes only by 20% from 0.5 ms to 10 ms [ 8 ] and remains relatively constant thereafter [ 9 ]. Because of the complementary information they provide about brain structure, architecture, and organization, it is prudent, if possible, to measure diffusivity and shear modulus simultaneously in the brain, and examine their respective features, as we do here. Diffusion tensor imaging (DTI) [ 5 , 10 ] and MR elastography (MRE) [ 11 ] are imaging modalities which measure and map the the diffusion tensor and tissue shear modulus, respectively, throughout an imaging volume. Both have been under continuous development since the early to mid-1990s. DTI has been extensively used in the brain to identify white matter pathways [ 12 , 13 ], study brain development [ 14 ] and diagnose a host of diseases, such as stroke [ 15 ] and cancers [ 16 ] via the DTI-derived mean apparent diffusion coefficient (mADC) or mean diffusivity (MD) [ 17 ]. Meanwhile, MRE has been primarily used to assess liver fibrosis [ 18 ] with limited applications to characterize brain tissue due to several factors. MRE, as originally proposed, measures displacements resulting from shear waves with a prescribed frequency applied to a sample using an external actuator or tamper. These displacements are then used to estimate the shear modulus based on a model that relates the material’s strain and stress [ 11 ]. Accurate estimate of the shear modulus using MRE requires sufficiently large deformations throughout the imaging volume to be detectable via MRI. The high acoustic attenuation of the skull and acoustic impedance mismatch occurring at various skull-cerebrospinal fluid (CSF)-brain parenchyma interfaces can lead to significant absorption and reflection and limit the transmission of external mechanical waves into the brain parenchyma. The large amplitude of external vibrations required to compensate for this wave energy loss may also potentially preclude scanning certain patient cohorts, such as those diagnosed with one of the various types of traumatic brain injury (TBI). The tamper can also be expensive and requires special training to operate, which further limits its application. Water diffusion and the mechanical properties in the human brain tissue are anisotropic [ 19 , 20 ]. In the linear elastic regime, stiffness is better described by a 4 th -order elasticity tensor instead of a scalar shear modulus [ 21 ]. This is largely ignored in many brain MRE studies owing to the difficulty of measuring the entire 4 th -order tensor [ 22 , 23 , 24 , 25 ]. This omission, however, introduces additional variability in the measured tissue mechanical properties as they become dependent on the placement of the external tamper with respect to the brain position and orientation across subjects [ 25 , 26 ]. Several studies have attempted to quantify mechanical anisotropy with MRE by solving a highly ill-posed problem. The full elasticity tensor has as many as 21 unknown elements but only 3 equations governing the material displacement are typically available. A common approach is to assume additional underlying symmetries, such as transverse isotropy of the material in coherent fibrous regions, which reduces the number of unknowns to five and this can be further reduced to three by assuming tissue incompressibility [ 27 ]. This simplification, however, requires a priori knowledge of the symmetry axis and hence may be limited to skeletal muscle tissues or phantoms with known principal axes [ 28 , 29 , 30 ]. Qin et al. had used principal directions from a separate DTI scan to estimate the transverse isotropic stiffness tensor in phantoms with a single fiber direction but the performance in heterogeneous brain parenchyma has not been established [ 31 ]. Recently, Smith et al. presented a non-linear reconstruction approach on live brain tissue with a tamper vibrated along two different orientations and solved for material parameters using a computation time-intensive finite element analysis (FEA) framework with principal directions obtained from separate DTI scans [ 32 ]. The most complex stiffness tensor estimated in the brain to date was obtained using waveguide elastography in which waves traveling along all three principal axes of the diffusion tensor were analyzed in the principal frame to estimate stiffness tensors with orthotropic symmetry (i.e., having 9 independent elements) [ 4 ]. The approach is nonetheless computationally intensive and was demonstrated using a tamper. Given the complexity and experimental requirements for conventional brain MRE, a more pragmatic and practical approaches would be welcomed. Here we perform brain MRE by employing the intrinsic or endogenous deformation of the brain tissue caused by the subject’s own cardiac pulsations, overcoming the aforementioned drawbacks of MRE using an external tamper. Moreover, the magnitude images that are sensitive to molecular diffusion, provide a means to concurrently estimate the fiber orientation within a voxel, which can inform the estimate of the stiffness tensor. The tissue deformation induced by the pressure pulse-waves carried by the ascending aorta (i.e., Monroe-Kellie doctrine), and the very low frequency of excitation (approximately 1 Hz) results in less wave attenuation thus mechanically deforming the entire brain. A hurdle to overcome, however, is that the resulting brain tissue deformation is still small (i.e., on the order of several microns within a 2 mm voxel) for conventional imaging acquisitions, which makes it challenging to measure [ 33 ] but useful for MRE as the stress-strain relationship can be assumed to be linear in this infinitesimal strain regime, simplifying elasticity reconstruction and mapping. It should be noted that there have been several studies describing MR imaging of heart-driven brain displacements [ 33 , 34 , 35 ] often using stimulated echo displacement encoding (DENSE) [ 36 , 37 ], which can be difficult to implement and is not SNR efficient (i.e., there is a 50% SNR loss using stimulated echo as compared to spin echo). Weaver et al., and Ingeberg et al., inverted these displacements into shear moduli using a computationally intensive FEA framework with orders of magnitude differences in their reported estimated stiffness values (8 kPa vs 200 Pa, respectively) [ 24 , 38 ]. Herthum et al. based on the wave speed measured across a brain slice, estimated stiffness values of tens of Pa [ 7 ]. Given the large inconsistency among these experiments and the importance of measuring mechanical properties of brain tissue, there is a need to develop a robust and accurate method to measure shear modulus throughout the brain and across subjects using only the intrinsic pulsations produced by the beating heart. In this study, we introduce a new experimental design to reliably acquire whole-brain MRE and DTI data simultaneously throughout the cardiac cycle, by using standard pulsed gradient spin echo (PGSE) MRI measurements. We use a novel outlier rejection strategy to overcome spurious phase errors and build up consistent complex-valued 3D motion encoded MRI data volumes across the phases of the cardiac cycle. We estimate the diffusion tensor from the magnitude of the MRI signal and compare its features with the measured displacement vector fields. We concomitantly reconstruct the elasticity tensor in the whole brain from the measured displacement field (obtained from the phase signal), assuming transverse isotropy in white matter, where the symmetry axis of the elasticity tensor is generally given by the eigenvector associated with the largest eigenvalue of the estimated diffusion tensor, and using the “cross property” concept [ 5 ]. Finally, we use the wellestablished Helmholtz decomposition into scalar and vector potentials to determine the elasticity tensor. Materials and Methods MRI acquisition and processing The tissue displacement in this study is measured at multiple phases within the cardiac cycle using the standard pulsed gradient spin-echo echo planar imaging (PGSE-EPI). To improve sensitivity to slow coherent motion induced by cardiac pulsation while preserving adequate diffusion sensitivity for DTI reconstruction, narrow gradient pulses with long diffusion times were chosen [ 39 ]. MRI data were acquired in five healthy volunteers who provided informed written consent to participate in the NINDS IRB approved research protocol ( NCT00004577 ), on a 3T scanner (Prisma, Siemens Healthineers) with 80 mT/m peak gradient strength and a 200 T/m/s slew rate using 20-channel receive RF coil. Whole-brain displacement-encoded MRI data were acquired along the six directions of the icosahedron [ 11 ] at b = 350 s/ mm 2 and v enc = 0.4 mm/s along with a b = 0 s/ mm 2 scan using the following parameters: δ/ Δ = 7/48 ms, field of view = 210 × 210 × 120 mm, GRAPPA acceleration factor = 2, TR/TE = 5,600/71 ms, NEX = 144, and a 2 mm isotropic spatial resolution. The pulse-oximeter signal and MRI triggers were simultaneously recorded using a Biopac System (Biopac, Goleta, CA, USA) for retrospective gating. The image phase was unwrapped for each slice, gradient direction, and time point using a Fourier-based method [ 40 ]. Linear phase errors arising from eddy currents, rigid body motion, etc., were removed using linear regression performed on a slice-by-slice basis. The B 0 -induced geometric distortion was corrected using FSL’s Topup software [ 41 , 42 ]. The displacement-encoded images were then partitioned into ten different bins each approximately 100 ms long covering the entire cardiac cycle using the measured pulse-oximeter (pSO 2 ) signal to indicate phase in the cardiac cycle. Outlier rejection and displacement estimation MRE reconstruction involves computing both spatial and temporal derivatives, which require smoothly varying 4D displacement fields (i.e., three dimensions in space and one dimension in time or frequency). The displacement field is however not measured instantaneously since it requires data from multiple directions which are acquired over multiple scan repetitions. Given the high scan sensitivity to bulk motion and the multitude of factors affecting the signal phase, complex phase errors are introduced between these acquisitions in live brain imaging data, especially along the slice-encoding direction in EPI. These errors will not be corrected by linear regression and can arise from brain sloshing accompanying unpredictable head motion [ 33 ], phase errors from heating of passive shims [ 43 ], etc. While previous work by Barnhill, et al. addressed this issue by using dejittering algorithms and wavelet transforms to remove these errors [ 44 ], we employ a simpler and more robust method to reject the inconsistent phase measurements from the multiple repetitions of data acquired in each bin for a given direction. Assuming a non-zero signal magnitude, the voxelwise phase distribution follows a Gaussian profile. Therefore, for each encoding direction, we exclude from MRE and DTI estimation voxels whose phase values fall outside one standard deviation from the mean phase. Given the linear relationship between phase and displacement, the consistent phase images from all directions are then Fourier transformed in time and converted to harmonic displacement vectors using linear regression [ 45 ]. The measured displacement field is spatially smoothed using a local 3D Gaussian kernel prior to calculating spatial derivatives required for the stiffness estimation. Diffusion tensor estimation The magnitude signal encodes information about the diffusion of water molecules. We acquire a sufficient number of DWI measurements to simultaneously estimate the diffusion tensor field within each cardiac bin [ 5 , 10 ]. If we assume the cross property concept holds, the principal directions of the diffusion tensor should be aligned with those of the elasticity tensor in anisotropic tissue. The DTI maps also serve as an anatomical reference with which to interpret the displacement and shear modulus maps by helping us assess the deformation in different tissue types, as defined by their diffusion properties, and study possible effects of local displacements on the measured diffusion tensor parameters themselves. The outlier rejection approach described above for the phase also corrects the magnitude signal. The consistent magnitude signals were averaged over each bin and direction, and denoised using Marchenko-Pastur principal component analysis (MP-PCA) [ 46 ] implemented in the MRTrix software environment [ 47 ] to estimate the time-varying diffusion tensor field by solving the following optimization problem in each voxel, where M + is the manifold of symmetric positive definite matrices, “:” is the tensor dot product, and S ( t, B) is the magnitude signal measured at time, t , in the cardiac cycle using the diffusion-weighted b-tensor, B, and D( t ) is the diffusion tensor as a function of time in the cardiac cycle. A positive definiteness constraint is applied on the diffusion tensor, and positivity constraint was applied on S 0 to ensure physicality. The above problem was solved separately at each time point using COBYLA, a non-linear optimization routine [ 48 ], implemented in the Scipy software environment [ 49 ]. The various features of the diffusion tensor such as fractional anisotropy (FA), MD, direction-encoded color (DEC) maps were all calculated from the estimated diffusion tensor in each cardiac phase [ 50 , 51 ]. Helmholtz decomposition of displacement field The measured 3D displacement field is expressed in terms of its longitudinal ( u L ) and transverse ( u T ) components using the Helmholtz decomposition to separate the compression and shear modulus contributions, respectively [ 52 ]. These components are expressed using the scalar (Φ) and solenoidal vector potential fields ( A ) as shown below, The individual components are estimated by solving the Poisson equations below obtained from taking the divergence and curl of the above equation, The above equations are solved for the scalar and vector potentials using algebraic multigrid method [ 53 ] with their values set to zero outside the brain, which was segmented from the imaging volume using the brain extraction tool (BET) implemented in FSL software environment [ 54 , 55 ]. The resulting longitudinal and transverse components of the displacement vector field are used to reconstruct the elasticity tensor as described in the next sections. Governing equation for the displacement field The governing equation for the displacement field in an elastic medium is given by the momentum conservation principle (i.e., Navier’s equation), where σ is the 2 nd -order stress tensor and ρ is the density of the medium. Assuming a Hookean material with a linear stress-strain relationship, σ = C : ε , where C is the 4 th -order elasticity tensor and ε is the 2 nd -order strain tensor. The strain tensor for the longitudinal and transverse components taking into account the symmetry of the longitudinal component is given below, Assuming a transversely isotropic material with symmetry about z -axis, the elasticity tensor in Voigt notation can be expressed as a 6 × 6 matrix in the principal frame as shown below [ 21 ], Substituting Equations ( 6 ) and ( 7 ) into Equation (5) results in the following wave equation for the longitudinal and transverse components (derived in appendix Sections 1.1 and 1.2), Where is the Laplacian operator. The above two sets of equations provide a complete description of the wave propagation in transverse isotropic linearly elastic media whose simplified version was used in [ 52 ] for estimating the shear modulus parallel and perpendicular to the fibers in the breast tissue. It can be observed that transverse wave propagation depends on all the unique tensor components while the longitudinal waves are independent of the x-y transverse component, C 12 . Estimation of the stiffness tensor Isotropic tensor model Since not all voxels in the brain are anisotropic, an isotropic stiffness tensor is assumed in voxels whose FA of the diffusion tensor in the quiescent phase of the cardiac cycle is less than 0.2. For an isotropic stiffness tensor, following relations apply [ 56 ]. Applying the above relations in Equations ( 8 ) and ( 9 ), the governing equation for the time-harmonic longitudinal and transverse components of the displacement field, û , is given by, In terms of engineering constants, C 11 = λ M is the P -wave modulus, and is the isotropic (S-wave) shear modulus. The two unknown parameters are computed by rewriting the above governing equations into the following optimization problem which is solved in each voxel, Where A Iso is a 6 × 2 matrix representing the operator multiplying the vector of unknowns, x Iso , which in this case is C 11 and C 12 , and b is the vector of left hand side of the governing equations (i.e., Equations ( 10 ) and ( 11 )). The positivity constraint was applied on the shear modulus and Poisson’s ratio to ensure physicality. The optimization problem was solved using the splitting conical solver (SCS) [ 57 ] implemented in the CVXPY software environment [ 58 ] with displacement derivatives estimated using Savitzky-Golay filter [ 59 ]. Anisotropic tensor model In regions with large FA (i.e., FA > 0.2), we assume a transverse isotropy model holds. Both the elasticity and stiffness tensors are assumed to share the same principal coordinate axes with the axons acting as mechanical waveguides [ 4 ]. The five unknown tensor elements were estimated by solving the following optimization problem using the six equations of motion similar to the isotropic model (i.e., Equations ( 8 ) and ( 9 )), where A Aniso is a 6 × 5 matrix representing the operator multiplying the vector of unknowns of the elasticity tensor, x Aniso . The positivity constraint for the isotropic shear and P-wave modulus translates to a positive definiteness constraint for the elasticity tensor to ensure physicality [ 60 ]. Since the above equations assume the fibers are oriented along z-axis, the displacement field and its derivatives are rotated appropriately in each voxel using a rotation matrix, R, derived from the principal eigenvector of the corresponding diffusion tensor in the quiescent phase of the cardiac cycle using the following relation in tensor notation, The estimated stiffness tensor is then rotated into the lab coordinate system with the inverse of the rotation matrix (i.e., transpose) to compare across voxels and correlate with the diffusion tensor as shown below, We ensure that R is a proper right-handed rotation matrix. Visualization The kinematics of the motion are visualized using 3D vector plots of measured displacement field along with their longitudinal and transverse components to show shear and compression wave motion, respectively. The divergence and curl of the harmonic displacement field are calculated and displayed as scalar and 3D vector plots to visualize the amount of compressive and shear strain respectively. The diffusion tensor derived maps are shown as a function of the cardiac phase to investigate their variability due to brain motion and/or deformations. Streamline tractography is performed using the diffusion orientation distribution function (ODF) in the MRTrix software environment [ 47 ], and the tracts are colored using the scalar maps quantifying features of the estimated elasticity tensor as discussed below. The features of the estimated elasticity tensor are visualized using a set of stains and glyphs. The mechanical anisotropy, MA , is quantified as a measure of deviation of the elasticity tensor from its isotropic equivalent, C iso , using the following relation that is adapted from [ 61 ], The isotropic part of an elasticity tensor is given by averaging it over all orientations resulting in the following [ 62 ], where δ is the Kronecker delta, and K, G are the effective isotropic bulk and shear modulus, respectively, for a given elasticity tensor. The Einstein convention is used above, which means that repeated indices imply summation over that index. The average stiffness, AS , is given by the average trace of the elasticity tensor which is one of the rotational invariants of the elasticity tensor [ 60 ], Above, the Voigt notation is again used to write elements C mn of a 6 × 6 matrix that correspond to elements of the 4 th -order elasticity tensor C ijkl . The above stiffness measures can also be expressed as a function of local wavelength, λ , to account for heart rate variations and brain size differences across subjects, which is given by, where A corresponds to values of AS, K , and/or G stiffness and f is the actuation frequency. The symmetric part of the elasticity tensor, E , is displayed as a 3D glyph by projecting onto the 3D space as [ 60 ], where r i is the unit vector on a sphere. The asymmetric part of the elasticity tensor is described by the Poisson’s ratio, ν , averaged over all lateral orientations orthogonal to a given direction which is displayed as a 3D glyph whose equation is given by [ 63 ], where S ijkl is the compliance tensor, which is the inverse of the elasticity tensor. Results First, we examine features of the displacement vector field throughout the cardiac cycle. Specifically, we report the real part of the mean displacement field oscillating at the cardiac frequency, which is approximately 1 Hz, in Figure 1 . We also report the two contributions to the mean displacement field obtained from the components that give rise to longitudinal and shear wave propagation. These are obtained using the Helmholtz decomposition, which allows us to solve for both displacement fields separately. An effective means to visualize these displacement vector fields is to superimpose them on the DTI-derived FA map, which is obtained at the quiescent phase of the cardiac cycle. This way it is possible to discern possible differences in the displacement vector field in white and gray matter. Moreover, the FA map provides an anatomical reference to help locate brain structures in which the displacement vector field glyphs are displayed. The mean displacement at the cardiac frequency had a peak displacement approximately equal to 75 µ m which translates to 1.56 mm/s velocity based on the diffusion time used in the measurement. The mean displacement field had a funnel-shaped profile along the inferior-superior axis. The longitudinal component of displacement was non-zero, albeit with smaller magnitude than the transverse component. Both the components did not show any preference to gray or white matter. Download figure Open in new tab Figure 1: 3D vector plots of the real part of the mean, longitudinal, and transverse displacement field oscillating at the cardiac frequency (i.e., ≈ 1 Hz) for a representative healthy volunteer. The fractional anisotropy (FA) map obtained at the quiescent phase of the cardiac cycle is overlaid on the displacement field to provide anatomical context. The displacement vectors are colored based on their magnitude, and anatomical axes (A - Anterior, P - Posterior, S - Superior, I - Inferior, R - Right, L - Left) are indicated. The mean displacement field had a funnel-shaped profile along the I - S axis. The longitudinal component of displacement was non-zero albeit with smaller magnitude than the transverse component. Second, we explore the repeatability of the displacement vector field measurements from which the elasticity tensor is computed using a test/retest paradigm, which was possible given that we could perform scan repetitions in the same imaging session. The harmonic displacement vector field obtained at the cardiac frequency in two repetitions are shown in Figure 2 . We see high reproducibility with data obtained during different times in the scanning session on the same volunteer. The displacement profiles are noisier than the mean displacement vector field shown in Figure 1 but the features such as the displacement magnitude and shape of the profile were reproducible. Download figure Open in new tab Figure 2: Test-retest repeatability of the displacement field measurement shown using 3D vector plots of the real part of the displacement field oscillating at the cardiac frequency (i.e., ≈ 1 Hz) for a representative healthy volunteer. The fractional anisotropy (FA) map obtained at the quiescent phase of the cardiac cycle is overlaid on the displacement field to provide anatomical context. The displacement vectors are colored based on their magnitude, and anatomical axes (A - Anterior, P - Posterior, S - Superior, I - Inferior, R - Right, L - Left) are indicated. The displacement fields were highly reproducible albeit noisier than the mean displacement vector field. Third, we show the compressive and shear strains in the brain tissue resulting from cardiac pulsations using maps of divergence and curl of the harmonic displacement field expressed as percent in Figure 3 . Overall, the curl is higher in magnitude than the divergence but both have a median less than 0.5% over the whole brain. By comparison with the FA map, the curl and divergence are similarly heterogeneous in gray or white matter regions. The curl vector in the brain predominantly points in the inferior-superior direction aligning with the direction of the cardiac pulse wave. Download figure Open in new tab Figure 3: The intrinsic dilatation and shear motion in the brain shown in a “3-D slicer” format using the real part of the divergence and curl of the harmonic mean displacement field for a representative healthy volunteer. The former is a scalar map showing dilatation while the latter shows shearing motions, and is depicted using 3D vectors overlaid on the fractional anisotropy (FA) map that provides anatomical context. The curl vectors are colored based on their magnitude, and anatomical axes (A - Anterior, P - Posterior, S - Superior, I - Inferior, R - Right, L - Left) are indicated. The curl was overall higher in magnitude than the divergence, and predominantly pointing in the inferior-superior direction aligning with the direction of the cardiac pulse wave. We report the time-varying diffusion tensor and displacement vector fields at different phases of the cardiac cycle in a representative axial slice from a normal volunteer in Figure 4 . We observed variations in the diffusion tensor field as a function of the cardiac phase. The MD map showed variations as high as 30% in the corpus callosum (red arrow in the figure), and DEC maps showed variations in the conspicuity of certain white matter fiber tracts (yellow and white arrows in the figure), which correlated with the sign of inferior-superior (I-S) component of the displacement vector. For example, the MD was higher in the corpus callosum when the I-S component of the displacement vector there was negative and vice versa. Download figure Open in new tab Figure 4: Time-varying diffusion tensor and displacement fields at different phases of the cardiac cycle for a representative mid-brain axial slice from a representative healthy volunteer. The DTI-derived maps including S 0 , mean diffusivity (MD), and direction-encoded color (DEC) along with the color sphere are displayed as a function of the cardiac phase (given as percent of total period after the p SO 2 trigger). The three components of the displacement vector field in the patient coordinate system (A - Anterior, P - Posterior, S - Superior, I - Inferior, R - Right, L - Left) are provided for comparison with a map of fractional anisotropy (FA) overlaid for anatomical reference. The location of the slice in the sagittal plane from an anatomical scan is provided on the top right using a violet dashed line. For clarity, the time axis is down-sampled in the figure by a factor of 2. Some of the variations in the DTI stains across the cardiac cycle likely due to partial volume effects induced by the pulsation are shown using arrows. White arrows represent the increase in FA in CSF regions compared to the quiescent phase (i.e., t = 20%), yellow arrows represent the decrease in FA in a white matter region close to the cortex, and the red arrow represents the increase in MD in corpus callosum. We also compare the diffusion and elasticity tensor maps in axial, coronal, and sagittal slices from a representative volunteer in Figure 5 . The diffusion tensor maps include MD and FA while the elasticity tensor maps include the MA, AS, isotropic shear modulus, and isotropic bulk modulus. Whole brain distribution of these stains in gray and white matter, segmented based on their MD and FA values, were also included in the figure. The isotropic CSF-filled ventricles exhibited large MD (≈ 3 µm 2 /ms ), zero anisotropy (both diffusion and mechanical), and near-zero stiffness values. The MD is fairly uniform in the brain parenchyma (≈ 1 µm 2 /ms ) while the AS map was highly heterogeneous and showed white matter to be 50% stiffer than gray matter averaged over the entire brain. The absolute value of the stiffness, however, was small at the cardiac frequency peaking around 7 Pa for the entire brain. Differences in AS were observed among various white matter regions, for example, the internal capsule is three times stiffer than the corpus callosum. The MA measure closely followed FA albeit more pronounced in certain white matter regions. The isotropic shear modulus was heterogeneous with gray-white matter contrast ( G gm ≈ 2 G wm averaged over the entire brain). The isotropic bulk modulus of gray and white matter was similarly averaged over the entire brain. Download figure Open in new tab Figure 5: Diffusion and elasticity tensor maps along axial, coronal, and sagittal slices, and their distributions in gray and white matter across the entire brain from a representative healthy volunteer. These include the mean diffusivity (MD), diffusion anisotropy (FA), mechanical anisotropy (MA), average stiffness (AS), isotropic shear modulus, and isotropic bulk modulus. The anatomical axes (A - Anterior, P - Posterior, S - Superior, I - Inferior, R - Right, L - Left) are indicated in the figure. Cerebrospinal fluid (CSF) has zero stiffness and anisotropy while exhibiting large MD as expected. White matter is stiffer than gray matter with differences noted among various white matter regions. MA closely followed FA albeit more pronounced in certain tracts. The shear modulus was heterogeneous with gray-white matter contrast while the bulk modulus was similar. We show elasticity and diffusion tensor glyphs in an axial slice from a representative healthy volunteer in Figure 6 . Corpus callosum and a crossing fiber regions of interest (ROI) were chosen for illustration. The glyphs include the diffusion tensor orientational distribution function (DT-ODF), elasticity tensor, and Poisson’s ratio which were overlaid on a FA map for anatomical reference. In the central region of the corpus callosum ROI, the stiffness and ODF glyphs match indicating the stiffness along the fibers is greater than that perpendicular to it. This translates to an opposite effect on the Poisson’s ratio with its value along the fiber less than that perpendicular to it as shown in their glyphs. At the interface between the two brain hemispheres where the FA is reduced, the DT-ODF is no longer unidirectional and slightly bulges in anterior-posterior (A-P) direction likely due to fiber crossings. The two fiber populations were, however, clearly captured in the stiffness glyphs. The Poisson’s ratio in this region resembles the DT-ODF glyphs as the tissue is compliant in both directions. The gray matter region in the crossing fiber ROI has an isotropic DT-ODF, elasticity, and Poisson ratio tensor as expected. The relationship between the three tensor glyphs in the white matter within this ROI was similar to that observed in the corpus callosum. Download figure Open in new tab Figure 6: Diffusion and elasticity tensor glyphs in an axial slice from a representative healthy volunteer in two regions of interest (ROIs), crossing fiber region (green box) and corpus callosum (red box) highlighted in a fractional anisotropy (FA) map. The glyphs include the diffusion tensor orientational distribution function (DT-ODF), and the 4 th -order elasticity tensor and Poisson’s ratio tensor. In the central region of the corpus callosum, it can be observed that stiffness is greatest along fibers than perpendicular to them while a complex stiffness pattern is observed at the tissue boundaries where the DT-ODFs have no preferred orientation. Poisson’s ratio was greatest perpendicular to the fibers and exhibited complex patterns in regions of crossing fibers. We show the differences in mechanical properties across fiber tracts by overlaying them on diffusion tractograms derived from DT-ODFs for a representative subject in Figure 7 . We observed significant stiffness differences among fiber tracts, for example, the internal capsule, corona radiata, and U-fibers were much stiffer than other white matter tracts even though they had similar MA. The bulk modulus was sparse and often high in regions where the shear modulus is low. Download figure Open in new tab Figure 7: Stiffness of fiber tracts in the brain shown by coloring the diffusion tractogram based on the average stiffness, mechanical anisotropy, bulk and shear modulus measured using MRE. It is clear that internal capsule and corona radiata fibers are stiffer than other fibers. The tracts exhibit different degrees of mechanical anisotropy. The bulk and shear modulus were highly heterogeneous across tracts. Finally, we compare the results across subjects using scalar maps and tractograms in Figure 8 . The stiffness is expressed in terms of the local wavelength of the mechanical wave to adjust for heart rate differences across subjects. The results were consistent across subjects with white matter being stiffer than gray matter. The tractograms recapture the stiffness heterogeneity among fiber tracts with internal capsule and U-fibers being significantly stiffer than other white matter tracts. The MA values were also comparable across subjects. Download figure Open in new tab Figure 8: Variability in the elasticity tensors across three subjects shown using scalar maps in the brain. The stiffness measures are replaced with local wavelength to account for variations in heart rate across subjects. The maps include the mechanical anisotropy (MA), and wavelengths associated with average stiffness (AS), isotropic shear modulus (G), and isotropic bulk modulus (K). The anatomical axes (A - Anterior, P - Posterior, S - Superior, I - Inferior, R - Right, L - Left) are also indicated in the figure. The fiber tract stiffness is shown by mapping the local wavelength associated with stiffness measure across subjects. The maps are arranged as columns and subjects as rows. The maps and the tractograms were consistent across subjects with similar values and degree of heterogeneity. Discussion In this study, we present a new method to measure and map the 4 th -order elasticity tensor in live human brains without an external tamper. We use the principal directions of the concurrently measured diffusion tensor as a priori information for the reconstruction of the elasticity tensor. Our results recapture previous findings and reveal new mechanical heterogeneity. We show how the diffusion measurement is affected by intrinsic brain deformation and introduce new stains and glyphs that characterize mechanical properties in each voxel. We map mechanical properties along white matter tracts illustrating their mechanical heterogeneity. We compared the results across subjects to validate our findings. Measuring diffusion and displacement profile in pulsing brain Measuring both intra-voxel coherent and incoherent motion simultaneously in a live human brain is challenging for several reasons; 1) pulsations of the brain could affect the MR signal magnitude due to tissue deformation [ 64 ] or from changing voxel tissue composition particularly at the CSF-tissue boundaries which confounds the diffusion measurement, 2) the coherent displacement induced by the heart is very small and can get entangled with incoherent diffusive displacements [ 65 ], and 3) the phase that encodes coherent motion may be corrupted by gradient hardware imperfections, random head motions, etc. [ 33 ]. While cardiac gating helps mitigate some of these effects, it does not fully resolve them, especially in the presence of unpredictable head movements and non-linear brain deformations throughout the cardiac cycle [ 66 ]. Obtaining a continuous 3D displacement field is necessary for the accurate reconstruction of stiffness as it involves taking the spatial derivatives of the displacement field. In this study, we have employed a number of strategies to overcome these aforementioned challenges. We used a standard pulsed-field gradient experiment with short gradient duration and long diffusion time to encode slow flows while minimizing diffusion weighting [ 39 ]. We used image oversampling and outlier rejection with retrospective cardiac gating to correct for random phase errors in the measurement and account for continuous brain displacement throughout the cardiac cycle. Furthermore, during the scanning session, we collected enough samples to retain, after outlier removal, multiple repetitions of the time-dependent complex MRI dataset at each cardiac phase. With this data we demonstrate a high degree of precision in the measurement of the displacement fields across repetitions. The observed funnel-shaped displacement profile with peak brain velocities on the order of 1.6 mm/s, and divergence and curl on the order of 0.5% largely agree with previous studies [ 33 , 67 ]. The harmonic displacement vector plots on the three orthogonal planes show continuously varying displacement fields in 3D, free of inter-slice discontinuities also known as slice jitter [ 44 ]. It should be noted that the scan time can be reduced at least by a factor of two in the future. Effect of cardiac pulsation on DTI We studied the effect of cardiac pulsations on DTI and correlated them with the simultaneously measured displacement fields - an analysis seldom carried out in previous studies [ 68 , 69 ]. Given that the DWI signal is not just sensitive to water diffusion but to various physiological motions [ 70 ] manifesting as “pseudo-diffusion”, our proposed method has the potential to control for and possibly isolate various types of these non-diffusive motions which can be conflated with and pose as diffusion [ 70 ], for example, affecting the MD and the apparent diffusion tensor in DTI. These physiological processes may involve cardiac and respiratory induced tissue motions, microvascular and CSF pulsations resulting in intravoxel shearing motions [ 64 , 71 ], or periodic tissue compression or expansion, inter alia . Analyzing the complex MRI data as a function of cardiac phase, we now have a means to isolate these physiologically-induced sources of pseudo-diffusion. Unlike the heart, which undergoes strains as high as 20% [ 72 ], the intrinsic deformation of the brain from cardiac pulsations is orders of magnitude smaller (i.e., 0.5%). The resulting deformation is not sufficient to cause observable dephasing of the MR signal at the low diffusion weightings we used and does not explain the changes we observed in the DTI metrics across cardiac phases. Instead, these changes are explained by mean tissue displacement especially in CSF-tissue boundaries such as in the corpus callosum as evidenced by the increase in MD at certain cardiac phases. These are due to CSF in the fissures above it being displaced into the region from inferior-superior brain motion, as shown in the displacement images. This was also evident in the white matter fiber bundle that was pushed in and out of the ventricles due to the brain displacement resulting in a larger FA in the ventricles when the fibers were inside the ventricles and smaller when they were outside. Elasticity tensor estimation We applied the “cross-property” relationships arising from effective medium theory [ 5 , 73 ] to make the elasticity tensor estimation problem well-conditioned. We expect the principal directions of the transverse isotropic elasticity tensor would coincide with those of the diffusion tensor in voxels with coherent anisotropic material structure [ 5 ], although their principal diffusivities and stiffnesses are not obviously related. These quantities have different physical units arising from different constitutive laws describing relationships between generalized fluxes and generalized forces with governing equations potentially having different boundary conditions. In the case of diffusion, the flux is a mass flux and the generalized force is a concentration gradient. In the case of the material deformation the generalized flux is the material displacement, and the generalized force is the stress. These tensors are also related to different MR-derived quantities in the DTI experiment, the magnitude signal for the diffusivity, and the phase signal for the stiffness. Reconstruction of the transverse isotropic elasticity tensor with a priori information about the fiber orientation has been presented previously for muscle [ 28 ], breast [ 52 ], brain [ 4 , 32 ], and phantoms [ 31 ]. Our approach differs from those studies in several key ways, 1) we use the intrinsic pulsations of the brain instead of a tamper which is often expensive and could potentially introduce variability in the measurement; 2) the resulting low frequency of actuation sensitizes the signal to poroelastic effects which maybe important in normal and abnormal brain conditions; 3) we use a standard pulse sequence readily available in many scanners to measure these deformations as opposed to DENSE; 4) we obtain the fiber orientation from a single MRI dataset instead of separate DTI and MRE scans, thereby preventing errors due to subject motion between scans and differing imaging distortions, maintaining a reasonable scan duration, and properly accounting for the effect of tissue displacement on diffusion measurement; 5) since the harmonic divergence of brain deformation is non-zero in many parts of the brain, we do not assume tissue incompressibility and remove the modulation of the transverse displacement component by the longitudinal excitation from the heart using Helmholtz decomposition [ 52 ]; 6) we make the estimation well-posed by introducing physically motivated positive definiteness constraint to ensure the stability of the estimated elasticity tensor [ 60 ] along with the six governing equations (both longitudinal and transverse components) to estimate the five independent parameters of the transverse isotropic tensor; 7) we use a fast direct inversion of the displacement field using convex optimization; and 8) we introduce new glyphs and invariants for use as stains to quantify the elasticity tensor independent of the coordinate system. Heterogeneity of the diffusion and elasticity tensor fields We see that the MD maps at different phases of the cardiac cycle are homogeneous throughout the human brain, as was previously reported [ 19 ], however, there is significant variability in the trace of the elasticity tensor in different brain ROIs, both in gray and white matter. We ascribe these to regional differences in the meso and microscopic determinants of stiffness to complex soft matter, such as intracellular and extracellular polymer type and content, local extracellular matrix (ECM) stiffness variations, degree of cross-linking, etc. These discontinuities in mechanical properties at internal boundaries lead to mechanical impedance mismatches, local stress concentrations, and may predispose such sites to vulnerability in TBI [ 74 ]. These internal boundaries within the brain, for instance, do not appear in MD images except at CSF/parenchyma interfaces. The increased MD and near zero stiffness values in CSF-filled ventricles are due to its free water composition and the inability of fluids to withstand shear stresses and the wavelength associated with its bulk modulus is much larger than the head size, respectively. The higher stiffness observed in the white matter compared to the gray matter has been demonstrated in several MRE studies for a wide range of excitation frequencies [ 20 , 25 , 75 ], which may be due to the higher degree of crosslinking resulting from myelination [ 76 ]. The fiber tracts showed large variations in stiffness with internal capsule and corona radiata fibers exhibiting larger stiffness values compared to other fibers. This is in agreement with a study conducted on ex-vivo human and porcine brain tissue specimens [ 77 , 78 ] but opposite to that obtained on an in-vivo MRE study at 50 Hz with FEA reconstruction [ 32 ] which maybe due to differences in the actuation frequency and analysis method employed. Our findings could be explained by the fact that despite having a lower axon density than corpus callosum, the corona radiata [ 79 ] is known to have higher protein content such as collagen [ 80 ] likely due to the need to support the fanning fibers. The bulk modulus, often ignored in many MRE studies due to its supposedly large values resulting from large tissue water content, was non-zero and heterogeneous throughout the brain tissue. This is likely due to the compressibility of the tissue matrix as it squeezes water in and out throughout the cardiac cycle [ 67 ]. The regional differences in the bulk modulus could be explained by the differences in hydraulic permeability with tissues having higher hydraulic permeability having smaller bulk modulus and vice-versa. We do however note that our measured tissue stiffness values overall fall on the lower end of values for brain tissue reported in the literature obtained in vivo and in vitro , which vary in orders of magnitude from Pascals (Pa) to kPa [ 81 ]. This is not surprising owing to the difficulty of making such measurements, the frequency of deformation, differences in experimental design, the diversity of model systems in which brain material properties have been measured, and the variety of mathematical/physical models used to interpret displacement, velocity, and strain data. Low values of overall average tissue stiffness, however, likely mask greater ECM stiffness, which occupies only about 20 percent of the tissue volume in the brain [ 82 ], the rest largely taken up by cells, which may behave like incompressible micro-balloons at these timescales, but have low shear stiffness [ 83 ]. Our voxel-wise measurement of stiffness is of the same order of magnitude as the coarse estimate of the whole brain stiffness (≈ 14 Pa) derived from long wavelength mechanical waves we observe, which are on the order of the width of the brain (i.e., ≈ 12 cm) at 1 Hz, and by assuming tissue density equal to that of water. Moreover, if one ignores dispersion the corresponding value of shear modulus at 100 Hz given it is proportional to the square of the actuation frequency is approximately 20 kPa which agrees with a MRE study conducted in the brain with a 100 Hz tamper [ 75 ]. Anisotropy of the diffusion and elasticity tensor fields Diffusion anisotropy is well characterized in DTI in areas with coherent white matter organization but is known to drop in more complex white matter areas with crossing fibers, such as in parietal and frontal white matter, in deep temporal white matter, and in the centrum semiovale. One could speculate that in such areas the shear stiffness could be elevated given the interdigitating fiber structure, whereas the diffusion anisotropy would decrease. This is evident in the elasticity tensor glyphs where the second fiber direction is accentuated in certain crossing fiber regions resulting in larger mechanical anisotropy. The diffusion anisotropy in gray matter is quite low, despite the higher microscopic anisotropy measured in diffusion tensor distribution MRI studies [ 84 ]. There is an open question of how this microstructural motif contributes to the overall mechanical stiffness of brain parenchyma and whether we could use changes in stiffness measurements in such tissue to infer changes in microstructure associated with development, degeneration, diseases, and/or trauma. We compared the FA from DTI to the MA (and other maps) in our MRE method. Generally, we see anisotropy appearing in the white matter regions in both tensor fields, however, stiffness-tensor-derived parameters tend to be much noisier and accentuated compared to DTI parameters. This is partly due to differences in post-processing of the MRI data used to calculate them, with elasticity values being obtained from second numerical derivatives of experimental phase parameters in the case of MRE. DTI and MRE experimental designs Of course, a powerful feature of our study and experimental design is the possibility to test whether the principal diffusivities obtained using DTI coincide with the principal directions of the elasticity tensor. This is often expected from effective medium theory [ 17 ] but may not hold after inspection. We are currently using the minimal number of gradient directions (i.e., six) [ 17 ] to obtain an isotropic DTI experimental design in the interest of minimizing scan time, although we recognize the value of using a greater number of gradient directions, not only to improve the estimates of the diffusion tensor in each voxel and at each phase of the cardiac cycle, but also to enable a more complex 4 th -order tensor representations of the diffusion and elasticity tensors. Our current design limits the material model of brain tissue to be transverse isotropic but it is prudent to be able to measure high-order tensor (HOT) models, which may be appropriate, particularly in complex brain tissue areas. The DWI experimental design can readily be extended to accommodate High Angular Resolution Diffusion Imaging (HARDI) data, and methods such as mean-apparent propagator (MAP)-MRI [ 85 ], allowing us to identify complex fiber architectures in areas of the brain not adequately described by the 2 nd -order elasticity or diffusion tensor frameworks. Future challenges and opportunities Respiratory and heart-rate fluctuations can cause some blurring and variability in the complex timeseries signal data, and also increase noise in quantities computed from the measured displacements. We plan to improve our time-series analysis pipeline and registration methods to better account for these expected variations. This method is currently designed to be performed on subjects with fairly steady heart rates and normal blood pressure ranges, so these have to be monitored to assess data quality and improve retrospective analysis and post-processing. Opportunities abound for this approach. It naturally lends itself to studying material properties of other tissues and organs, particularly given the relatively recent improvement in whole-body diffusion MRI sequences and data acquisition methods. The stiffness changes in the brain tissue in physiological and pathophysiological states such as neuronal activation, sleep via the glymphatic clearance pathway can be readily studied. Innovations in diffusion MRI sequence calibration should improve the quantitative character (i.e., accuracy and precision) of measurements of both diffusivity and displacements. Moreover, to obtain the MRE data, our approach does not require a specialized setting (e.g., hospital or out-patient radiological suite) equipped with custom tampers and actuators, nor specially trained imaging personnel. Conclusion We propose a powerful image acquisition, processing, and analysis pipeline to implement actuatorfree or “intrinsic” magnetic resonance elastography (MRE) in the human brain, in conjunction with diffusion tensor imaging (DTI). Besides providing estimates of bulk and shear moduli throughout the brain it also produces diffusion tensor MRI-derived “stains,” which both inform the models of mechanical properties and help co-register maps of brain material properties to those of anatomical features and landmarks provided by DTI. This implementation of MRE also has the potential to measure and map low-frequency material properties and parameters in other tissues and organs throughout the body, providing novel “stains” and contrasts, permitting remote palpation without an external actuator or tamper. Author Contributions KNM and PJB designed and conceived of the research project. KNM also carried out the parameter estimation, performed the experiments, and drafted the article. AVA assisted in performing experiments and conducted the fiber tractography analysis. JES assisted in performing the clinical experiments. PJB, AVA, and JES edited the article. All authors reviewed the manuscript. Competing interests The author(s) declare no competing interests. Acknowledgments KNM was supported by the Department of Defense through the Military Traumatic Brain Injury Initiative (MTBI 2 ) under award, HU0001-22-2-0058. PJB was supported by the Intramural Research Program (IRP) of the Eunice Kennedy Shriver National Institute of Child Health and Human Development, and JES by the National Institute of Neurological Diseases and Stroke. AVA received support from the Connectome 2.0 project under the auspices of the NIH BRAIN Initiative grant 5U01EB026996-05. The authors have no conflicts of interest to disclose. This research was supported (in part) by the Intramural Research Program of the NIH, NINDS. 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