Onset location of periventricular white matter hyperintensities co-localizes with peak ependymal cell stretch

Deep and periventricular white matter hyperintensities (dWMH/pvWMH) are bright appearing white matter tissue lesions in T2-weighted ﬂuid attenuated inversion recovery magnetic resonance images and are frequent observations in the aging human brain. While early stages of these white matter lesions are only weakly associated with cognitive impairment, their progressive growth is a strong indicator for long-term functional decline. DWMHs are typically associated with di ﬀ use vascular degeneration; for pvWMHs, however, no unifying theory exists to explain their characteristic onset locations and progression patterns. We use structural and functional patient imaging data to create anatomically accurate ﬁnite element models of the lateral ventricles, white and gray matter, and cerebrospinal ﬂuid. We simulated the mechanical loading of the ependymal cells forming the primary brain-ﬂuid interface, the ventricular wall, and its surrounding tissues at peak ventricular pressure during the hemodynamic cycle. We observe that both the maximum principal tissue strain and the largest ependymal cell stretch consistently localize in the anterior and posterior horns. Strikingly, these locations coincide with the pvWMHs observed in FLAIR images. We submit that the tight junctions between ependymal cells experience signiﬁcant loads that cause the ventricular wall to be stretched thin and ultimately begin to leak. Besides age-related vascular degeneration, progressive wall failure causes neurotoxic ﬂuid to di ﬀ use into surrounding white matter structures and appear as growing pvWMHs. The physics-based approach presented here provides a novel model system to systematically study the progressive tissue deterioration associated with pvWMHs. and horn radii increase as well. These consistent trends are indicative of ventricular shape-related brain and mi-crostructural changes.


Introduction
White matter hyperintensities (WMH) are bright appearing white matter tissue lesions in T2-weighted fluid attenuated inversion recovery (FLAIR) magnetic resonance imaging (MRI) [1,2] and are a frequent observation in the aging human brain [3,4]. WMHs have been linked to vascular degeneration during aging [5,6]. It is typically described that hypertension [7,8], smoking [9,10], diabetes [11,12], and heart disease [13,8] are common risk factors that exacerbate the vascular involvement leading to white matter changes. WMHs are classified as deep white matter hyperintensities (dWMH) and periventricular white matter hyperintensities (pvWMH) on the basis of anatomical localization [14]. While cerebral ischemia and small vessel disease are the primary pathophysiological observations in WMHs [5,6,15,16], we pose, here, that the onset of pvWMHs is subject to additional mechanical damage mechanisms. Specifically, we hypothesize that a lifetime of cyclic mechanical of the ependymal cells lining the ventricular wall due to a combination of hemodynamic forces and CSF flow leads to cell damage, structural degeneration of the lateral ventricular wall, and its progressive functional failure. We use a finite element modeling approach to show that ependymal cells experience peak mechanical loading in the ventricular horns that co-localizes with WMH masks based on clinical patient data. The finite element modeling approach is particularly useful because it allows us to create anatomically accurate brain models of various ventricle shapes to demonstrate that ependymal call stretch patterns are consistent across subjects.
Clinically, WMHs are a common observation in medical images of the elderly and their severity typically increases with age [17,18,19]. By the age of 44, there is a 50.9% likelihood of incidental WMH findings in healthy, cognitively normal subjects [20] and by age 60, nearly every brain exhibits signs of white matter lesions [21,22]. While early stages of these white matter lesions are only weakly associated with cognitive impairment [23], the accumulation and expansion of white matter lesions is considered a reliable indicator for long-term functional decline [24,25]. In particular, the volume of pvWMHs is associated with accelerated functional decline [26].
The pathophysiology of white matter lesions is poorly understood, but is strongly linked to location. PVWMHs are much more likely to be observed in the aging brain than dWMHs. DWMHs are linked to ischaemic damage, hypoxia, and hypoperfusion [27,28]. Although pvWMHs are associated with ischaemia of perforating arterioles as well, they are further characterized by ependymal cell thinning, leakage of cerebrospinal fluid (CSF) into the tissue behind the ventricular wall, and, as inflammatory processes expand, manifests as demyelination, axonal loss, reduced glial density, tissue atrophy [29, 30, 31, ?], and the formation of astroglial scarring [32,33,34]. Fazekas et al. reported that pvWMHs consistently first appear in the ventricular horns and expand towards deep white matter tissue over time [1]. This observation is reflected in the evaluation criteria proposed by Fazekas et al. yielding a score from 1 to 3. The Fazekas score (FS) differentiates between caps or pencil-thin linings in the horns associated with the earliest manifestation of pvWMHs (FS=1), smooth halos linked to progressively growing pvWMH volumes (FS=2), and ultimately irregular periventricular signal that extends into deep white matter (FS=3) [1]. Incidental white matter findings in young healthy adults further support the notion that pvWMHs first emerge in ventricular horns [20]. To date, however, no theory has been proposed to explain the underlying mechanism. Moreover, temporal changes of white matter lesions are poorly understood [35]. White matter lesion volume has been shown to grow on average by 14.6% per year in dWMH and by 9.9% per year in pvWMH [36]. There remain critical knowledge gaps, however, in explaining WMH volume growth over time and the progressive expansion of WMHs along the ventricular wall, on the one hand, and the diffusion of CSF and white matter inflammation radiating out from the ventricular horns into deep white matter on the other.
Anatomically, the ventricular epithelium is lined by the ependymal wall that is composed of distinct layers, see Figure 1, with varying thicknesses and densities as shown in Figure 1. Going from ventricle Figure 1: The ventricular epithelium is a functional barrier between the brain and CSF. It consists of four distinct layers: a monolayer of cuboidal multiciliated ependymal cells (Layer I), a prominent hypocellular gap very rich in processes from ependymal cells and astrocytes (Layer II), a ribbon of cells composed of astrocytes (Layer III), and a transitional zone into the brain parenchyma (Layer IV) [37]. A) In a healthy state, the ependymal wall regulates the exchange of fluid and nutrients between the lateral ventricle and brain tissue. B) With age, the thin layer of ependymal cells degrades leading to the unregulated influx of CSF into the hypocellular layer first and deeper white matter tissue next. Once breached, white matter lesions emerge and propagate. C) Given the morphology of the ventricular wall, ependymal cells are stretched thin due to pulsatile fluid flow in the lateral ventricles [30]. towards brain parenchyma, one observes a monolayer of cuboidal multiciliated ependymal cells (Layer I), a prominent hypocellular gap rich in processes from ependymal cells and astrocytes (Layer II), a ribbon of cells composed of astrocytes (Layer III), and a transitional zone into the brain parenchyma (Layer IV) [37]. The multiciliated ependymal cells in Layer I are tightly joined by connexins and cadherins, or gap junction proteins, which form tight inter-cellular connections [31]. Layer II is present in the entire ependymal wall in the lateral ventricles, but varies in thickness from region to region. The presence of aquaporin 4 in the basolateral plasma membranes of ependymal cells results in a directed water flow [38]. Aquaporin 4 junctions facilitate the reabsorption of interstitial fluid into the parenchymal vasculature [39] and drive the unidirectional fluid drainage into ventricular spaces [38]. If the ependyma is disrupted ( Figure 1B), reactive astrocytes will line the ventricular wall in an attempt to reestablish homeostasis [31,32]. The reactive replacement of ependymal wall with gliotic tissue is associated with the lack of polarized aquaporin 4 junctions. This leads to an undirected transport of CSF through the ependyma [32, ?]. Over time, the dysregulated CSF-brain parenchyma barriers leads to excessive influx of CSF into the hypocellular layer and the accumulation of fluid and dysregulated homeostasis [40].
Computational modeling of the mechanical loading state of the ventricular wall is a suitable approach to demonstrate the consistent localization of maximum wall loading in the ventricular horns irrespective of ventricle size. Here, we combine subject-specific finite element model generation via medical image segmentation with FLAIR image-derived WMH masks to test our proposed damage mechanisms. Previous computational models of the (peri)ventricular space primarily focused on assessing hydrocephalus [41,42,43,44,45] or white matter damage during traumatic brain injury [46]. While these models provide valuable insight into organ-level tissue response, they are unsuitable to determine the cellular loading state along the ventricular wall and in the ventricular horns. Our present contribution consists of the generation of eight subject-specific, anatomically accurate finite element models of a representative axial brain section in order to identify the locations of maximum loading along the ventricular wall. We subsequently compare wall loading at peak hemodymanic pressure with the locations of pvWMHs observed in the subject's accompanying medical scans. We show that peak ependymal cell loading nearly always coincides with pvWMH locations in our cohort. Thus, we suggest that the mechanical loading of ependymal cells is one of the most important risk factors for the emergence of pvWMHs and is a physics-based mechanisms to explain the gradual growth of pvWMH into deep white matter tissue.

Image selection and WMH segmentation
We obtained magnetic resonance images (MRI) from cognitively normal subjects in the imaging database of the New York University Alzheimer's Disease Research Center. The standardized MRI protocol included FLAIR and high-resolution structural MPRAGE volumetric sequences. In order to capture a wide-range of ventricular shapes and various stages of brain atrophy, the cohort of 464 active subjects was sorted by cerebrospinal fluid volumes (vCSF), and we selected four male and four female subjects at the 20 th , 40 th , 60 th and 80 th percentile of the vCSF distribution. From a mechanics perspective, 8 subjects is a reasonable sample size to demonstrate the repeatable ependymal cell loading state along the ventricular wall across a wide range of ventricular shapes. For all eight subjects, a white matter hyperintensity (WMH) mask was obtained based on their FLAIR images using the freely available software package FireVoxel [www.firevoxel.org] following the procedure described by Chen et al. [47]. Briefly, the algorithm estimates the mean signal intensity µ and the standard deviation σ of FLAIR signal s within the brain region Ω. White matter hyperintensity masks are computed as {v | v ∈ Ω ∧ s(v) > µ + kσ}, where k was set at 2.5. WMH masks were provided in the form of binarized images registered to the subjects' MRI.

Finite Element Model Generation
We generated personalized finite element models of each subject based on a semi-automatic segmentation approach. We segmented each structural MR image using Freesurfer and imported both, the structural scan and the Freesurfer segmentation, into the 3D image processing and model generation software Simpleware T M Figure 2: We generated finite element models for each subject individually by segmenting axial MRI through the lateral ventricle. A) We identified the boundaries of gray matter, white matter, lateral ventricles, and cerebral spinal fluid surrounding the cortex. B) The model was kinematically constrained along the outer boundary, and we applied a pressure normal to the ventricular wall (B1) and normal to the outer gray matter surface (B2). C) Accompanying FLAIR images superposed with a mask of white matter hyperintensities show the localization of early leukoaraiosis in the ventricular horns (C3). We simulated peak loading during the hemodynamic pressure cycle in order to obtain the strain field (D4) and ependymal cell stretch along the ventricular wall (D5).
(Synopsys, Inc., Mountain View, CA) [48,49,50]. We identified the axial slice with the largest ventricular area showing the anterior and posterior horns and manually corrected the imported Freesurfer segmentation of the lateral ventricle, white and gray matter, and surrounding CSF based on the co-registered structural scan. Figure 2 shows the model generation process. Using the FE Module of Simpleware, we converted our segmentations into finite element meshes and imported our models into Abaqus (Dassault Systémes, Providence, RI). We constrained our model against out-of-plane deformations (plane strain simulation) and applied pressure boundary conditions to two surfaces: a normal pressure to the ventricular wall (green arrows in Figure 2B1) and a normal pressure to the gray matter-CSF interface (blue arrows in Figure 2B2). These loading conditions represent the peak pressure in the ventricular cavity (LV pressure) during the pulsation cycle and the pressure from the fluid circulating through the subarachnoid space (SAS), respectively. We prescribed an LV pressure of 20 Pa [51] and an SAS pressure of 1 Pa in line with observations that SAS pressure is only 10-20% of the ventricular pressure [51]. Lastly, we fully constrained all displacements of the outer boundary of the CSF layer, shown in gray in Figure 2, to mimic the interface with the skull which was not included in our models. The CSF layer was approximated as an ultrasoft, compressible material with a Young's modulus of 0.1 kPa and a Poisson's ratio of 0.3. Brain tissues were modeled as an Ogden-type hyperelastic material model [52,53]. Following basic continuum theory of finite deformations, we introduce the deformation gradient F as the gradient of the nonlinear deformation field φ with respect to the material coordinates X in the reference configuration. Assuming nearly incompressible behavior of brain tissue, we decompose the deformation gradient F into a volumetric contribution characterized through the Jacobian J and an isochoric contributionF, As a characteristic deformation measure, we introduce the right Cauchy-Green deformation tensor C which obeys a similar decomposition into a volumetric contribution in terms of the Jacobian J and an isochoric contributionC, We can then introduce the isochoric first and second invariants,Ī 1 andĪ 2 , either in terms of the isochoric right Cauchy-Green deformation tensor C, or in terms of the isochoric principal stretchesλ 1 ,λ 2 , andλ 3 , recalling thatĪ 3 = J 2 = 1,Ī 1 = tr(C) =λ 2 1 +λ 2 2 +λ 2 3 , It has been shown that the mechanical response of brain tissue is best captured by a one-term Ogden model given by the strain energy density function [52] with shear modulus µ governing isochoric, distortional deformations and bulk modulus κ governing dilatational deformation. We assume our material to be nearly incompressible with a Poisson's ratio of 0.45 and a white-gray matter stiffness ratio of 2 [52]. Specifically, we chose experimentally-informed constants µ = 0.34 kPa and κ = 0.0033 kPa for gray matter and µ = 0.68 kPa and κ = 0.0067 kPa for white matter [51,52,54,55,56]. We implemented the Ogden model in a user material subroutine (UMAT) following the example of [53] and compute ventricular wall stretches as outlined further below.

Ventricular geometry as a measure for WMH severity
We propose two measures for the analysis of horn geometry and its impact on WMH severity. For each horn, we fit a circle through three points: the location of maximum cell tension, and the two locations left and right of this point where cell tension has dropped to 10% of the maximum value. We measure the radius r of the sphere as a critical measure for horn geometry. Mechanically, curvature κ, which is inversely proportional to horn radius r with κ = 1/r, directly correlates with cell tension and cell compression. Ventricles with small horn radius, that is with smaller volumes, are characterized by increased ependymal cell stretches; therefore, horn radius provides a predictive measure for the severity of cellular loading. Biologically, horn radius increases with age due to ventricular enlargement caused by tissue degeneration. We also determine the sections of the ventricular wall that are exposed to cell stretches above 10% of the maximum value. Specifically, we measure the length of the ventricular wall exposed to this critical cell stretch for each horn and divide this measure by the total wall length. The resulting measure provides the wall fraction with stretch exceeding a damaging ependymal cell stretch level.

Mechanomarkers for WMH formation
The ventricular wall is lined with cuboidal multiciliated cells that are tightly connected by cadherin junctions [30,31]. Our proposed damage mechanism rests on the hypothesis that ependymal cells experience a mechanical loading state that compromises their integrity. Specifically, we submit that the intercellular connections are particularly vulnerable to mechanical deformations and that their increased loading ultimately leads to failure and the leakage of CSF into the surrounding white matter, which appears as hyperintensities in FLAIR images. To that end, we determine cellular deformations and differentiate between ependymal cell tension in the direction tangential to the ventricular wall and ependymal cell compression in the direction normal to the ventricular wall, see Figure 2d5. We determine the normal and tangential wall directions from a Laplacian diffusion simulation for each of our eight FE models. We prescribe a temperature boundary condition of 1.0 • C on the nodes outlining the ventricular wall, 0.2 • C on the interface between gray and white matter, and of 0.0 • C for all nodes on the interface between gray matter and CSF. The resulting flux field allows us to identify the directions of the steepest temperature gradient n 0 , normal to the undeformed ventricular wall, and isothermes t 0 , tangential to the undeformed ventricular wall. We import the two vector fields into our simulations and project the right Cauchy-Green deformation tensor C onto these directions to obtain cell tension and cell compression. Specifically, we calculate the right Cauchy-Green strain tensor and project strains onto the normal and tangential directions, respectively, During post-processing of each simulation, we identify the nodes lining the ventricular wall, starting at the midpoint between the two posterior horns of the lateral ventricle and move counter-clockwise along the ventricular wall, see Figure 2d5. We then determine ependymal cell tension and ependymal cell compression in each node to arrive at the representations shown in Figures 5 and 6. Furthermore, we compute the maximum principal strains (MPS) from the Green-Lagrange strain field given by E = 1/2 (C − I), with identity tensor I. As shown in Figure 5, MPS is a representative measure for tissue loading in the vicinity of the ventricular wall and takes on a similar outline as the WMH mask.

Volumetric reconstruction of WMH volumes
We selected eight cognitively normal subjects from the NYU Alzheimer's Disease Research Center's imaging database (NYU ADRC). We separated the subjects by gender and sorted based on their total intracranial CSF volume [57]. We selected male and female subjects from the 20 th , 40 th , 60 th , and 80 th percentile of CSF volume, as shown in Figure 3, which are labeled as F20/F40/F60/F80 (females) and M20/M40/M60/M80 (males), respectively. Table 1  In males, WMH volume is 1.2 times larger than in females with a mean WMH volume of 9.4 cm 3 for male subjects and 7.8 cm 3 for female subjects. Figure 3 shows WMH caps around the anterior horns for F/M20, smooth WMH halos for F/M40-60, and increasingly diffuse and deep-reaching WMHs for F/M80.
The correlation between WMH volume growth and ventricular volume growth indicates that the process is driven by mechanics. Figure 4 shows the quantitative data of our cohort including CSF volume, LV volume, WMH volume, and horn radii. Our subjects' CSF volumes range from 421 cm 3 (20 th percentile) to 581 cm 3 (80 th percentile). Correspondingly, ventricular volumes range from 14 cm 3 (20 th percentile) to 74 cm 3 (80 th percentile). We observe a gradual increase in the WMH volumes with increasing LV volume, with WMH volumes ranging from 1.1 cm 3 to 20.7 cm 3 . Finally, we fitted a circle into each of the four horns visible in the selected axial slice, two anterior horns and two posterior (occipital) horns, respectively [58,59]. In our subjects, a consistent trend of increasing radius for brains with increasing LV volume is reported; we observe an average horn radius of 3.8 mm, 4.6 mm, 7.2 mm, and 8.5 mm for F20, F40, F60, and F80, respectively; and 2.9 mm, 6.3 mm, 7.5 mm, and 7.5 mm for M20, M40, M60, and M80, respectively. An increasing horn radius is a characteristic morphological manifestation of aging brains with increasing LV volume [60,29,8].

Ventricular changes in the aging brain
The CSF and LV volumes reported here are consistent with studies analyzing brain volume changes with age [61,62,63]. Taken together, our subjects are representative examples of age-related brain changes associated with healthy aging and the progressive worsening of WMHs starting with caps and resulting in irregular periventricular signal spreading into the surrounding white matter tissue [1].

Ependymal cell stretch along the ventricular wall
We created a detailed finite element model that incorporated structural properties of cerebral tissue for each subject. Cortical gray and white matter tissue, surrounding CSF, and the ventricular cavity are reconstructed as outlined in the methods section. We mimic the skull, which is orders of magnitudes stiffer than cerebral tissues, by prescribing zero-displacement boundary conditions on the outer periphery of our model. The brain deforms cyclically due to a combination of hemodynamic forces and CSF flow [64]. The lateral ventricles, in particular, undergo a piston-like motion causing cyclic volumetric expansion during systole [65]. Here, we represent this process as a quasi-static loading case during peak hydrostatic phase. We prescribe a hydrostatic pressure on the ventricular wall of 20 Pa, or 0.15 mmHg, and 1 Pa, or 0.0075 mmHg, on the gray matter-CSF interface [66,67,68]. Figure 5 shows the WMH mask in FLAIR images of our eight subjects, the maximum principal strain, and the computed ependymal cell stretches (EC stretch), associated with We simulated quasistatic ventricular expansion during peak loading to determine ventricular wall strain and ependymal cell stretch. The distribution of maximum principal strain (middle row) is consistent across all individuals, with peak strain localizing around the anterior and posterior horns of the lateral ventricles. Based on the deformation fields, we determine ependymal cell stretch along the ventricular wall. We calculate ependymal cell tension, which is tangential to the ependymal wall, and ependymal cell compression, which is perpendicular to the ependymal wall. We observe four distinct locations with maximum stretches along the wall. These coincide with the horns, as indicated by points A, B, C, and D. We report both stretch components for every point along the ependymal wall as shown in the ventricular representation in the legend.
cell tension (elongation) and cell compression (squeezing), see Figure 1c. We observe a significant increase in maximum principal strain in ventricular horns, with maximum values of up to 1.07 in female and 1.08 in male subjects. The maximum principal strain field is highest at the edge of the ventricles and diffuses towards deeper white matter. All eight subjects show a remarkably similar pattern of four sharp focal points with significantly increased cell stretches in both tension and compression. The locations of the four focal points coincide with the anterior and posterior horns of the lateral ventricles.

Patient-specific prediction of ventricular wall loading
We determine ependymal cell tension (tangential to wall) and ependymal cell compression (normal to the wall) by projecting the right Cauchy-Green deformation tensor onto the principal directions of the ependymal cells lining the ventricular wall. Despite pronounced variations in lateral ventricle geometry across our subjects, as Figure 6 shows, peak cell tension and cell compression consistently localize in the anterior (B, C) and posterior (A, D) horns. Comparison with the location of pvWMHs along the ventricular wall, as shown in Figure 5 (bottom row), reveals that tissue damage co-localizes in regions of peak cell stretches. The loading condition in these regions leads to ependymal cells being stretched thin and imposes a particularly high load on intercellular cadherin junctions [31]. The exterior sides of the ventricular wall (between points A and B, and between points C and D) experience negligible cell stretches. The anterior and posterior attachment points of the septum pellucidum (the wall section between points D and A, and between points B and C) exhibit slightly elevated stretches and cause cell compaction, i.e. the opposite loading state than in the horns. Therefore, we pose that the clinical observation of pvWMHs first appearing as localized caps in the anterior and posterior horn is in part driven by the particular mechanical loading state of ependymal cells [32]. Once initiated, pvWMHs deteriorate into bright-appearing linings and ultimately deeper reaching WMHs as LV wall failure worsens and CSF diffuses into deeper white matter regions [30,31,40]. Based on our initial analysis, it would be possible to model the progressive deterioration of periventricular tissue and the spreading of astrogliosis after wall failure.

Ventricular deterioration changes ependymal cell loading
Despite the significant reproducibility of the cellular loading pattern shown in Figure 6, we observe distinct differences between our subjects with larger LV volume and a clear trend towards an expanding ventricular geometry. As LV volume increases and ventricular horns enlarge, cellular stretch magnitude decreases, but the region of elevated cell stretch increases in comparison to sharp peaks in younger brains. Figure 7 shows how peak cell stretch and wall fraction with elevated cell tension relate to horn radius. As ventricular volume increases, horn radii increase as well. More strikingly, in spite of the small sample size, a Spearman's rank correlation test revealed a statistically significant negative correlation between peak stretch and horn radius (p¡0.0001, ρ=-0.65). While peak ependymal cell tension magnitude decreases for increasing horn radius, we observe that the ventricular wall fraction affected by elevated stretch increases with horn radius by up to a factor 3. These observations are critical in understanding the impact of mechanical loading on the progressive deterioration of the ependymal wall [8,29]. The ventricular geometry in young, healthy subjects is characterized by higher cell stretches. In older subjects, ependymal cells appear to experience mechanical fatigue due to their repeated mechanical loading. Accompanying cellular deterioration leads to CSF leakage into periventricular white matter and facilitates secondary tissue damage mechanisms in layers II-IV, see Figure 1. We pose that horn radius may be a reliable biomarker for the clinical assessment of a subject's Figure 7: Ventricular geometry is an indicator for peak cell stretch (top row) and the wall fraction exposed to elevated cell stretch (bottom row). We measure the radius of a sphere fitted to the anterior and posterior horns as a representative marker for ventricular geometry. We observe that peak cell stretch decreases for increasing horn radii and that an increasing wall section experiences elevated cell stretch as horn radius increases. Our observations suggest that younger brains with sharper ventricular horns, i.e., smaller horn radii, experience higher ependymal cell loading while aged brains (with larger horn radii) experience lower cell loads but elevated stretches on larger wall sections, i.e., increased width of cell stretch.
risk of developing pvWMHs or leukoaraiosis [60]. Figure 8: Sensitivity analysis of ventricular pressure level (top row) and mechanical brain tissue stiffness (bottom row) uncovers the impact on ependymal wall stretches. A ten-fold increase in referential ventricular pressure leads to cell stretch of up to 1.56 and cell compression as low as 0.71. In comparison, a four-fold increase in tissue stiffness reduces peak cell stretches by a factor 0.97 and a four-times lower shear modulus leads to a 1.07-fold increase in peak cell stretch. (All values are relative to tissue stiffness reported in the Methods section). Ventricular pressure is highly heterogeneous across subjects [71]. As discussed in the next section, ventricular pressure appears to be the critical parameter in the etiology of ependymal cell fatigue.

Sensitivity analysis of model parameters
We analyzed our model's sensitivity to ventricular wall pressure and white matter tissue stiffness, and show the results for subject F40 in Figure 8. We applied intracranial pressures of 0.5, 5, and 10 times the referential pressure of 20 Pa and observe a significant increase in the average peak cell stretch value of up to 1.56. Specifically, when applying 5-times the referential pressure, maximum cell tension increases by a factor of 1.21 and maximum cell compression increases by a factor of 1.18; when applying 10-times the referential pressure, maximum cell tension increases by a factor of 1.48 and maximum cell compression increases by a factor of 1.41. Strikingly, we observe a minimal effect on the lateral sides of the ventricular cavity and no shift in the location of peak stretches. The wall fraction exposed to increased cell tension increases with increasing pressure while the location of peak load remains unchanged. The range of ventricular pressures was based on literature reporting significant pressure variations for healthy subjects and subjects with hypertension and hydrocephalus [69,70,71]. This implies that subjects with increased intracranial or hemodynamic pressure are at an elevated risk to damage their ventricular wall and are more likely to develop leukoaraiosis [17]. We simulated variable tissue stiffness and compared cell stretches for white matter stiffness ranging from 25% to 400% of the original, experimentally observed stiffness to represent the range of values reported in literature [52,55,72]. In comparison to the variation in pressure, we observe a significantly lower effect, with a maximum 1.07-fold increase in peak cell loading, see Figure 8b. It is important to note, however, that tissue softening leads to increased cell loads. This provides further evidence that tissue degeneration is a mechanically driven mechanism that leads to accelerated tissue aging and pvWMH volume growth.

Risk factors for the onset of periventricular white matter lesions
Hydrocephalus and other neurological diseases that lead to increased intracranial and blood pressure pose a significant risk to the mechanical integrity of the ventricular wall [73,74,75]. It has been shown experimentally that a rapid increase in ventricular pressure leads to ependymal wall failure and the diffusion of CSF into white matter tissue [40]. Strikingly, this was observed to occur first in the ventricular horns, which agrees with our hypothesis that ependymal cells experience peak mechanical load in these locations which leads to functional failure. Therefore, our unifying physics-driven damage model explains the onset location of pvWMHs and is supported by histopathological studies on ventricle surface gliosis [76] and the observation of decreased white matter integrity [77]. Moreover, our model provides a rational for the different stages of pvWMHs as they evolve in parallel with the extended strain field observed in our simulations. Clearly, aging and small vessel disease are important risk factor as well. Peak wall loading in the form of ependymal cell thinning occurs in the horns and extends radially into deeper white matter. Lateral sides of the ventricles are exposed to negligible loads and are subsequently more protected [76]. Once the ventricular wall is disrupted, ependymal wall layers II-IV experience CSF influx and tissue damage due to inflammation and astrogliosis [30, ?]. It was shown that astrocytes cover the denuded ventricular walls of hydrocephalic hyh mutant mice to form a new cell layer with a cell organization that resembles the ependyma [35]. The fluid accumulation in the hypocellular layer triggers subsequent damage mechanisms such as astroglial scarring and the depletion of progenitor cells, which are required for tissue regeneration [34,35]. PVWMHs first appear as caps in the ventricular horns and are independent of a subject's ventricular shape at the time of onset. Although vascular damage is a driving force in WMHs, the consistent localization in horns suggests the involvement of additional factors. Based on our mechanics-driven hypothesis, sharp horns, i.e., small horn radii, cause high ependymal cell loads and therefore represent a critical additional risk factor for wall failure.

Predictive capabilities of our modeling approach
We use a single sample T-test to demonstrate the statistical significance of elevated cell stretch as a predictor for the presence of pvWMHs. To obtain an independent dataset, we sample every 50th point, or every 3.3 mm, along the ventricular wall from all eight subjects. We differentiate between cell stretch along the ventricular wall where pvWMHs are present (mean and standard deviation cell stretch 1.011±0.017) and compare them to the cell stretch where there are no pvWMHs (mean and standard deviation cell stretch 1.004±0.017).
The resulting dataset of 240 points reveals a significantly higher EC stretch where there are pvWMHs with t(238) = 2.63 and p < 0.01. Our numerical modeling approach proves most accurate for early stages of pvWMH formation, i.e., models M/F20 and M/F40. As pvWMHs increase and penetrate into deeper white matter regions, our current model requires additional mechanisms to propagate tissue deterioration from the ventricular wall into deeper layers of the periventricular zone. Specifically, our model requires a constitutive damage mechanism to quantify the degree of ependymal cell fatigue in order to trigger local tissue softening and the subsequent expansion of the critically loaded wall segments [78]. Distinct structural brain changes, such as cerebral atrophy [79,80] or white matter pathology [81], are useful biomarkers for diagnosis of abnormal aging. Our model identifies ependymal cell loading as a predictor for periventricular white matter lesion location. Cell loading magnitude is directly affected by ventricular pressure and LV shape. Therefore, identification of subjects with critical ventricular geometry, i.e. small horn radii, or increased cardiovascular risk would allow for early intervention via anti-hypertensive therapy [82]. Previous computational models of hydrocephalus have observed elevated interstitial pressure and tissue stress concentrations in the posterior and anterior horns as well [41,42,45]. While these models appear similar in the simulation approach, our primary interest in quantifying the cellular stretches of ependymal cells forming the ventricular wall is distinctly different. Our modeling approach is not without limitations. We select a representative axial slice showing the largest cross-sectional area of the lateral ventricles in order to create subject-specific two-dimensional finite element models. As shown in Figure 3, lateral ventricles have a complex geometry and are subject to threedimensional loading [46]. Even though we expect differences in the predicted deformation field between a 2D and 3D model, peak ependymal stretches will always appear in locations with high curvature, see Figure 7. Therefore, we anticipate that a 3D model would provide high cell stretches for cells lining the lateral sides of the lateral ventricles which would provide a more accurate overlap with WMHs observed in subjects with enlarged ventricles, see 3D reconstructions of WMHs in Figure 3. Next steps should aim at generating volumetric models to assess the full deformation field of the lateral ventricles. Secondly, we currently do not consider changes in mechanical properties associated with brain aging [83]. Neurodegeneration is associated with tissue softening of gray and white matter [84]. As indicated by our parameter sensitivity analysis, tissue softening leads to increased cell stretch, which is likely a major contributor to pvWMH volume growth. Future models should account for these changes in order to increase the predictive capabilities of our approach. Lastly, we assess ependymal cell stretch via a quasi-static loading case instead of studying the dynamic effects of CSF flow in the ventricles and pulsatile motion from the hemodynamic cycle. The lack of in vivo data on the ventricular wall motion, however, is a major limitation to validating a dynamic simulation [44]. Here, we juxtapose our subject-specific model results with their structural and functional image data to test our proposed mechanism. Measuring in vivo wall motion via novel MRI techniques [64] and a histological study of the temporal decay of the ventricular wall would provide valuable data to further support and improve the accuracy of our model.
In conclusion, our model is a first step in formulating a unifying theory for a physics-driven mechanism that explains the onset location of pvWMHs in the aging brain. We observe a mechanical loading state of the ventricular wall that causes ependymal cells to be stretched thin during each hemodynamic cycle. This particular loading state represents a major risk factor for cellular damage and functional and structural failure of the ventricular wall as it is repeatedly observed in pathology and histological studies on wall damage in aged brains. While vascular damage is a key contributor to pvWMHs, the consistent initial appearance as caps in the ventricular horns, is strongly indicative of a mechanical contribution to ventricular wall failure. We therefore suggest further investigation into the concise etiology and progression of pvWMHs and its prevention strategies.