A multiphysics model to predict periventricular white matter hyperintensity growth during healthy brain aging

Abstract

Periventricular white matter hyperintensities (WMH) are a common finding in medical images of the aging brain and are associated with white matter damage resulting from cerebral small vessel disease, white matter inflammation, and a degeneration of the lateral ventricular wall. Despite extensive work, the etiology of periventricular WMHs remains unclear. We pose that there is a strong coupling between age-related ventricular expansion and the degeneration of the ventricular wall which leads to a dysregulated fluid exchange across this brain-fluid barrier. Here, we present a multiphysics model that couples cerebral atrophy-driven ventricular wall loading with periventricular WMH formation and progression. We use patient data to create eight 2D finite element models and demonstrate the predictive capabilities of our damage model. Our simulations show that we accurately capture the spatiotemporal features of periventricular WMH growth. For one, we observe that damage appears first in both the anterior and posterior horns and then spreads into deeper white matter tissue. For the other, we note that it takes up to 12 years before periventricular WMHs first appear and derive an average annualized periventricular WMH damage growth rate of 15.2 ± 12.7 mm²/year across our models. A sensitivity analysis demonstrated that our model parameters provide sufficient sensitivity to rationalize subject-specific differences with respect to onset time and damage growth. Moreover, we show that the septum pellucidum, a membrane that separates the left and right lateral ventricles, delays the onset of periventricular WMHs at first, but leads to a higher WMH load in the long-term.

Keywords: Finite element modeling; Multiphysics damage model; Periventricular white matter hyperintensities; Ventricular wall loading.

Fig. 1.

Atrophy-driven periventricular white matter hyperintensity (WMH) formation and growth. Progressive neurodegeneration causes ventricular expansion (blue region) that creates increasing ventricular wall loading and is accompanied by increasing WMH volume (red region). The healthy ventricular wall, i.e. the functional barrier between fluid and tissue formed by ependymal cells, gradually degenerates causing cerebrospinal fluid to leak into periventricular white matter forming thin linings at first which devolve into smooth halos and irregular large WMH areas in the long-term [17]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 2.

Patient data-based 2D finite element models used to simulate periventricular white matter hyperintensity (WMH) formation (first row). For various levels of ventricular enlargement (columns), we show the underlying age-related brain atrophy (second row) that drives brain deformation (third row) and related ependymal cell thinning (fourth row). Our multiphysics model couples atrophy to a periventricular WMH damage field that captures the white matter regions associated with WMHs (fifth row).

Fig. 3.

Atrophy-related simulation results. For each model, we show the displacement magnitude field for the undeformed (left hemisphere) and deformed configuration (right hemisphere) to visualize ventricular enlargement (top row). We interpret brain deformations with respect to normal (left hemisphere) and tangential stretch (right hemisphere) in the tissue based on direction vectors obtained from a Laplacian problem a priori. We use these fields to calculate the thinning ratio which we exclusively evaluate along the ventricular wall [25,27] (third row). In the line plots, the solid line in each plot indicates the thinning ratio at 20% ventricular enlargement.

Fig. 4.

Periventricular white matter hyperintensity (WMH) damage field progression evaluated at 0%, 10%, 12.5%, 15%, 17.5%, and 20% ventricular enlargement for each of our eight models. We observe various damage onset times and spatial progression behaviors that are dependent on initial ventricle and brain shape. We obtain the periventricular WMH damage field after binarizing the damage field variable c which allows us to differentiate between healthy white matter, normal-appearing white matter, and periventricular WMH. We summarized periventricular WMH areas in Table 1 in the Appendix.

Fig. 5.

Comparison between models with and without the septum pellucidum: (a) periventricular white matter hyperintensity (WMH) progression over time for all eight models without the septum and (b) model with the septum. Markers indicate when predicted periventricular WMH area matches our patients’ MRI findings; (c) relative difference between model without and with septum to see the temporal delay of periventricular WMH onset. Rows two and three show the periventricular WMH damage field after 20 years of aging and indicate that the septum exacerbates the damage field in the long-term. The last row shows the FLAIR patient data associated with our eight models and demonstrates excellent agreement between predicted and clinically observed periventricular WMH locations (red regions). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 6.

Averaged periventricular white matter hyperintensity (WMH) damage onset time for models without the septum (left) and with the septum (right). Anterior and posterior horns are affected up to 6 years earlier than most other ventricular wall sections. Moreover, the septum delays periventricular WMH onset on the one hand and adds two additional onset locations, i.e., the anterior and posterior innervation points with white matter, on the other.

Fig. 7.

Model parameter sensitivity analysis. We vary both the damage severity parameter α (left) and white-gray-matter atrophy ratio γ (right). While damage severity predominantly increases periventricular white matter hyperintensity area, varying the atrophy rate significantly influences damage onset time.