Insights into the Mechanical Characterization of Mouse Brain Tissue Using Microindentation Testing.

Indentation testing is the most common approach to quantify mechanical brain tissue properties. Despite a myriad of studies conducted already, reported stiffness values vary extensively and continue to be subject of study. Moreover, the growing interest in the relationship between the brain's spatially heterogeneous microstructure and local tissue stiffness warrants the development of standardized measurement protocols to enable comparability between studies and assess repeatability of reported data. Here, we present three individual protocols that outline (1) sample preparation of a 1000-µm thick coronal slice, (2) a comprehensive list of experimental parameters associated with the FemtoTools FT-MTA03 Micromechanical Testing System for spherical indentation, and (3) two different approaches to derive the elastic modulus from raw force-displacement data. Lastly, we demonstrate that our protocols deliver a robust experimental framework that enables us to determine the spatially heterogeneous microstructural properties of (mouse) brain tissue. © 2024 Wiley Periodicals LLC. Basic Protocol 1: Mouse brain sample preparation Basic Protocol 2: Indentation testing of mouse brain tissue using the FemtoTools FT-MTA03 Micromechanical Testing and Assembly System Basic Protocol 3: Tissue stiffness identification from force-displacement data.

Brain Stiffness Follows Cuprizone-Induced Variations in Local Myelin Content.

Brain maturation and neurological diseases are intricately linked to microstructural changes that inherently affect the brain's mechanical behavior. Animal models are frequently used to explore relative brain stiffness changes as a function of underlying microstructure. Here, we are using the cuprizone mouse model to study indentation-derived stiffness changes resulting from acute and chronic demyelination during a 15-week observation period. We focus on the corpus callosum, cingulum, and cortex which undergo different degrees of de- and remyelination and, therefore, result in region-specific stiffness changes. Mean stiffness of the corpus callosum starts at 1.1 ± 0.3 kPa in untreated mice, then cuprizone treatment causes stiffness to drop to 0.6 ± 0.1 kPa by week 3, temporarily increase to 0.9 ± 0.3 kPa by week 6, and ultimately stabilize around 0.7 ± 0.1 kPa by week 9 for the rest of the observation period. The cingulum starts at 3.2 ± 0.9 kPa, then drops to 1.6 ± 0.4 kPa by week 3, and then gradually stabilizes around 1.4 ± 0.3 kPa by week 9. Cortical stiffness exhibits less stiffness variations overall; it starts at 4.2 ± 1.3 kPa, drops to 2.4 ± 0.6 kPa by week 3, and stabilizes around 2.7 ± 0.9 kPa by week 6. We also assess the impact of tissue fixation on indentation-based mechanical tissue characterization. On the one hand, fixation drastically increases untreated mean tissue stiffness by a factor of 3.3 for the corpus callosum, 2.9 for the cingulum, and 3.6 for the cortex; on the other hand, fixation influences interregional stiffness ratios during demyelination, thus suggesting that fixation affects individual brain tissues differently. Lastly, we determine the spatial correlation between stiffness measurements and myelin density and observe a region-specific proportionality between myelin content and tissue stiffness. STATEMENT OF SIGNIFICANCE: Despite extensive work, the relationship between microstructure and mechanical behavior in the brain remains mostly unknown. Additionally, the existing variation of measurement results reported in literature requires in depth investigation of the impact of individual cell and protein populations on tissue stiffness and interregional stiffness ratios. Here, we used microindentation measurements to show that brain stiffness changes with myelin density in the cuprizone-based demyelination mouse model. Moreover, we explored the impact of tissue fixation prior to mechanical characterization because of conflicting results reported in literature. We observe that fixation has a distinctly different impact on our three regions of interest, thus causing region-specific tissue stiffening and, more importantly, changing interregional stiffness ratios.

AI-dente: an open machine learning based tool to interpret nano-indentation data of soft tissues and materials.

Nano-indentation is a promising method to identify the constitutive parameters of soft materials, including soft tissues. Especially when materials are very small and heterogeneous, nano-indentation allows mechanical interrogation where traditional methods may fail. However, because nano-indentation does not yield a homogeneous deformation field, interpreting the resulting load-displacement curves is non-trivial and most investigators resort to simplified approaches based on the Hertzian solution. Unfortunately, for small samples and large indentation depths, these solutions are inaccurate. We set out to use machine learning to provide an alternative strategy. We first used the finite element method to create a large synthetic data set. We then used these data to train neural networks to inversely identify material parameters from load-displacement curves. To this end, we took two different approaches. First, we learned the indentation forward problem, which we then applied within an iterative framework to identify material parameters. Second, we learned the inverse problem of directly identifying material parameters. We show that both approaches are effective at identifying the parameters of the neo-Hookean and Gent models. Specifically, when applied to synthetic data, our approaches are accurate even for small sample sizes and at deep indentation. Additionally, our approaches are fast, especially compared to the inverse finite element approach. Finally, our approaches worked on unseen experimental data from thin mouse brain samples. Here, our approaches proved robust to experimental noise across over 1000 samples. By providing open access to our data and code, we hope to support others that conduct nano-indentation on soft materials.

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

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.

Exploring the multiphysics of the brain during development, aging, and in neurological diseases.

The human brain remains an endless source of wonder and represents an intruiging scientific frontier. Multiphysics approaches naturally lend themselves to combine our extensive knowledge about the neurobiology of aging and diseases with mechanics to better capture the multiscale behavior of the brain. Our group uses experimental methods, medical image analysis, and constitutive modeling to develop better disease models with the long-term goal to improve diagnosis, treatment, and ultimately enable prevention of many prevalent age- and disease-related brain changes. In the present perspective, we outline on-going work related to neurodevelopment, aging, and neurodegenerative disease.

Mechanical loading of the ventricular wall as a spatial indicator for periventricular white matter degeneration.

Progressive white matter degeneration in periventricular and deep white matter regions appears as white matter hyperintensities (WMH) on MRI scans. To date, periventricular WMHs are often associated with vascular dysfunction. Here, we demonstrate that ventricular inflation resulting from cerebral atrophy and hemodynamic pulsation with every heartbeat leads to a mechanical loading state of periventricular tissues that significantly affects the ventricular wall. Specifically, we present a physics-based modeling approach that provides a rationale for ependymal cell involvement in periventricular WMH formation. Building on eight previously created 2D finite element brain models, we introduce novel mechanomarkers for ependymal cell loading and geometric measures that characterize lateral ventricular shape. We show that our novel mechanomarkers, such as maximum ependymal cell deformations and maximum curvature of the ventricular wall, spatially overlap with periventricular WMH locations and are sensitive predictors for WMH formation. We also explore the role of the septum pellucidum in mitigating mechanical loading of the ventricular wall by constraining the radial expansion of the lateral ventricles during loading. Our models consistently show that ependymal cells are stretched thin only in the horns of the ventricles irrespective of ventricular shape. We therefore pose that periventricular WMH etiology is strongly linked to the deterioration of the over-stretched ventricular wall resulting in CSF leakage into periventricular white matter. Subsequent secondary damage mechanisms, including vascular degeneration, exacerbate lesion formation and lead to progressive growth into deep white matter regions.

3D finite-element brain modeling of lateral ventricular wall loading to rationalize periventricular white matter hyperintensity locations.

Aging-related periventricular white matter hyperintensities (pvWMHs) are a common observation in medical images of the aging brain. The underlying tissue damage is part of the complex pathophysiology associated with age-related microstructural changes and cognitive decline. PvWMH formation is linked to blood-brain barrier dysfunction from cerebral small vessel disease as well as the accumulation of cerebrospinal fluid in periventricular tissue due to progressive denudation of the ventricular wall. In need of a unifying theory for pvWMH etiology, image-based finite-element modeling is used to demonstrate that ventricular expansion from age-related cerebral atrophy and hemodynamic loading leads to maximum mechanical loading of the ventricular wall in the same locations that show pvWMHs. Ventricular inflation, induced via pressurization of the ventricular wall, creates significant ventricular wall stretch and stress on the ependymal cells lining the wall, that are linked to cerebrospinal fluid leaking from the lateral ventricles into periventricular white matter tissue. Eight anatomically accurate 3D brain models of cognitively healthy subjects with a wide range of ventricular shapes are created. For all models, our simulations show that mechanomarkers of mechanical wall loading are consistently highest in pvWMHs locations (p < 0.05). Maximum principal strain, the ependymal cell thinning ratio, and wall curvature are on average 14%, 8%, and 24% higher in pvWMH regions compared to the remaining ventricular wall, respectively. Computational modeling provides a powerful framework to systematically study pvWMH formation and growth with the goal to develop pharmacological interventions in the future.

Peak ependymal cell stretch overlaps with the onset locations of periventricular white matter lesions.

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 vascular degeneration in diffuse white matter locations; for pvWMHs, however, no unifying theory exists to explain their consistent onset around the horns of the lateral ventricles. We use patient imaging data to create anatomically accurate finite element models of the lateral ventricles, white and gray matter, and cerebrospinal fluid, as well as to reconstruct their WMH volumes. 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. Our simulations show that ependymal cells experience a loading state that causes the ventricular wall to be stretched thin. Moreover, we show that maximum wall loading coincides with the pvWMH locations observed in our patient scans. These results warrant further analysis of white matter pathology in the periventricular zone that includes a mechanics-driven deterioration model for the ventricular wall.

Brain aging mechanisms with mechanical manifestations.

Brain aging is a complex process that affects everything from the subcellular to the organ level, begins early in life, and accelerates with age. Morphologically, brain aging is primarily characterized by brain volume loss, cortical thinning, white matter degradation, loss of gyrification, and ventricular enlargement. Pathophysiologically, brain aging is associated with neuron cell shrinking, dendritic degeneration, demyelination, small vessel disease, metabolic slowing, microglial activation, and the formation of white matter lesions. In recent years, the mechanics community has demonstrated increasing interest in modeling the brain's (bio)mechanical behavior and uses constitutive modeling to predict shape changes of anatomically accurate finite element brain models in health and disease. Here, we pursue two objectives. First, we review existing imaging-based data on white and gray matter atrophy rates and organ-level aging patterns. This data is required to calibrate and validate constitutive brain models. Second, we review the most critical cell- and tissue-level aging mechanisms that drive white and gray matter changes. We focuse on aging mechanisms that ultimately manifest as organ-level shape changes based on the idea that the integration of imaging and mechanical modeling may help identify the tipping point when normal aging ends and pathological neurodegeneration begins.

The Geometry of Incompatibility in Growing Soft Tissues: Theory and Numerical Characterization.

Tissues in vivo are not stress-free. As we grow, our tissues adapt to different physiological and disease conditions through growth and remodeling. This adaptation occurs at the microscopic scale, where cells control the microstructure of their immediate extracellular environment to achieve homeostasis. The local and heterogeneous nature of this process is the source of residual stresses. At the macroscopic scale, growth and remodeling can be accurately captured with the finite volume growth framework within continuum mechanics, which is akin to plasticity. The multiplicative split of the deformation gradient into growth and elastic contributions brings about the notion of incompatibility as a plausible description for the origin of residual stress. Here we define the geometric features that characterize incompatibility in biological materials. We introduce the geometric incompatibility tensor for different growth types, showing that the constraints associated with growth lead to specific patterns of the incompatibility metrics. To numerically investigate the distribution of incompatibility measures, we implement the analysis within a finite element framework. Simple, illustrative examples are shown first to explain the main concepts. Then, numerical characterization of incompatibility and residual stress is performed on three biomedical applications: brain atrophy, skin expansion, and cortical folding. Our analysis provides new insights into the role of growth in the development of tissue defects and residual stresses. Thus, we anticipate that our work will further motivate additional research to characterize residual stresses in living tissue and their role in development, disease, and clinical intervention.

Brain Shape Changes Associated With Cerebral Atrophy in Healthy Aging and Alzheimer's Disease.

Both healthy and pathological brain aging are characterized by various degrees of cognitive decline that strongly correlate with morphological changes referred to as cerebral atrophy. These hallmark morphological changes include cortical thinning, white and gray matter volume loss, ventricular enlargement, and loss of gyrification all caused by a myriad of subcellular and cellular aging processes. While the biology of brain aging has been investigated extensively, the mechanics of brain aging remains vastly understudied. Here, we propose a multiphysics model that couples tissue atrophy and Alzheimer's disease biomarker progression. We adopt the multiplicative split of the deformation gradient into a shrinking and an elastic part. We model atrophy as region-specific isotropic shrinking and differentiate between a constant, tissue-dependent atrophy rate in healthy aging, and an atrophy rate in Alzheimer's disease that is proportional to the local biomarker concentration. Our finite element modeling approach delivers a computational framework to systematically study the spatiotemporal progression of cerebral atrophy and its regional effect on brain shape. We verify our results via comparison with cross-sectional medical imaging studies that reveal persistent age-related atrophy patterns. Our long-term goal is to develop a diagnostic tool able to differentiate between healthy and accelerated aging, typically observed in Alzheimer's disease and related dementias, in order to allow for earlier and more effective interventions.

Multiphysics of Prionlike Diseases: Progression and Atrophy.

Many neurodegenerative diseases are related to the propagation and accumulation of toxic proteins throughout the brain. The lesions created by aggregates of these toxic proteins further lead to cell death and accelerated tissue atrophy. A striking feature of some of these diseases is their characteristic pattern and evolution, leading to well-codified disease stages visible to neuropathology and associated with various cognitive deficits and pathologies. Here, we simulate the anisotropic propagation and accumulation of toxic proteins in full brain geometry. We show that the same model with different initial seeding zones reproduces the characteristic evolution of different prionlike diseases. We also recover the expected evolution of the total toxic protein load. Finally, we couple our transport model to a mechanical atrophy model to obtain the typical degeneration patterns found in neurodegenerative diseases.

Location-specific mechanical response and morphology of facial soft tissues.

The facial tissue of 9 healthy volunteers (m/f; age: 23-60y) is characterized at three different locations using a procedure combining suction measurements and 18MHz ultrasound imaging. The time-dependent and multilayered nature of skin is accounted for by adopting multiple loading protocols which differ with respect to suction probe opening size and rate of tissue deformation. Over 700 suction measurements were conducted and analyzed according to location-specific mechanical and morphological characteristics. All corresponding data are reported and made available for facial tissue analysis and biomechanical modeling. Higher skin stiffness is measured at the forehead in comparison to jaw and parotid; these two regions are further characterized by lower creep deformation. Thicker tissue regions display a tendency towards a more compliant and less dissipative response. Comparison of superficial layer thickness and corresponding mechanical measurements suggests that connective tissue density determines the resistance to deformation in suction experiments.

Magnetic resonance elastography of the brain: A comparison between pigs and humans.

Magnetic resonance elastography holds promise as a non-invasive, easy-to-use, in vivo biomarker for neurodegenerative diseases. Throughout the past decade, pigs have gained increased popularity as large animal models for human neurodegeneration. However, the volume of a pig brain is an order of magnitude smaller than the human brain, its skull is 40% thicker, and its head is about twice as big. This raises the question to which extent established vibration devices, actuation frequencies, and analysis tools for humans translate to large animal studies in pigs. Here we explored the feasibility of using human brain magnetic resonance elastography to characterize the dynamic properties of the porcine brain. In contrast to humans, where vibration devices induce an anterior-posterior displacement recorded in transverse sections, the porcine anatomy requires a dorsal-ventral displacement recorded in coronal sections. Within these settings, we applied a wide range of actuation frequencies, from 40Hz to 90Hz, and recorded the storage and loss moduli for human and porcine brains. Strikingly, we found that optimal actuation frequencies for humans translate one-to-one to pigs and reliably generate shear waves for elastographic post-processing. In a direct comparison, human and porcine storage and loss moduli followed similar trends and increased with increasing frequency. When translating these frequency-dependent storage and loss moduli into the frequency-independent stiffnesses and viscosities of a standard linear solid model, we found human values of µ1=1.3kPa, µ2=2.1kPa, and η=0.025kPas and porcine values of µ1=2.0kPa, µ2=4.9kPa, and η=0.046kPas. These results suggest that living human brain is softer and less viscous than dead porcine brain. Our study compares, for the first time, magnetic resonance elastography in human and porcine brains, and paves the way towards systematic interspecies comparison studies and ex vivo validation of magnetic resonance elastography as a whole.

Dimensional, Geometrical, and Physical Constraints in Skull Growth.

After birth, the skull grows and remodels in close synchrony with the brain to allow for an increase in intracranial volume. Increase in skull area is provided primarily by bone accretion at the sutures. Additional remodeling, to allow for a change in curvatures, occurs by resorption on the inner surface of the bone plates and accretion on their outer surfaces. When a suture fuses too early, normal skull growth is disrupted, leading to a deformed final skull shape. The leading theory assumes that the main stimulus for skull growth is provided by mechanical stresses. Based on these ideas, we first discuss the dimensional, geometrical, and kinematic synchrony between brain, skull, and suture growth. Second, we present two mechanical models for skull growth that account for growth at the sutures and explain the various observed dysmorphologies. These models demonstrate the particular role of physical and geometrical constraints taking place in skull growth.

Weekly Time Course of Neuro-Muscular Adaptation to Intensive Strength Training.

Detailed description of the time course of muscular adaptation is rarely found in literature. Thus, models of muscular adaptation are difficult to validate since no detailed data of adaptation are available. In this article, as an initial step toward a detailed description and analysis of muscular adaptation, we provide a case report of 8 weeks of intense strength training with two active, male participants. Muscular adaptations were analyzed on a morphological level with MRI scans of the right quadriceps muscle and the calculation of muscle volume, on a voluntary strength level by isometric voluntary contractions with doublet stimulation (interpolated twitch technique) and on a non-voluntary level by resting twitch torques. Further, training volume and isokinetic power were closely monitored during the training phase. Data were analyzed weekly for 1 week prior to training, pre-training, 8 weeks of training and 2 weeks of detraining (no strength training). Results show a very individual adaptation to the intense strength training protocol. While training volume and isokinetic power increased linearly during the training phase, resting twitch parameters decreased for both participants after the first week of training and stayed below baseline until de-training. Voluntary activation level showed an increase in the first 4 weeks of training, while maximum voluntary contraction showed only little increase compared to baseline. Muscle volume increased for both subjects. Especially training status seemed to influence the acute reaction to intense strength training. Fatigue had a major influence on performance and could only be overcome by one participant. The results give a first detailed insight into muscular adaptation to intense strength training on various levels, providing a basis of data for a validation of muscle fatigue and adaptation models.

The mechanical importance of myelination in the central nervous system.

Neurons in the central nervous system are surrounded and cross-linked by myelin, a fatty white substance that wraps around axons to create an electrically insulating layer. The electrical function of myelin is widely recognized; yet, its mechanical importance remains underestimated. Here we combined nanoindentation testing and histological staining to correlate brain stiffness to the degree of myelination in immature, pre-natal brains and mature, post-natal brains. We found that both gray and white matter tissue stiffened significantly (p≪0.001) upon maturation: the gray matter stiffness doubled from 0.31±0.20kPa pre-natally to 0.68±0.20kPa post-natally; the white matter stiffness tripled from 0.45±0.18kPa pre-natally to 1.33±0.64kPa post-natally. At the same time, the white matter myelin content increased significantly (p≪0.001) from 58±2% to 74±9%. White matter stiffness and myelin content were correlated with a Pearson correlation coefficient of ρ=0.92 (p≪0.001). Our study suggests that myelin is not only important to ensure smooth electrical signal propagation in neurons, but also to protect neurons against physical forces and provide a strong microstructural network that stiffens the white matter tissue as a whole. Our results suggest that brain tissue stiffness could serve as a biomarker for multiple sclerosis and other forms of demyelinating disorders. Understanding how tissue maturation translates into changes in mechanical properties and knowing the precise brain stiffness at different stages of life has important medical implications in development, aging, and neurodegeneration.

Stress Singularities in Swelling Soft Solids.

When a swelling soft solid is rigidly constrained on all sides except for a circular opening, it will bulge out to expand as observed during decompressive craniectomy, a surgical procedure used to reduce stresses in swollen brains. While the elastic energy of the solid decreases throughout this process, large stresses develop close to the opening. At the point of contact, the stresses exhibit a singularity similar to the ones found in the classic punch indentation problem. Here, we study the stresses generated by swelling and the evolution of the bulging shape associated with this process. We also consider the possibility of damage triggered by zones of either high shear stresses or high fiber stretches.

Tri-layer wrinkling as a mechanism for anchoring center initiation in the developing cerebellum.

During cerebellar development, anchoring centers form at the base of each fissure and remain fixed in place while the rest of the cerebellum grows outward. Cerebellar foliation has been extensively studied; yet, the mechanisms that control anchoring center initiation and position remain insufficiently understood. Here we show that a tri-layer model can predict surface wrinkling as a potential mechanism to explain anchoring center initiation and position. Motivated by the cerebellar microstructure, we model the developing cerebellum as a tri-layer system with an external molecular layer and an internal granular layer of similar stiffness and a significantly softer intermediate Purkinje cell layer. Including a weak intermediate layer proves key to predicting surface morphogenesis, even at low stiffness contrasts between the top and bottom layers. The proposed tri-layer model provides insight into the hierarchical formation of anchoring centers and establishes an essential missing link between gene expression and evolution of shape.