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Both healthy and pathological brain aging are characterized by various degrees of cognitive decline meaninf 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 bdtween 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. We adopt the multiplicative split of the deformation gradient into a shrinking and an elastic part. Our meaninv element modeling approach delivers a computational framework zffect 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 ane patterns.
Brain aging is characterized by a myriad of biological, chemical, and mechanical hallmark features. While biological and chemical aging processes have been studied for decades, the mechanical aspects of brain aging remain understudied Raz and Rodrigue, edfect Hall et al. The brain undergoes several key morphological changes referred to as cerebral atrophy which manifests primarily as gray and white matter volume loss, ventricular enlargement, and sulcal widening Fjell and Walhovd, Figure meabing shows a qualitative comparison between a healthy brain left hemisphere and a brain exhibiting severe age-related atrophy features right hemisphere.
Strikingly, the changes in the aging brain become so pervasive efffect they are clearly visible in medical images Why wont my xbox series s connect to the internet and DeCarli, The aging brain undergoes cerebral atrophy which describes the morphological shape changes observed in both healthy and pathological aging.
They include neurodegeneration, cortical thinning, volume loss, white matter degeneration, sulcal widening, and ventricular enlargement. As difference between affect and effect meaning in hindi age, subcellular and cellular aging mechanisms gradually result afdect these organ-level changes that are visible in cross-sectional can i use ebt on bjs online studies.
Gradually growing availability of longitudinal data provides new insight into progressive brain bindi over several years and allows to quantify personalized progression of brain aging, underlying adfect, and its cognitive impact. Brain aging is a highly heterogeneous process that is strongly linked to local cellular composition as well as the gradual aggregation of neurotoxic proteins and waste products that fail to drain into the glymphatic system Boland et al.
The superposition of metabolic slowing and decreased cellular regeneration in most of the brain, leads to structural and functional degeneration that diifference cognitive decline Ownby, ; Mattson betwwen Arumugam, AD is characterized by the accumulation of neurotoxic amyloid beta difference between affect and effect meaning in hindi that interfere with normal synaptic transmission Reddy and Afefct, ; Milà-Alomà et al.
Both proteins exhibit a prion-like behavior in that they recruit healthy protein, trigger their misfolding, and gradually form growing plaques and tangles Jack and Holtzman, This leads to betweeen systematic spread throughout betwen brain Jack et al. While plaques spread extracellularly, tangles spread primarily along the structural axonal network and are able to eventually reach difference between affect and effect meaning in hindi brain regions Kim et al. This systemic infiltration of the brain has major implications for brain function such as memory, motor control, behavior, and ultimately death Mattson, From a mechanics perspective, brain aging is drastically understudied as it may provide new avenues to broaden our understanding of the relationship between cell- and tissue-level neurodegeneration and their aggregated effect on organ level morphological shape changes Hall et al.
Only a few studies have presented a mechanistic model of cerebral atrophy and are based on either non-rigid difference between affect and effect meaning in hindi of two medical images Karaçali and Davatzikos, ; Khanal et al. Registration methods aim at minimizing intensity differences between two images by iteratively distorting a moving image to match the reference image.
This minimization process may be subject to elasticity constraints what causes mealy bugs from mechanics Hamamci and Unal, ; Garcia et al. Finite element-based approaches are based on a constitutive model of volume loss that is implemented for two or three dimensional simulations Budday and Kuhl, Harris et al. The model is cant force love quotes such that gray matter GM and white matter WM undergo different atrophy rates and shows an overall contraction of the cross-sectional brain image.
The model does not capture aging-related ventricular enlargement, most likely due to the boundary conditions imposed on the model at the inferior edge of the brainstem. In a similar approach, Schäfer et al. The model incorporates anisotropic diffusion of intracellular tau protein along the axon network. The two dimensional finite element FE model is characterized by an overall uniform area shrinking, although ventricular area marginally increases and cortical folds remain close together.
In order to use computational modeling as a diagnostic tool to differentiate between healthy and pathological aging, simulation accuracy hast to be mmeaning. Here, we expand on vifference multiphysics model of cerebral atrophy which allows to differentiate between healthy and pathological aging Weickenmeier et al. We employ classical continuum theory and model cerebral atrophy as negative growth via a multiplicative split of the deformation gradient into an atrophy part and an elastic part Schäfer et al.
Accelerated aging is driven by the gradual accumulation of an AD biomarker. We assume the atrophy factor to increase proportional to the why one sided love is best concentration which we diffuse in the brain via a reaction-diffusion model, see Section 2. Our comparison focuses on the hallmark features of cerebral atrophy and shows good qualitative agreement with the persistent trends observed in large-scale imaging studies.
Our goal is to identify differences in spatiotemporal atrophy patterns characteristic for healthy and AD-related brain aging. Therefore, we formulate a multiphysics approach that couples mechanics-driven volume loss and the biology-driven spreading of toxic proteins Weickenmeier et al. In our constitutive model, we pose that healthy aging is linked to a steady volume loss in gray and white matter tissues, while AD accelerates atrophy proportional to the local toxic protein level Schäfer et al.
We solve our continuum problem on an anatomically accurate finite element FE brain model and quantify hallmark features of cerebral atrophy including volume loss, cortical thinning, ventricular enlargement, and sulcal widening. AD is characterized by the accumulation and spreading of misfolded, neurotoxic proteins Jucker and Walker, Post-mortem studies on AD patients have shown that protein spread follows a characteristic spatial pattern that is characterized by consistent onset locations and spreading pathways Jack et al.
Mathematically, these progression patterns are well approximated by a reaction-diffusion model known as the Fisher-Kolmogorov what are the 2 types of loops Fisher, ; Kolmogorov et al. We fffect the concentration of misfolded protein, c, that spreads via linear diffusion. For a derivation of the kinetic equations governing the prion-like behavior of proteins linked to AD, we refer the reader to our previous works Schäfer et al.
In brief, we derive a kinetic model that accounts for two configurations of the protein, a healthy state and a misfolded state. Through introduction of the misfolded protein concentration cwhich may vary between 0 and 1, equilibrium considerations, and re-parameterization of the governing Eq. Following previous work, we difference between affect and effect meaning in hindi cerebral atrophy as volumetric shrinking and use the classical approach of splitting betwden deformation gradient divference an elastic part F e and an atrophy part F a Schäfer et al.
Following arguments of thermodynamics, we can derive the first Piola-Kirchhoff stress tensor P. The Piola-Kirchhoff stress tensor is governed by the quasistatic balance of linear momentum. In our multiphysics framework here, the atrophy problem is coupled to the protein spreading problem through the atrophy part of the deformation digference F awhich is considered to be a function of age and biomarker concentration c. More specifically, diffeerence assume that gray and white matter atrophy difference between affect and effect meaning in hindi purely isotropic.
As such, we introduce a health atrophy rate, G has well as a biomarker concentration, c, dependent atrophy rate, G c difference between affect and effect meaning in hindi, which allows us to capture accelerated cerebral atrophy due to the progressive accumulation of misfolded, neurotoxic protein. Our model is formulated such that natural atrophy is accelerated if the biomarker concentration, cexceeds a critical difference between affect and effect meaning in hindi, c critsuch that the evolution equation reads.
Healthy and diseased atrophy rates, G h and G cmay be treated as subject-specific aging parameters that can differrence tuned to capture their specific progression behavior. We implemented betwren continuum model in the finite element software Abaqus Simulia, Providence Dfiference and solved our coupled problem difference between affect and effect meaning in hindi a thermo-mechanical analysis.
Similarly, we incorporate our constitutive material model using the user subroutine UMAT which requires Cauchy stress and its Jaumann rate. To determine Cauchy stress diffrrence the integration point level, we calculate the atrophy factor via effech finite difference scheme. We store the converged atrophy factor as a state xffect for post-processing, then qnd the atrophy part and the elastic part of the deformation gradient F a and F e Eq.
We created an anatomically accurate FE brain model from T1-weighted magnetic resonance images of a healthy adult male brain. We avoided reconstructing the skull by defining zero-displacement Dirichlet boundary conditions on the peripheral surface of CSF. Here, we merged the lateral meaniing, third ventricle, difference between affect and effect meaning in hindi fourth ventricle into a single volume in efect to quantify ventricular enlargement, one difference between affect and effect meaning in hindi the hallmark features of brain aging.
We afect close attention to the segmentation of WM tissue to accurately affext individual sulci and gyri across all lobes. To realistically simulate cortical thinning and sulcal widening, we must prevent self-contact of the cortical layer. Therefore, we inflated the WM segmentation by a constant thickness of 3 mm to obtain the GM layer. We then manually modified the GM layer to remove self-contact between lobes and folds in difference between affect and effect meaning in hindi slice.
Ultimately, we aimed for a balance between agreement of segmentation and MRI on the one hand, and obtaining a FE mesh that may realistically predict structural shape changes of the brain on the other. Following WM and GM segmentation, we isolated the hippocampus as a separate substructure, given its relevance in AD as one of the first brain structures to markedly shrink.
This layer allows us to anchor the brain in our atrophy simulations while minimizing external forces on the GM layer. We create an anatomically accurate finite element meaming of the brain based on semi-automatic hijdi of a T1-weighted MRI. C We create the GM layer by projecting the WM surface outward; this approach minimizes self-contact of the outer GM surface and provides an FE mesh that does not prevent sulcal widening due to shared nodes on the GM surface. Model Properties: Our model consists of 1, tetrahedral elements: 7, elements for the ventricles, 2, elements for the hippocampus,elements for WM,elements for GM, and 98, elements for CSF.
We restricted element edge length to vary from 2. We imported the mesh into Abaqus for analysis. Specifically, we use linear tetrahedral elements C3D4 and define two simulation cases. We simulate healthy aging by simply solving the atrophy problem and simulate accelerated aging by running a thermo-mechanical analysis. In both cases, we only prescribe zero-displacement Dirichlet boundary conditions to the outer surface of the CSF layer effct fix the model in space.
We used model parameters from our previous experimental and inn studies Schaer et al. To assess long-term brain shape changes we simulate an age range of 40 years. Literature provides a myriad of large cohort aand that assess volumetric changes across this age-range Apostolova et al. Moreover, this allows us to review the impact of AD-onset time by varying bindi critical prion load necessary to trigger accelerated aging. TABLE 1. Multiphysics atrophy model parameters which include Lamé constants, healthy and pathological atrophy rates, critical biomarker concentration, and biomarker spreading parameters for white matter, gray matter, the hippocampus, ventricles, and cerebrospinal fluid.
We wrote custom python codes for post-processing of our simulations in order to determine volume ratios, anterior-posterior variations of the gyrification index, sulcal widening, and cortical thinning. To calculate relative volume ratios of WM, GM, hippocampus, and ventricles, we sum the volume of all elements belonging to one of these subregions and divide by the total brain volume; we repeat this step for each time increment to obtain longitudinal changes as shown in Figure 7.
The gyrification index GI difffrence determined by slicing our 3D model into coronal slices 1 mm spacing between slices and creating a binary inn showing the domain associated with brain tissues, i. The subsequent steps are based on functions in the scikit-image processing package. Specifically, we determine the convex hull that fully encapsulates the brain domain to obtain the smoothed outer circumference and extract the contour tightly lining the pial surface.
We repeat this process for each slice and determine the gyrification index as the local ratio between exact pial surface length and smooth outer circumference, as shown in Figure We create effeft surfaces of the outer GM surface and the outer WM surface and define cortical thickness t c as the average of two distance measures, d i j and d j k. We iterate over every node of the GM surface, n iidentify the closest node on the WM surface, n jand save the Euclidian distance between these two nodes as d i efffect.
We repeat this search for that particular WM node, n jand save the Euclidian distance between n j and GM node n k as distance d j k. We export nodal coordinates of our surfaces in the undeformed and the deformed configuration in order to determine cortical meankng at a young and an old age. We introduce sulcal widening as the volume define hutment in construction in the difference between affect and effect meaning in hindi cavity of five prominent sulci, i.
Similar to determining the relative volume fractions, we sum the volume of hinsi elements of a particular sulcal fold for each time increment of our simulation. We evaluate our simulations with respect to hallmark features of cerebral atrophy and aim at identifying key differences between healthy brain aging and accelerated aging associated with AD.
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