We propose a novel image-informed glioblastoma mathematical model within a reactive multiphase poromechanical framework. Poromechanics offers to model in a coupled manner the interplay between tissue deformation and pressure-driven fluid flows, these phenomena existing simultaneously in cancer disease. The model also relies on two mechano-biological hypotheses responsible for the heterogeneity of the GBM: hypoxia signaling cascade and interaction between extra-cellular matrix and tumor cells. The model belongs to the category of patient-specific image-informed models as it is initialized, calibrated and evaluated by the means of patient imaging data. The model is calibrated with patient data after 6 cycles of concomitant radiotherapy chemotherapy and shows good agreement with treatment response 3 months after chemotherapy maintenance. Sensitivity of the solution to parameters and to boundary conditions is provided. As this work is only a first step of the inclusion of poromechanical framework in image-informed glioblastoma mathematical models, leads of improvement are provided in the conclusion.
Statement of Significance: In this study, we employ mechanics of reactive porous media to effectively model the dynamic progression of a glioblastoma. Traditionally, glioblastoma tumors are surgically removed a few weeks post-diagnosis. To address this, we focus on a non-operable clinical scenario which allows us to have sufficient time points for the calibration and subsequent validation of our mathematical model. It is paramount to underscore that the tumor’s evolution is significantly influenced by chemotherapy and radiotherapy. These therapeutic effects find incorporation within our mathematical framework. Notably, the approach we present is distinctive for two key reasons: Firstly, the mathematical model inherently captures the complex multiphase and hierarchical nature of brain tissue. Secondly, our constitutive laws factor in the ever-changing properties of cells and tissues, mirroring the local phenotypic alterations observed within the tumor. This work constitutes an initial stride towards systematically integrating multiphase poromechanics into patient-specific glioblastoma growth modeling. As we look ahead, we acknowledge areas for potential enhancement in pursuit of advancing this promising direction.
{"title":"Non-operable glioblastoma: Proposition of patient-specific forecasting by image-informed poromechanical model","authors":"Stéphane Urcun , Davide Baroli , Pierre-Yves Rohan , Wafa Skalli , Vincent Lubrano , Stéphane P.A. Bordas , Giuseppe Sciumè","doi":"10.1016/j.brain.2023.100067","DOIUrl":"https://doi.org/10.1016/j.brain.2023.100067","url":null,"abstract":"<div><p>We propose a novel image-informed glioblastoma mathematical model within a reactive multiphase poromechanical framework. Poromechanics offers to model in a coupled manner the interplay between tissue deformation and pressure-driven fluid flows, these phenomena existing simultaneously in cancer disease. The model also relies on two mechano-biological hypotheses responsible for the heterogeneity of the GBM: hypoxia signaling cascade and interaction between extra-cellular matrix and tumor cells. The model belongs to the category of patient-specific image-informed models as it is initialized, calibrated and evaluated by the means of patient imaging data. The model is calibrated with patient data after 6 cycles of concomitant radiotherapy chemotherapy and shows good agreement with treatment response 3 months after chemotherapy maintenance. Sensitivity of the solution to parameters and to boundary conditions is provided. As this work is only a first step of the inclusion of poromechanical framework in image-informed glioblastoma mathematical models, leads of improvement are provided in the conclusion.</p><p><strong>Statement of Significance:</strong> In this study, we employ mechanics of reactive porous media to effectively model the dynamic progression of a glioblastoma. Traditionally, glioblastoma tumors are surgically removed a few weeks post-diagnosis. To address this, we focus on a non-operable clinical scenario which allows us to have sufficient time points for the calibration and subsequent validation of our mathematical model. It is paramount to underscore that the tumor’s evolution is significantly influenced by chemotherapy and radiotherapy. These therapeutic effects find incorporation within our mathematical framework. Notably, the approach we present is distinctive for two key reasons: Firstly, the mathematical model inherently captures the complex multiphase and hierarchical nature of brain tissue. Secondly, our constitutive laws factor in the ever-changing properties of cells and tissues, mirroring the local phenotypic alterations observed within the tumor. This work constitutes an initial stride towards systematically integrating multiphase poromechanics into patient-specific glioblastoma growth modeling. As we look ahead, we acknowledge areas for potential enhancement in pursuit of advancing this promising direction.</p></div>","PeriodicalId":72449,"journal":{"name":"Brain multiphysics","volume":"4 ","pages":"Article 100067"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49817662","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01Epub Date: 2023-03-08DOI: 10.1016/j.brain.2023.100065
Ramin Balouchzadeh, Philip V Bayly, Kara E Garcia
The majority of human brain folding occurs during the third trimester of gestation. Although many studies have investigated the physical mechanisms of brain folding, a comprehensive understanding of this complex process has not yet been achieved. In mechanical terms, the "differential growth hypothesis" suggests that the formation of folds results from a difference in expansion rates between cortical and subcortical layers, which eventually leads to mechanical instability akin to buckling. It has also been observed that axons, a substantial component of subcortical tissue, can elongate or shrink under tensile or compressive stress, respectively. Previous work has proposed that this cell-scale behavior in aggregate can produce stress-dependent growth in the subcortical layers. The current study investigates the potential role of stress-dependent growth on cortical surface morphology, in particular the variations in folding direction and curvature over the course of development. Evolution of sulcal direction and mid-cortical surface curvature were calculated from finite element simulations of three-dimensional folding in four different initial geometries: (i) sphere; (ii) axisymmetric oblate spheroid; (iii) axisymmetric prolate spheroid; and (iv) triaxial spheroid. The results were compared to mid-cortical surface reconstructions from four preterm human infants, imaged and analyzed at four time points during the period of brain folding. Results indicate that models incorporating subcortical stress-dependent growth predict folding patterns that more closely resemble those in the developing human brain.
Statement of significance: Cortical folding is a critical process in human brain development. Aberrant folding is associated with disorders such as autism and schizophrenia, yet our understanding of the physical mechanism of folding remains limited. Ultimately mechanical forces must shape the brain. An important question is whether mechanical forces simply deform tissue elastically, or whether stresses in the tissue modulate growth. Evidence from this paper, consisting of quantitative comparisons between patterns of folding in the developing human brain and corresponding patterns in simulations, supports a key role for stress-dependent growth in cortical folding.
{"title":"Effects of stress-dependent growth on evolution of sulcal direction and curvature in models of cortical folding.","authors":"Ramin Balouchzadeh, Philip V Bayly, Kara E Garcia","doi":"10.1016/j.brain.2023.100065","DOIUrl":"10.1016/j.brain.2023.100065","url":null,"abstract":"<p><p>The majority of human brain folding occurs during the third trimester of gestation. Although many studies have investigated the physical mechanisms of brain folding, a comprehensive understanding of this complex process has not yet been achieved. In mechanical terms, the \"differential growth hypothesis\" suggests that the formation of folds results from a difference in expansion rates between cortical and subcortical layers, which eventually leads to mechanical instability akin to buckling. It has also been observed that axons, a substantial component of subcortical tissue, can elongate or shrink under tensile or compressive stress, respectively. Previous work has proposed that this cell-scale behavior in aggregate can produce stress-dependent growth in the subcortical layers. The current study investigates the potential role of stress-dependent growth on cortical surface morphology, in particular the variations in folding direction and curvature over the course of development. Evolution of sulcal direction and mid-cortical surface curvature were calculated from finite element simulations of three-dimensional folding in four different initial geometries: (i) sphere; (ii) axisymmetric oblate spheroid; (iii) axisymmetric prolate spheroid; and (iv) triaxial spheroid. The results were compared to mid-cortical surface reconstructions from four preterm human infants, imaged and analyzed at four time points during the period of brain folding. Results indicate that models incorporating subcortical stress-dependent growth predict folding patterns that more closely resemble those in the developing human brain.</p><p><strong>Statement of significance: </strong>Cortical folding is a critical process in human brain development. Aberrant folding is associated with disorders such as autism and schizophrenia, yet our understanding of the physical mechanism of folding remains limited. Ultimately mechanical forces must shape the brain. An important question is whether mechanical forces simply deform tissue elastically, or whether stresses in the tissue modulate growth. Evidence from this paper, consisting of quantitative comparisons between patterns of folding in the developing human brain and corresponding patterns in simulations, supports a key role for stress-dependent growth in cortical folding.</p>","PeriodicalId":72449,"journal":{"name":"Brain multiphysics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11213281/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"54406126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.1016/j.brain.2023.100071
Shuolun Wang , Xincheng Wang , Maria A. Holland
The neuron serves as the basic computational unit for the brain. Altered neuronal morphologies are usually found in various neurological diseases, such as Down syndrome, Williams syndrome, and idiopathic autism. Compelling biological evidence demonstrates that neuronal morphology can be dynamically regulated by neuronal activity through the mediation of calcium signaling pathways. Moreover, studies have revealed that exposure to an applied electric field can induce directional migration of neurites toward the cathode. In this study, we developed a coupled system that combines an advective Gray–Scott model with Gauss’s law to gain a better understanding of dendrite growth and response to electrical polarization. Our simulation results successfully capture key features such as dendrite branching, space-filling, self-avoidance, and electrical polarization. With the help of the convolutional neural network, we inversely identified model parameters of real dendrite morphologies from an online open source. Finally, we calibrated our model using experimental data on growing neurons under applied electric fields.
Statement of Significance: The work sheds light on the underlying mechanisms that govern the growth of neuronal dendrites under electrical polarization via mathematical modeling and numerical simulations. We also use a machine-learning technique to calibrate the model against real neuron images. Our numerical implementations and machine-learning pipeline provided online would benefit researchers in understanding the development of various abnormal neuronal morphologies and related neurological diseases.
{"title":"Multi-physics modeling and finite-element formulation of neuronal dendrite growth with electrical polarization","authors":"Shuolun Wang , Xincheng Wang , Maria A. Holland","doi":"10.1016/j.brain.2023.100071","DOIUrl":"10.1016/j.brain.2023.100071","url":null,"abstract":"<div><p>The neuron serves as the basic computational unit for the brain. Altered neuronal morphologies are usually found in various neurological diseases, such as Down syndrome, Williams syndrome, and idiopathic autism. Compelling biological evidence demonstrates that neuronal morphology can be dynamically regulated by neuronal activity through the mediation of calcium signaling pathways. Moreover, studies have revealed that exposure to an applied electric field can induce directional migration of neurites toward the cathode. In this study, we developed a coupled system that combines an advective Gray–Scott model with Gauss’s law to gain a better understanding of dendrite growth and response to electrical polarization. Our simulation results successfully capture key features such as dendrite branching, space-filling, self-avoidance, and electrical polarization. With the help of the convolutional neural network, we inversely identified model parameters of real dendrite morphologies from an online open source. Finally, we calibrated our model using experimental data on growing neurons under applied electric fields.</p><p><strong>Statement of Significance</strong>: The work sheds light on the underlying mechanisms that govern the growth of neuronal dendrites under electrical polarization via mathematical modeling and numerical simulations. We also use a machine-learning technique to calibrate the model against real neuron images. Our numerical implementations and machine-learning pipeline provided online would benefit researchers in understanding the development of various abnormal neuronal morphologies and related neurological diseases.</p></div>","PeriodicalId":72449,"journal":{"name":"Brain multiphysics","volume":"4 ","pages":"Article 100071"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44158647","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.1016/j.brain.2022.100061
Rahul Gulati, Shiva Rudraraju
Action potential propagation along the axons and across the dendrites is the foundation of the electrical activity observed in the brain and the rest of the nervous system. Theoretical and numerical modeling of this action potential activity has long been a key focus area of electro-chemical neuronal modeling, and over the years, electrical network models of varying complexity have been proposed. Specifically, considering the presence of nodes of Ranvier along the myelinated axon, single-cable models of the propagation of action potential have been popular. Building on these models, and considering a secondary electrical conduction pathway below the myelin sheath, the double-cable model has been proposed. Such cable theory based treatments, including the classical Hodgkin–Huxley model, single-cable model, and double-cable model have been extensively studied in the literature. But these have inherent limitations in their lack of a representation of the spatio-temporal evolution of the neuronal electro-chemistry. In contrast, a Poisson–Nernst–Planck (PNP) based electro-diffusive framework accounts for the underlying spatio-temporal ionic concentration dynamics and is a more general and comprehensive treatment. In this work, a high-fidelity implementation of the PNP model is demonstrated. This electro-diffusive model is shown to produce results similar to the cable theory based electrical network models, and in addition, the rich spatio-temporal evolution of the underlying ionic transport is captured. Novel to this work is the extension of PNP model to axonal geometries with multiple nodes of Ranvier, its correlation with cable theory based models, and multiple variants of the electro-diffusive model — PNP without myelin, PNP with myelin, and PNP with the myelin sheath and peri-axonal space. Further, we apply this spatio-temporal model to numerically estimate conduction velocity in a rat axon using the three model variants. Specifically, spatial saltatory conduction due to the presence of myelin sheath and the peri-axonal space is investigated.
Statement of Significance: In this work, we present a comprehensive PDE based treatment for modeling neuronal action potential generation and propagation and provide a first-of-its-kind framework for computationally estimating action potential conduction velocities. This electro-diffusive model, based on a Poisson-Nernst-Planck (PNP) formulation, is shown to produce results similar to the cable theory based electrical network models, and in addition, the rich spatio-temporal evolution of the underlying ionic transport is captured. Novel to this work is the extension of PNP model to axonal geometries with multiple nodes of Ranvier, its correlation with cable theory based models, and multiple variants of the electro-diffusive model - PNP without myelin, PNP with myelin, and PNP with the myelin sheath and periaxonal space. Further, we apply this spatio-temporal model to numerically
{"title":"Spatio-temporal modeling of saltatory conduction in neurons using Poisson–Nernst–Planck treatment and estimation of conduction velocity","authors":"Rahul Gulati, Shiva Rudraraju","doi":"10.1016/j.brain.2022.100061","DOIUrl":"https://doi.org/10.1016/j.brain.2022.100061","url":null,"abstract":"<div><p>Action potential propagation along the axons and across the dendrites is the foundation of the electrical activity observed in the brain and the rest of the nervous system. Theoretical and numerical modeling of this action potential activity has long been a key focus area of electro-chemical neuronal modeling, and over the years, electrical network models of varying complexity have been proposed. Specifically, considering the presence of nodes of Ranvier along the myelinated axon, single-cable models of the propagation of action potential have been popular. Building on these models, and considering a secondary electrical conduction pathway below the myelin sheath, the double-cable model has been proposed. Such cable theory based treatments, including the classical Hodgkin–Huxley model, single-cable model, and double-cable model have been extensively studied in the literature. But these have inherent limitations in their lack of a representation of the spatio-temporal evolution of the neuronal electro-chemistry. In contrast, a Poisson–Nernst–Planck (PNP) based electro-diffusive framework accounts for the underlying spatio-temporal ionic concentration dynamics and is a more general and comprehensive treatment. In this work, a high-fidelity implementation of the PNP model is demonstrated. This electro-diffusive model is shown to produce results similar to the cable theory based electrical network models, and in addition, the rich spatio-temporal evolution of the underlying ionic transport is captured. Novel to this work is the extension of PNP model to axonal geometries with multiple nodes of Ranvier, its correlation with cable theory based models, and multiple variants of the electro-diffusive model — PNP without myelin, PNP with myelin, and PNP with the myelin sheath and peri-axonal space. Further, we apply this spatio-temporal model to numerically estimate conduction velocity in a rat axon using the three model variants. Specifically, spatial saltatory conduction due to the presence of myelin sheath and the peri-axonal space is investigated.</p><p><strong>Statement of Significance</strong>: In this work, we present a comprehensive PDE based treatment for modeling neuronal action potential generation and propagation and provide a first-of-its-kind framework for computationally estimating action potential conduction velocities. This electro-diffusive model, based on a Poisson-Nernst-Planck (PNP) formulation, is shown to produce results similar to the cable theory based electrical network models, and in addition, the rich spatio-temporal evolution of the underlying ionic transport is captured. Novel to this work is the extension of PNP model to axonal geometries with multiple nodes of Ranvier, its correlation with cable theory based models, and multiple variants of the electro-diffusive model - PNP without myelin, PNP with myelin, and PNP with the myelin sheath and periaxonal space. Further, we apply this spatio-temporal model to numerically","PeriodicalId":72449,"journal":{"name":"Brain multiphysics","volume":"4 ","pages":"Article 100061"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49817663","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.1016/j.brain.2023.100076
Silvia Budday
{"title":"Exploring human brain mechanics by combining experiments, modeling, and simulation","authors":"Silvia Budday","doi":"10.1016/j.brain.2023.100076","DOIUrl":"https://doi.org/10.1016/j.brain.2023.100076","url":null,"abstract":"","PeriodicalId":72449,"journal":{"name":"Brain multiphysics","volume":"5 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49856611","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.1016/j.brain.2023.100063
Robert Bazala , Giorgio Zoppellaro , Gunther Kletetschka
Nanosized magnetite inside ferritin may control the progression of neurodegenerative disease (ND) by creating an electronic noise in the neural cells. We discovered that brains with ND have a unique electron paramagnetic resonance (EPR) spectrum. Our measurements showed that the collapse of the broad ferritin maximum contained in the EPR spectra possibly relates to the onset and progression of the ND. Ferritin malfunction triggers the perturbation of iron concentration that either increases or decreases over the normal levels in brain without ND. This supports a conjecture that accumulated iron results in an increased volume of magnetite crystals, whose fluctuated magnetic moments may interfere with the normal function of neural synapses and contribute to the neurodegenerative disease. The mechanism of the iron mobility relates to iron canals in the neural cell's membrane by which the iron enters and leaves the neural cells. This gate keeper malfunction may relate to a speculation that this is due to the appearance of 2Fe-2S in EPR spectra of brains with ND.
Statement of significance
In this manuscript we describe feedback between electronic structure of atoms in the brain, easiness of becoming magnetized in a magnetic field and the ability of the brain to hold the magnetic field on its own in cases of neurodegenerative-diseased and healthy brain. This contribution is novel and significant for a number of reasons, as follows: We revealed that diseased brains have a distinct electronic structure from healthy brains. We identified the easiness of brain samples to become magnetized in a magnetic field and the brains’ ability to hold the magnetic field on its own in cases of neurodegenerative-diseased and healthy brains. This paper addresses a new hypothesis, and we consider that it will generate broad that may be of broad interdisciplinary interest and generate further debate.
{"title":"Iron level changes in the brain with neurodegenerative disease","authors":"Robert Bazala , Giorgio Zoppellaro , Gunther Kletetschka","doi":"10.1016/j.brain.2023.100063","DOIUrl":"10.1016/j.brain.2023.100063","url":null,"abstract":"<div><p>Nanosized magnetite inside ferritin may control the progression of neurodegenerative disease (ND) by creating an electronic noise in the neural cells. We discovered that brains with ND have a unique electron paramagnetic resonance (EPR) spectrum. Our measurements showed that the collapse of the broad ferritin maximum contained in the EPR spectra possibly relates to the onset and progression of the ND. Ferritin malfunction triggers the perturbation of iron concentration that either increases or decreases over the normal levels in brain without ND. This supports a conjecture that accumulated iron results in an increased volume of magnetite crystals, whose fluctuated magnetic moments may interfere with the normal function of neural synapses and contribute to the neurodegenerative disease. The mechanism of the iron mobility relates to iron canals in the neural cell's membrane by which the iron enters and leaves the neural cells. This gate keeper malfunction may relate to a speculation that this is due to the appearance of 2Fe-2S in EPR spectra of brains with ND.</p></div><div><h3>Statement of significance</h3><p>In this manuscript we describe feedback between electronic structure of atoms in the brain, easiness of becoming magnetized in a magnetic field and the ability of the brain to hold the magnetic field on its own in cases of neurodegenerative-diseased and healthy brain. This contribution is novel and significant for a number of reasons, as follows: We revealed that diseased brains have a distinct electronic structure from healthy brains. We identified the easiness of brain samples to become magnetized in a magnetic field and the brains’ ability to hold the magnetic field on its own in cases of neurodegenerative-diseased and healthy brains. This paper addresses a new hypothesis, and we consider that it will generate broad that may be of broad interdisciplinary interest and generate further debate.</p></div>","PeriodicalId":72449,"journal":{"name":"Brain multiphysics","volume":"4 ","pages":"Article 100063"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45552328","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.1016/j.brain.2023.100079
Beatrice Bisighini, M. Aguirre, B. Pierrat, S. Avril
{"title":"Patient-specific computational modelling of endovascular treatment for intracranial aneurysms","authors":"Beatrice Bisighini, M. Aguirre, B. Pierrat, S. Avril","doi":"10.1016/j.brain.2023.100079","DOIUrl":"https://doi.org/10.1016/j.brain.2023.100079","url":null,"abstract":"","PeriodicalId":72449,"journal":{"name":"Brain multiphysics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"54406499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.1016/j.brain.2023.100066
Sarah R. St. Pierre, Kevin Linka, Ellen Kuhl
The soft tissue of the brain deforms in response to external stimuli, which can lead to traumatic brain injury. Constitutive models relate the stress in the brain to its deformation and accurate constitutive modeling is critical in finite element simulations to estimate injury risk. Traditionally, researchers first choose a constitutive model and then fit the model parameters to tension, compression, or shear experiments. In contrast, constitutive artificial neural networks enable automated model discovery without having to choose a specific model before learning the model parameters. Here we reverse engineer a constitutive artificial neural network that uses the principal stretches, raised to a wide range of exponential powers, as activation functions. Upon training, the network autonomously discovers a subclass of models with multiple Ogden terms that outperform popular constitutive models including the neo Hooke, Blatz Ko, and Mooney Rivlin models. While invariant-based networks fail to capture the pronounced tension–compression asymmetry of brain tissue, our principal-stretch-based network can simultaneously explain tension, compression, and shear data for the cortex, basal ganglia, corona radiata, and corpus callosum. Without fixing the number of terms a priori, our model self-selects the best subset of terms out of more than a million possible combinations, while simultaneously discovering the best model parameters and best experiment to train itself. Eliminating user-guided model selection has the potential to induce a paradigm shift in soft tissue modeling and democratize brain injury simulations. Our source code, data, and examples are available at https://github.com/LivingMatterLab/CANN.
Statement of Significance: Understanding the constitutive response of the brain is critical to estimate brain injury risk, design protective devices, and predict surgical intervention. The current gold standard in constitutive modeling, first choosing a constitutive model and then fitting its parameters to data, is largely biased by user experience and personal preference. Constitutive artificial neural networks eliminate the need for user-guided model selection and enable automated model discovery. Here we reverse-engineer a constitutive artificial neural network with custom-designed activation functions from principal stretches raised to a wide range of exponential powers. When trained with data from human gray and white matter tissue, our network autonomously discovers a subclass of models with multiple Ogden terms that outperform popular constitutive models including the neo Hooke, Blatz Ko, and Mooney Rivlin models. While these classical invariant-based networks fail to capture the pronounced tension-compression asymmetry of brain tissue, our discovered principal-stretch-based models can simultaneously explain tension, compression, and shear data from the human cortex, bas
{"title":"Principal-stretch-based constitutive neural networks autonomously discover a subclass of Ogden models for human brain tissue","authors":"Sarah R. St. Pierre, Kevin Linka, Ellen Kuhl","doi":"10.1016/j.brain.2023.100066","DOIUrl":"https://doi.org/10.1016/j.brain.2023.100066","url":null,"abstract":"<div><p>The soft tissue of the brain deforms in response to external stimuli, which can lead to traumatic brain injury. Constitutive models relate the stress in the brain to its deformation and accurate constitutive modeling is critical in finite element simulations to estimate injury risk. Traditionally, researchers first choose a constitutive model and then fit the model parameters to tension, compression, or shear experiments. In contrast, constitutive artificial neural networks enable automated model discovery without having to choose a specific model before learning the model parameters. Here we reverse engineer a constitutive artificial neural network that uses the principal stretches, raised to a wide range of exponential powers, as activation functions. Upon training, the network autonomously discovers a subclass of models with multiple Ogden terms that outperform popular constitutive models including the neo Hooke, Blatz Ko, and Mooney Rivlin models. While invariant-based networks fail to capture the pronounced tension–compression asymmetry of brain tissue, our principal-stretch-based network can simultaneously explain tension, compression, and shear data for the cortex, basal ganglia, corona radiata, and corpus callosum. Without fixing the number of terms a priori, our model self-selects the best subset of terms out of more than a million possible combinations, while simultaneously discovering the best model parameters and best experiment to train itself. Eliminating user-guided model selection has the potential to induce a paradigm shift in soft tissue modeling and democratize brain injury simulations. Our source code, data, and examples are available at <span>https://github.com/LivingMatterLab/CANN</span><svg><path></path></svg>.</p><p><strong>Statement of Significance</strong>: Understanding the constitutive response of the brain is critical to estimate brain injury risk, design protective devices, and predict surgical intervention. The current gold standard in constitutive modeling, <em>first</em> choosing a constitutive model and then fitting its parameters to data, is largely biased by user experience and personal preference. Constitutive artificial neural networks eliminate the need for user-guided model selection and enable automated model discovery. Here we reverse-engineer a constitutive artificial neural network with custom-designed activation functions from principal stretches raised to a wide range of exponential powers. When trained with data from human gray and white matter tissue, our network autonomously discovers a subclass of models with multiple Ogden terms that outperform popular constitutive models including the neo Hooke, Blatz Ko, and Mooney Rivlin models. While these classical invariant-based networks fail to capture the pronounced tension-compression asymmetry of brain tissue, our discovered principal-stretch-based models can simultaneously explain tension, compression, and shear data from the human cortex, bas","PeriodicalId":72449,"journal":{"name":"Brain multiphysics","volume":"4 ","pages":"Article 100066"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49858457","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.1016/j.brain.2022.100062
Joseph Sutlive , Hamed Seyyedhosseinzadeh , Zheng Ao , Haning Xiu , Sangita Choudhury , Kun Gou , Feng Guo , Zi Chen
Morphogenesis in the central nervous system has received intensive attention as elucidating fundamental mechanisms of morphogenesis will shed light on the physiology and pathophysiology of the developing central nervous system. Morphogenesis of the central nervous system is of a vast topic that includes important morphogenetic events such as neurulation and cortical folding. Here we review three types of methods used to improve our understanding of morphogenesis of the central nervous system: in vivo experiments, organoids (in vivo), and computational models (in silico). The in vivo experiments are used to explore cellular- and tissue-level mechanics and interpret them on the roles of neurulation morphogenesis. Recent advances in human brain organoids have provided new opportunities to study morphogenesis and neurogenesis to compensate for the limitations of in vivo experiments, as organoid models are able to recapitulate some critical neural morphogenetic processes during early human brain development. Due to the complexity and costs of in vivo and in vitro studies, a variety of computational models have been developed and used to explain the formation and morphogenesis of brain structures. We review and discuss the advantages and disadvantages of these methods and their usage in the studies on morphogenesis of the central nervous system. Notably, none of these methods alone is sufficient to unveil the biophysical mechanisms of morphogenesis, thus calling for the interdisciplinary approaches using a combination of these methods in order to test hypotheses and generate new insights on both normal and abnormal development of the central nervous system.
Statement of Significance: The understanding of the central nervous system is essential to provide supports to treat and prevent neurological conditions. Mechanisms of morphogenesis therein can be elucidated from multiple unique perspectives via multidisciplinary approaches. The in vivo experiments, organoid models, and computational modeling are three most effective ways to study brain morphogenesis. In vivo experiments on live animals provide important evidence for studying the roles of mechanical forces in morphogenetic events. The human brain organoid models can greatly assist to study early human brain development and closely simulate the in-vivo counterpart. Moreover, computational models based on physical principles can test hypotheses in conjunctions with experiments to facilitate understanding of the spatial and temporal evolution of these complex structures. The combination of these approaches can complement each other to unveil fundamental mechanisms of the neural morphogenesis and shed light on the development, prevention, and treatment of neurological disorders.
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