Final Report Summary - DINUMA (Development of an integrated numerical model of the intra-cranial space (including the brain parenchyma, blood flow and cerebrospinal fluid) for clinical application)
Background: Lack of specialized tools and protocols targeted to the different neurological disorders leads to diagnosis errors and/or inadequate treatment strategies. As an example, the diagnosis of normal pressure hydrocephalus (NPH) is a reoccurring problem faced by clinicians due to the overlap of symptoms and diagnostic findings with other neurodegenerative pathologies such as Alzheimer’s disease. Such scenario is not specific to NPH and treatment limitations due to a lack of understanding of the intra-cranial mechanics may be found throughout the spectrum of neurologic disorders. A major difficulty is that the large number of variables (inter-patient and inter-institution variability) and possible pathways (biochemical, electrical, mechanical), and the difficulty to acquire detailed measurements within the brain make it challenging to resolve disease mechanisms based on clinical data alone. This is the typical setting where numerical modeling could make a significant impact by providing a controlled hypothesis test-bed, ultimately allowing researchers to identify the most probable disease mechanism and later develop adequate diagnosis and treatment protocols.
Accordingly, the objective of this project was to develop a multi-scale numerical platform of the intra-cranial dynamics and set the grounds for further investigations of the mechanical processes underlying brain-disease onset and progression. This undertaking was casted into three main research axes: SA1) the development of a novel bottom-up structural model for the brain parenchyma, SA2) modelling the interaction between the parenchyma and its physiologic environment, and SA3) the investigation of global intra-cranial pressure dynamics with application to NPH diagnosis.
SA1, Bottom-Up Multi-Scale Structural Model of the Parenchyma. To reconcile the different mechanical behaviors reported in literature, we have developed a pilot multi-scale framework for brain mechanics based on the homogenization theory. With that formulation, the macro-scale behavior of the brain depends on macro-scale loading conditions such as changes in ventricular volume or intracranial pressure, and on its micro-scale structure such as the density and local arrangement of the neuronal fibers. Local macro-scale mechanical parameters are obtained from computations at the micro-scale, circumventing the need for parameter fitting and allowing for dynamic parameter adjustment throughout the deformation: Deformations at the macro-scale impact the micro-scale structure, which in turn affects the average micro-scale properties. Simulations of uniaxial compression and stretch demonstrated non-linear stress-strain curves, different stiffness during loading and unloading, Mullins effects and strain-rate dependence, all of which have also been reported experimentally [Franceschini, 2006]. It is worthwhile noting that these non-linearities were observed despite the fact that individual axons were assumed to be linearly elastic, and stem from the differential rates of fluid expulsion or intake as a function of the pore sizes. Strain rate dependence also finds its origin in the interaction between the interstitial fluid and cellular matrix. At low strain rates, fluid and solid stresses equilibrate at all time and the tissue behaves like a linear elastic solid. At higher strain rates, fluid pressure does not have the time to equilibrate throughout the tissue, yielding the non-linear effects reported above and non-uniform fluid distribution throughout the tissue. Finally, our results demonstrate that when subjecting brain tissue to a static load, the initial deformation is followed by a progressive consolidation as fluid is slowly expelled from the tissue. Brain consolidation, which was also reported experimentally, might be a critical feature in the context of NPH. Indeed, while the reported transmantle pressures in these patients were too small to explain the reported large deformation of the parenchyma based on an elastic or visco-elastic formulation, they might suffice to yield consolidation and over time a significant reduction in parenchymal volume.
SA1, Structural Atlas of the Parenchyma. Numerical experiments with isotropic and non-isotropic fiber arrangements demonstrated that variations in the microscopic organization of the axons result in drastically different macro-scale behaviors. This observation, although rather obvious, is of primary importance in the context of the brain, which shows strong variations in cellular composition and structure between gray and white matter and across different regions of the brain. A significant achievement of this period was thus the establishment of a detailed atlas of the brain micro-structure through an extensive literature review (also resulting in a Master thesis).
SA2, Near-Wall Cerebrospinal Fluid Dynamics. Cranio-spinal dynamics are produced by the complex interaction of brain, spinal cord, blood and cerebrospinal fluid (CSF) in a confined environment. Accordingly, significant efforts were put in understanding the detailed CSF dynamics and their interplay with parenchymal motion. Macro-scale CSF dynamics were simulated in the ventricular space using subject-specific anatomy, brain motion and choroid plexus pulsations derived from magnetic resonance imaging (MRI). The effect of the beating motion of the ependymal cilia lining the ventricular walls was quantified in selected subdomains from the right lateral ventricle, using the dynamic boundary conditions obtained from the macroscale simulations. Our results indicate that the near-wall dynamics and wall shear-stresses are likely to be dominated by the action of the ependymal cilia, while CSF dynamics in the center regions of the ventricles is affected predominantly by wall motion and choroid plexus pulsation. These findings are of direct relevance in developmental biology, elucidating the role of the ependymal cilia in CSF flow-mediated neuronal guidance.
SA3, Global Intra-Cranial Dynamics in Hydrocephalus: Visco-Elasticity Affects Infusion Tests. Clinically, one global measure for intra-cranial dynamics is the CSF outflow resistance, R0, which is employed for the selection of hydrocephalus patients for shunting and for assessing shunt performance. R0 is obtained by infusion tests, wherein one transiently increases the CSF volume, measures the resulting intra-cranial pressure (ICP), and estimates the corresponding R0 assuming that intra-cranial dynamics follow the idealized pressure-volume curve described by Marmarou. Among the three main types of infusion used, namely constant flow, constant pressure and bolus infusion, the bolus infusion method features the shortest examination times and shortest patient exposure to artificially increased ICP levels. However, for unknown reasons, it systematically underestimates R0. Using an in vitro experimental set-up and a lumped-parameter model of the global intra-cranial dynamics, we demonstrated that intracranial dynamics have a substantial viscoelastic component, which is neglected in Marmarou’s formulation. While Marmarou’s approximation provides satisfactory results in quasi-steady conditions (such as constant flow or constant pressure), it fails to capture the transient response to bolus infusion. When accounting for viscoelasticity, the bolus infusion test no longer underestimates R0. This work, of direct clinical relevance, highlights the need for accurate brain models even for the estimation of very global parameters such as R0.
Conclusion and Outlook: The results from both SA1 and SA2 underscore the fact that intra-cranial dynamics cannot be captured with macroscale approaches alone and effectively result from complex responses at the cellular level. Macroscale loads impact the brain microstructure, which in turns impacts its macroscale properties. Similarly, while bulk CSF dynamics are dominated by macroscale forces such as parenchymal motion and choroid pulsations, the near-wall CSF dynamics are in practice dominated by the beating action of the ependymal cilia, which will have a direct impact on the parenchymal response. Finally, results from SA3 demonstrate that an accurate understanding of brain dynamics is not only relevant to the research community but also has a direct clinical significance, having a clear impact on global diagnostic metrics such as CSF outflow resistance.
This work has laid the ground for two continuing research projects funded by the Swiss National Science Foundation (SNSF): a continuing Grant for the fellow, investigating the interplay between CSF dynamics and cell response (SNSF, Marie Heim Vögtlin Grant, PMPDP2_151255), and funding for a doctoral student investigating intracranial water flow and the communication between CSF and interstitial fluids, as part of a larger SNSF Grant (CINDY, SNSF Grant 20021_147193).
Accordingly, the objective of this project was to develop a multi-scale numerical platform of the intra-cranial dynamics and set the grounds for further investigations of the mechanical processes underlying brain-disease onset and progression. This undertaking was casted into three main research axes: SA1) the development of a novel bottom-up structural model for the brain parenchyma, SA2) modelling the interaction between the parenchyma and its physiologic environment, and SA3) the investigation of global intra-cranial pressure dynamics with application to NPH diagnosis.
SA1, Bottom-Up Multi-Scale Structural Model of the Parenchyma. To reconcile the different mechanical behaviors reported in literature, we have developed a pilot multi-scale framework for brain mechanics based on the homogenization theory. With that formulation, the macro-scale behavior of the brain depends on macro-scale loading conditions such as changes in ventricular volume or intracranial pressure, and on its micro-scale structure such as the density and local arrangement of the neuronal fibers. Local macro-scale mechanical parameters are obtained from computations at the micro-scale, circumventing the need for parameter fitting and allowing for dynamic parameter adjustment throughout the deformation: Deformations at the macro-scale impact the micro-scale structure, which in turn affects the average micro-scale properties. Simulations of uniaxial compression and stretch demonstrated non-linear stress-strain curves, different stiffness during loading and unloading, Mullins effects and strain-rate dependence, all of which have also been reported experimentally [Franceschini, 2006]. It is worthwhile noting that these non-linearities were observed despite the fact that individual axons were assumed to be linearly elastic, and stem from the differential rates of fluid expulsion or intake as a function of the pore sizes. Strain rate dependence also finds its origin in the interaction between the interstitial fluid and cellular matrix. At low strain rates, fluid and solid stresses equilibrate at all time and the tissue behaves like a linear elastic solid. At higher strain rates, fluid pressure does not have the time to equilibrate throughout the tissue, yielding the non-linear effects reported above and non-uniform fluid distribution throughout the tissue. Finally, our results demonstrate that when subjecting brain tissue to a static load, the initial deformation is followed by a progressive consolidation as fluid is slowly expelled from the tissue. Brain consolidation, which was also reported experimentally, might be a critical feature in the context of NPH. Indeed, while the reported transmantle pressures in these patients were too small to explain the reported large deformation of the parenchyma based on an elastic or visco-elastic formulation, they might suffice to yield consolidation and over time a significant reduction in parenchymal volume.
SA1, Structural Atlas of the Parenchyma. Numerical experiments with isotropic and non-isotropic fiber arrangements demonstrated that variations in the microscopic organization of the axons result in drastically different macro-scale behaviors. This observation, although rather obvious, is of primary importance in the context of the brain, which shows strong variations in cellular composition and structure between gray and white matter and across different regions of the brain. A significant achievement of this period was thus the establishment of a detailed atlas of the brain micro-structure through an extensive literature review (also resulting in a Master thesis).
SA2, Near-Wall Cerebrospinal Fluid Dynamics. Cranio-spinal dynamics are produced by the complex interaction of brain, spinal cord, blood and cerebrospinal fluid (CSF) in a confined environment. Accordingly, significant efforts were put in understanding the detailed CSF dynamics and their interplay with parenchymal motion. Macro-scale CSF dynamics were simulated in the ventricular space using subject-specific anatomy, brain motion and choroid plexus pulsations derived from magnetic resonance imaging (MRI). The effect of the beating motion of the ependymal cilia lining the ventricular walls was quantified in selected subdomains from the right lateral ventricle, using the dynamic boundary conditions obtained from the macroscale simulations. Our results indicate that the near-wall dynamics and wall shear-stresses are likely to be dominated by the action of the ependymal cilia, while CSF dynamics in the center regions of the ventricles is affected predominantly by wall motion and choroid plexus pulsation. These findings are of direct relevance in developmental biology, elucidating the role of the ependymal cilia in CSF flow-mediated neuronal guidance.
SA3, Global Intra-Cranial Dynamics in Hydrocephalus: Visco-Elasticity Affects Infusion Tests. Clinically, one global measure for intra-cranial dynamics is the CSF outflow resistance, R0, which is employed for the selection of hydrocephalus patients for shunting and for assessing shunt performance. R0 is obtained by infusion tests, wherein one transiently increases the CSF volume, measures the resulting intra-cranial pressure (ICP), and estimates the corresponding R0 assuming that intra-cranial dynamics follow the idealized pressure-volume curve described by Marmarou. Among the three main types of infusion used, namely constant flow, constant pressure and bolus infusion, the bolus infusion method features the shortest examination times and shortest patient exposure to artificially increased ICP levels. However, for unknown reasons, it systematically underestimates R0. Using an in vitro experimental set-up and a lumped-parameter model of the global intra-cranial dynamics, we demonstrated that intracranial dynamics have a substantial viscoelastic component, which is neglected in Marmarou’s formulation. While Marmarou’s approximation provides satisfactory results in quasi-steady conditions (such as constant flow or constant pressure), it fails to capture the transient response to bolus infusion. When accounting for viscoelasticity, the bolus infusion test no longer underestimates R0. This work, of direct clinical relevance, highlights the need for accurate brain models even for the estimation of very global parameters such as R0.
Conclusion and Outlook: The results from both SA1 and SA2 underscore the fact that intra-cranial dynamics cannot be captured with macroscale approaches alone and effectively result from complex responses at the cellular level. Macroscale loads impact the brain microstructure, which in turns impacts its macroscale properties. Similarly, while bulk CSF dynamics are dominated by macroscale forces such as parenchymal motion and choroid pulsations, the near-wall CSF dynamics are in practice dominated by the beating action of the ependymal cilia, which will have a direct impact on the parenchymal response. Finally, results from SA3 demonstrate that an accurate understanding of brain dynamics is not only relevant to the research community but also has a direct clinical significance, having a clear impact on global diagnostic metrics such as CSF outflow resistance.
This work has laid the ground for two continuing research projects funded by the Swiss National Science Foundation (SNSF): a continuing Grant for the fellow, investigating the interplay between CSF dynamics and cell response (SNSF, Marie Heim Vögtlin Grant, PMPDP2_151255), and funding for a doctoral student investigating intracranial water flow and the communication between CSF and interstitial fluids, as part of a larger SNSF Grant (CINDY, SNSF Grant 20021_147193).