Antoine Jérusalem

Computational biology - modeling of primary blast effects on the central nervous system.

OBJECTIVES Recent military conflicts in Iraq and Afghanistan have highlighted the wartime effect of traumatic brain injury (TBI). The reason for the prominence of TBI in these particular conflicts as opposed to others is unclear but may result from the increased survivability of blast due to improvements in body armor. In the military context blunt, ballistic and blast effects may all contribute to CNS injury, however blast in particular, has been suggested as a primary cause of military TBI. While blast effects on some biological tissues, such as the lung, are documented in terms of injury thresholds, this is not the case for the CNS. We hypothesized that using bio-fidelic models, allowing for fluid-solid interaction and basic material properties available in the literature, a blast wave would interact with CNS tissue and cause a possible concussive effect. METHODS The modeling approach employed for this investigation consisted of a computational framework suitable for simulating coupled fluid-solid dynamic interactions. The model included a complex finite element mesh of the head and intra-cranial contents. The effects of threshold and 50% lethal blast lung injury were compared with concussive impact injury using the full head model allowing upper and lower bounds of tissue injury to be applied using pulmonary injury as the reference tissue. RESULTS The effects of a 50% lethal dose blast lung injury (LD(50)) were comparable with concussive impact injury using the DVBIC-MIT full head model. INTERPRETATION CNS blast concussive effects were found to be similar between impact mild TBI and the blast field associated with LD(50) lung blast injury sustained without personal protective equipment. With the ubiquitous use of personal protective equipment this suggests that blast concussive effects may more readily ascertained in personnel due to enhanced survivability in the current conflicts.

Mechanics of the brain: perspectives, challenges, and opportunities

The human brain is the continuous subject of extensive investigation aimed at understanding its behavior and function. Despite a clear evidence that mechanical factors play an important role in regulating brain activity, current research efforts focus mainly on the biochemical or electrophysiological activity of the brain. Here, we show that classical mechanical concepts including deformations, stretch, strain, strain rate, pressure, and stress play a crucial role in modulating both brain form and brain function. This opinion piece synthesizes expertise in applied mathematics, solid and fluid mechanics, biomechanics, experimentation, material sciences, neuropathology, and neurosurgery to address today’s open questions at the forefront of neuromechanics. We critically review the current literature and discuss challenges related to neurodevelopment, cerebral edema, lissencephaly, polymicrogyria, hydrocephaly, craniectomy, spinal cord injury, tumor growth, traumatic brain injury, and shaken baby syndrome. The multi-disciplinary analysis of these various phenomena and pathologies presents new opportunities and suggests that mechanical modeling is a central tool to bridge the scales by synthesizing information from the molecular via the cellular and tissue all the way to the organ level.

Continuum modeling of a neuronal cell under blast loading.

Traumatic brain injuries have recently been put under the spotlight as one of the most important causes of accidental brain dysfunctions. Significant experimental and modeling efforts are thus underway to study the associated biological, mechanical and physical mechanisms. In the field of cell mechanics, progress is also being made at the experimental and modeling levels to better characterize many of the cell functions, including differentiation, growth, migration and death. The work presented here aims to bridge both efforts by proposing a continuum model of a neuronal cell submitted to blast loading. In this approach, the cytoplasm, nucleus and membrane (plus cortex) are differentiated in a representative cell geometry, and different suitable material constitutive models are chosen for each one. The material parameters are calibrated against published experimental work on cell nanoindentation at multiple rates. The final cell model is ultimately subjected to blast loading within a complete computational framework of fluid-structure interaction. The results are compared to the nanoindentation simulation, and the specific effects of the blast wave on the pressure and shear levels at the interfaces are identified. As a conclusion, the presented model successfully captures some of the intrinsic intracellular phenomena occurring during the cellular deformation under blast loading that potentially lead to cell damage. It suggests, more particularly, that the localization of damage at the nucleus membrane is similar to what has already been observed at the overall cell membrane. This degree of damage is additionally predicted to be worsened by a longer blast positive phase duration. In conclusion, the proposed model ultimately provides a new three-dimensional computational tool to evaluate intracellular damage during blast loading.

A computational model coupling mechanics and electrophysiology in spinal cord injury

Traumatic brain injury and spinal cord injury have recently been put under the spotlight as major causes of death and disability in the developed world. Despite the important ongoing experimental and modeling campaigns aimed at understanding the mechanics of tissue and cell damage typically observed in such events, the differentiated roles of strain, stress and their corresponding loading rates on the damage level itself remain unclear. More specifically, the direct relations between brain and spinal cord tissue or cell damage, and electrophysiological functions are still to be unraveled. Whereas mechanical modeling efforts are focusing mainly on stress distribution and mechanistic-based damage criteria, simulated function-based damage criteria are still missing. Here, we propose a new multiscale model of myelinated axon associating electrophysiological impairment to structural damage as a function of strain and strain rate. This multiscale approach provides a new framework for damage evaluation directly relating neuron mechanics and electrophysiological properties, thus providing a link between mechanical trauma and subsequent functional deficits.

A continuum model describing the reverse grain-size dependence of the strength of nanocrystalline metals

The breakdown of the Hall–Petch relation in the grain-size strength dependence of nanocrystalline metals has been rationalized by the activation of deformation mechanisms taking place at the grain boundary which compete with crystal plasticity and become dominant when grain sizes are sufficiently small. In this work, we develop a continuum description of the effective response of nanocrystalline metals. The model is based on a finite element formulation of the continuum three-dimensional problem describing the deformation of polycrystal grains explicitly and on the consideration of grain boundaries as surfaces of discontinuity with finite thickness embedded in the continuum. A phenomenological model formulated within the framework of variational constitutive updates is proposed to describe the operative grain-boundary deformation mechanisms of sliding and opening accommodation. The model parameters are fitted to atomistic results for copper at very high loading rate. Tensile test simulations using this model reproduce the inverse grain-size dependency of the macroscopic yield stress predicted by atomistic simulations. In particular, the model predicts that the grain-size dependency of the yield stress shows a linear relation to the inverse square root of the grain size, as in the traditional Hall–Petch law, but with a negative coefficient. The results are in good agreement with the atomistic simulations and also with quasi-static experimental tests. The ability to model the effective response of nanocrystals without the need of explicitly accounting for each individual atom opens the way for the analysis of nanocrystalline materials in sample sizes and under strain rates of technological significance.

A continuum model of nanocrystalline metals under shock loading

Recent atomistic simulations have shown that grain boundary sliding in nanocrystals is altered under shock loading conditions. It is found that the high state of compression inhibits grain boundary sliding and reactivates intragrain dislocation activity. This leads to higher material strength and postpones the transition between these two deformation mechanisms to smaller grain size. We present here a continuum model aimed at extending the model proposed by Jerusalem et al for quasi-static and high rates (2007 Phil. Mag. 87 2541–59) to shock loading. To this end, the shock response of nanocrystals is investigated by accounting specifically for additional frictional deformation-inhibiting effects. The model is based on a numerical finite element discretization of the polycrystal, considered as a continuum, with embedded surfaces of discontinuity accounting for the grain boundary response. Interface elements are formulated to account for the special kinematics of grain boundaries, i.e. to describe grain boundary frictional sliding and other accommodation mechanisms. The response of grain interiors is modeled with a high rate equation of state for the volumetric response and a simple plasticity model to describe their deviatoric response. A large-scale parallel computing framework is finally developed to calibrate and investigate the specificities of the deformation mechanisms under shock loading conditions, and the results are compared in detail with atomistic results. As a conclusion, this extended three-dimensional continuum model constitutes a promising first step for the characterization of large-scale nanocrystalline deformation under the most complete range of loading rates yet proposed in continuum simulations, namely, from quasi-static to shock loading.

On the mechanical behaviour of PEEK and HA cranial implants under impact loading

The human head can be subjected to numerous impact loadings such as those produced by a fall or during sport activities. These accidents can result in skull fracture and in some complex cases, part of the skull may need to be replaced by a biomedical implant. Even when the skull is not damaged, such accidents can result in brain swelling treated by decompressive craniectomy. Usually, after recovery, the part of the skull that has been removed is replaced by a prosthesis. In such situations, a computational tool able to analyse the choice of prosthesis material depending on the patients specific activity has the potential to be extremely useful for clinicians. The work proposed here focusses on the development and use of a numerical model for the analysis of cranial implants under impact conditions. In particular, two main biomaterials commonly employed for this kind of prosthesis are polyether-ether-ketone (PEEK) and macroporous hydroxyapatite (HA). In order to study the suitability of these implants, a finite element head model comprising scalp, skull, cerebral falx, cerebrospinal fluid and brain tissues, with a cranial implant replacing part of the skull has been developed from magnetic resonance imaging data. The human tissues and these two biocompatible materials have been independently studied and their constitutive models are provided here. A computational model of the human head under impact loading is then implemented and validated, and a numerical comparison of the mechanical impact response of PEEK and HA implants is presented. This comparison was carried out in terms of the effectiveness of both implants in ensuring structural integrity and preventing traumatic brain injury. The results obtained in this work highlight the need to take into account environmental mechanical considerations to select the optimal implant depending on the specific patient: whereas HA implants present attractive biointegration properties, PEEK implant can potentially be a much more appropriate choice in a demanding mechanical life style. Finally, a novel methodology is proposed to assess the need for further clinical evaluation in case of impact with both implants over a large range of impact conditions.

Growth, collapse, and stalling in a mechanical model for neurite motility.

Neurites, the long cellular protrusions that form the routes of the neuronal network, are capable of actively extending during early morphogenesis or regenerating after trauma. To perform this task, they rely on their cytoskeleton for mechanical support. In this paper, we present a three-component active gel model that describes neurites in the three robust mechanical states observed experimentally: collapsed, static, and motile. These states arise from an interplay between the physical forces driven by the growth of the microtubule-rich inner core of the neurite and the acto-myosin contractility of its surrounding cortical membrane. In particular, static states appear as a mechanical balance between traction and compression of these two parallel structures. The model predicts how the response of a neurite to a towing force depends on the force magnitude and recovers the response of neurites to several drug treatments that modulate the cytoskeleton active and passive properties.

The Specification of Geometric Edges by a Plant Rab GTPase Is an Essential Cell-Patterning Principle During Organogenesis in Arabidopsis

Summary Plant organogenesis requires control over division planes and anisotropic cell wall growth, which each require spatial patterning of cells. Polyhedral plant cells can display complex patterning in which individual faces are established as biochemically distinct domains by endomembrane trafficking. We now show that, during organogenesis, the Arabidopsis endomembrane system specifies an important additional cellular spatial domain: the geometric edges. Previously unidentified membrane vesicles lying immediately beneath the plasma membrane at cell edges were revealed through localization of RAB-A5c, a plant GTPase of the Rab family of membrane-trafficking regulators. Specific inhibition of RAB-A5c activity grossly perturbed cell geometry in developing lateral organs by interfering independently with growth anisotropy and cytokinesis without disrupting default membrane trafficking. The initial loss of normal cell geometry can be explained by a failure to maintain wall stiffness specifically at geometric edges. RAB-A5c thus meets a requirement to specify this cellular spatial domain during organogenesis.

Neurite, a finite difference large scale parallel program for the simulation of electrical signal propagation in neurites under mechanical loading.

With the growing body of research on traumatic brain injury and spinal cord injury, computational neuroscience has recently focused its modeling efforts on neuronal functional deficits following mechanical loading. However, in most of these efforts, cell damage is generally only characterized by purely mechanistic criteria, functions of quantities such as stress, strain or their corresponding rates. The modeling of functional deficits in neurites as a consequence of macroscopic mechanical insults has been rarely explored. In particular, a quantitative mechanically based model of electrophysiological impairment in neuronal cells, Neurite, has only very recently been proposed. In this paper, we present the implementation details of this model: a finite difference parallel program for simulating electrical signal propagation along neurites under mechanical loading. Following the application of a macroscopic strain at a given strain rate produced by a mechanical insult, Neurite is able to simulate the resulting neuronal electrical signal propagation, and thus the corresponding functional deficits. The simulation of the coupled mechanical and electrophysiological behaviors requires computational expensive calculations that increase in complexity as the network of the simulated cells grows. The solvers implemented in Neurite—explicit and implicit—were therefore parallelized using graphics processing units in order to reduce the burden of the simulation costs of large scale scenarios. Cable Theory and Hodgkin-Huxley models were implemented to account for the electrophysiological passive and active regions of a neurite, respectively, whereas a coupled mechanical model accounting for the neurite mechanical behavior within its surrounding medium was adopted as a link between electrophysiology and mechanics. This paper provides the details of the parallel implementation of Neurite, along with three different application examples: a long myelinated axon, a segmented dendritic tree, and a damaged axon. The capabilities of the program to deal with large scale scenarios, segmented neuronal structures, and functional deficits under mechanical loading are specifically highlighted.