Fixed negative charge and the Donnan effect: a description of the driving forces associated with brain tissue swelling and oedema

Simulating Cerebral Edema and Ischemia After Traumatic Acute Subdural Hematoma Using Triphasic Swelling Biomechanics

Poor outcome following traumatic acute subdural hematoma (ASDH) is associated with the severity of the primary injury and secondary injury including cerebral edema and ischemia. However, the underlying secondary injury mechanism contributing to elevated intracranial pressure (ICP) and high mortality rate remains unclear. Cerebral edema occurs in response to the exposure of the intracellular fixed charge density (FCD) after cell death, causing ICP to increase. The increased ICP from swollen tissue compresses blood vessels in adjacent tissue, restricting blood flow and leading to ischemic damage. We hypothesize that the mass occupying effect of ASDH exacerbates the ischemic injury, leading to ICP elevation, which is an indicator of high mortality rate in the clinic. Using FEBio (febio.org) and triphasic swelling biomechanics, this study modeled clinically relevant ASDHs and simulated post-traumatic brain swelling and ischemia to predict ICP. Results showed that common convexity ASDH significantly increased ICP by exacerbating ischemic injury, and surgical removal of the convexity ASDH may control ICP by preventing ischemia progression. However, in cases where the primary injury is very severe, surgical intervention alone may not effectively decrease ICP, as the contribution of the hematoma to the elevated ICP is insignificant. In addition, interhemispheric ASDH, located between the cerebral hemispheres, does not significantly exacerbate ischemia, supporting the conservative surgical management generally recommended for interhemispheric ASDH. The joint effect of the mass occupying effect of the blood clot and resulting ischemia contributes to elevated ICP which may increase mortality. Our novel approach may improve the fidelity of predicting patient outcome after motor vehicle crashes and traumatic brain injuries due to other causes.

Alterations in brain fluid physiology during the early stages of development of ischaemic oedema

Oedema occurs when higher than normal amounts of solutes and water accumulate in tissues. In brain parenchymal tissue, vasogenic oedema arises from changes in blood-brain barrier permeability, e.g. in peritumoral oedema. Cytotoxic oedema arises from excess accumulation of solutes within cells, e.g. ischaemic oedema following stroke. This type of oedema is initiated when blood flow in the affected core region falls sufficiently to deprive brain cells of the ATP needed to maintain ion gradients. As a consequence, there is: depolarization of neurons; neural uptake of Na+ and Cl- and loss of K+; neuronal swelling; astrocytic uptake of Na+, K+ and anions; swelling of astrocytes; and reduction in ISF volume by fluid uptake into neurons and astrocytes. There is increased parenchymal solute content due to metabolic osmolyte production and solute influx from CSF and blood. The greatly increased [K+]isf triggers spreading depolarizations into the surrounding penumbra increasing metabolic load leading to increased size of the ischaemic core. Water enters the parenchyma primarily from blood, some passing into astrocyte endfeet via AQP4. In the medium term, e.g. after three hours, NaCl permeability and swelling rate increase with partial opening of tight junctions between blood-brain barrier endothelial cells and opening of SUR1-TPRM4 channels. Swelling is then driven by a Donnan-like effect. Longer term, there is gross failure of the blood-brain barrier. Oedema resolution is slower than its formation. Fluids without colloid, e.g. infused mock CSF, can be reabsorbed across the blood-brain barrier by a Starling-like mechanism whereas infused serum with its colloids must be removed by even slower extravascular means. Large scale oedema can increase intracranial pressure (ICP) sufficiently to cause fatal brain herniation. The potentially lethal increase in ICP can be avoided by craniectomy or by aspiration of the osmotically active infarcted region. However, the only satisfactory treatment resulting in retention of function is restoration of blood flow, providing this can be achieved relatively quickly. One important objective of current research is to find treatments that increase the time during which reperfusion is successful. Questions still to be resolved are discussed.

Distinguishing poroelasticity and viscoelasticity of brain tissue with time scale

Brain tissue is considered to be biphasic, with approximately 80% liquid and 20% solid matrix, thus exhibiting viscoelasticity due to rearrangement of the solid matrix and poroelasticity due to fluid migration within the solid matrix. However, how to distinguish poroelastic and viscoelastic effects in brain tissue remains challenging. In this study, we proposed a method of unconfined compression-isometric hold to measure the force versus time relaxation curves of porcine brain tissue samples with systematically varied sample lengths. Upon scaling the measured relaxation force and relaxation time with different length-dependent physical quantities, we successfully distinguished the poroelasticity and viscoelasticity of the brain tissue. We demonstrated that during isometric hold, viscoelastic relaxation dominated the mechanical behavior of brain tissue in the short-time regime, while poroelastic relaxation dominated in the long-time regime. Furthermore, compared with poroelastic relaxation, viscoelastic relaxation was found to play a more dominant role in the mechanical response of porcine brain tissue. We then evaluated the differences between poroelastic and viscoelastic effects for both porcine and human brain tissue. Because of the draining of pore fluid, the Young's moduli in poroelastic relaxation were lower than those in viscoelastic relaxation; brain tissue changed from incompressible during viscoelastic relaxation to compressible during poroelastic relaxation, resulting in reduced Poisson ratios. This study provides new insights into the physical mechanisms underlying the roles of viscoelasticity and poroelasticity in brain tissue. STATEMENT OF SIGNIFICANCE: Although the poroviscoelastic model had been proposed to characterize brain tissue mechanical behavior, it is difficult to distinguish the poroelastic and viscoelastic behaviors of brain tissue. The study distinguished viscoelasticity and poroelasticity of brain tissue with time scales and then evaluated the differences between poroelastic and viscoelastic effects for both porcine and human brain tissue, which helps to accurate selection of constitutive models suitable for application in certain situations (e.g., pore-dominant and viscoelastic-dominant deformation).

A Hybrid Reactive Multiphasic Mixture With a Compressible Fluid Solvent

Mixture theory is a general framework that has been used to model mixtures of solid, fluid, and solute constituents, leading to significant advances in modeling the mechanics of biological tissues and cells. Though versatile and applicable to a wide range of problems in biomechanics and biophysics, standard multiphasic mixture frameworks incorporate neither dynamics of viscous fluids nor fluid compressibility, both of which facilitate the finite element implementation of computational fluid dynamics solvers. This study formulates governing equations for reactive multiphasic mixtures where the interstitial fluid has a solvent which is viscous and compressible. This hybrid reactive multiphasic framework uses state variables that include the deformation gradient of the porous solid matrix, the volumetric strain and rate of deformation of the solvent, the solute concentrations, and the relative velocities between the various constituents. Unlike standard formulations which employ a Lagrange multiplier to model fluid pressure, this framework requires the formulation of a function of state for the pressure, which depends on solvent volumetric strain and solute concentrations. Under isothermal conditions the formulation shows that the solvent volumetric strain remains continuous across interfaces between hybrid multiphasic domains. Apart from the Lagrange multiplier-state function distinction for the fluid pressure, and the ability to accommodate viscous fluid dynamics, this hybrid multiphasic framework remains fully consistent with standard multiphasic formulations previously employed in biomechanics. With these additional features, the hybrid multiphasic mixture theory makes it possible to address a wider range of problems that are important in biomechanics and mechanobiology.

Calculation of the Gibbs-Donnan factors for multi-ion solutions with non-permeating charge on both sides of a permselective membrane

Separation of two ionic solutions with a permselective membrane that is impermeable to some of the ions leads to an uneven distribution of permeating ions on the two sides of the membrane described by the Gibbs–Donnan (G–D) equilibrium with the G–D factors relating ion concentrations in the two solutions. Here, we present a method of calculating the G–D factors for ideal electroneutral multi-ion solutions with different total charge of non-permeating species on each side of a permselective membrane separating two compartments. We discuss some special cases of G–D equilibrium for which an analytical solution may be found, and we prove the transitivity of G–D factors for multi-ion solutions in several compartments interconnected by permselective membranes. We show a few examples of calculation of the G–D factors for both simple and complex solutions, including the case of human blood plasma and interstitial fluid separated by capillary walls. The article is accompanied by an online tool that enables the calculation of the G–D factors and the equilibrium concentrations for multi-ion solutions with various composition in terms of permeating ions and non-permeating charge, according to the presented method.

Protein Nanoparticle-Related Osmotic Pressure Modifies Nonselective Permeability of the Blood-Brain Barrier by Increasing Membrane Fluidity

BACKGROUND

Intracellular tension plays a crucial role in the destruction of the blood-brain barrier (BBB) in response to lesion stimuli. Tight junction structure could be primarily affected by tension activity. In this study, we aimed to determine the effects of extracellular BBB damage on intracellular tension activity, and elucidate the mechanism underlying the effects of intracellular protein nanoparticle-related osmotic pressure on BBB permeability.

METHODS

The intracellular tension for tight junction proteins occludin and ZO1 was evaluated using the fluorescence resonance energy transfer (FRET)-based tension probes and cpstFRET analysis. The changes in mobility ratios of occludin were evaluated via the fluorescence recovery after photobleaching (FRAP) test. The cytoplasmic osmotic pressure (OP) was measured using Osmometer. The count rate of cytoplasmic nanoparticles was detected by Nanosight NS300. The activation of cofilin and stathmin was examined by Western blot analysis. The BBB permeability in vivo was determined via the changes of Evans Blue (EB) injected into SD rats. The tight junction formation was assessed by the measurement of transendothelial electrical resistance (TEER). Intracellular calcium or chloride ions were measured using Fluo-4 AM or MQAE dyes.

RESULTS

BBB lesions were accompanied by changes in occludin/ZO1 tension. Increases in intracellular osmotic pressure were involved in alteration of BBB permeability, possibly through the depolymerization of microfilaments or microtubules and mass production of protein nanoparticles according to the Donnan effect. Recovery of protein nanoparticle-related osmotic pressure could effectively reverse the effects of changes in occludin/ZO1 tension under BBB lesions. Outward tension of intracellular osmotic potential also caused upregulation of membrane fluidity, which promoted nonselective drug influx.

CONCLUSION

Our results suggest a crucial mechanical mechanism underlying BBB lesions, and protein nanoparticle-related osmotic pressure could be a novel therapeutic target for BBB lesion-related brain diseases.

Reappraisal of anoxic spreading depolarization as a terminal event during oxygen-glucose deprivation in brain slices in vitro

Anoxic spreading depolarization (aSD) has been hypothesized as a terminal event during oxygen–glucose deprivation (OGD) in submerged cortical slices in vitro. However, mechanical artifacts caused by aSD-triggered edema may introduce error in the assessment of neuronal viability. Here, using continuous patch-clamp recordings from submerged rat cortical slices, we first confirmed that vast majority of L4 neurons permanently lost their membrane potential during OGD-induced aSD. In some recordings, spontaneous transition from whole-cell to out-side out configuration occurred during or after aSD, and only a small fraction of neurons survived aSD with reperfusion started shortly after aSD. Secondly, to minimize artifacts caused by OGD-induced edema, cells were short-term patched following OGD episodes of various duration. Nearly half of L4 cells maintained membrane potential and showed the ability to spike-fire if reperfusion started less than 10 min after aSD. The probability of finding live neurons progressively decreased at longer reperfusion delays at a rate of about 2% per minute. We also found that neurons in L2/3 show nearly threefold higher resistance to OGD than neurons in L4. Our results suggest that in the OGD ischemia model, aSD is not a terminal event, and that the “commitment point” of irreversible damage occurs at variable delays, in the range of tens of minutes, after OGD-induced aSD in submerged cortical slices.

Hyaluronidase reduced edema after experimental traumatic brain injury

Cerebral edema and the subsequent increased intracranial pressure are associated with mortality and poor outcome following traumatic brain injury. Previous in vitro studies have shown that the Gibbs-Donnan effect, which describes the tendency of a porous, negatively charged matrix to attract positive ions and water, applies to brain tissue and that enzymatic reduction of the fixed charge density can prevent tissue swelling. We tested whether hyaluronidase, an enzyme that degrades the large, negatively charged glycosaminoglycan hyaluronan, could reduce brain edema after traumatic brain injury. In vivo, intracerebroventricular injection of hyaluronidase after controlled cortical impact in mice reduced edema in the ipsilateral hippocampus at 24 h by both the wet-weight/dry-weight method (78.15 ± 0.65% vs. 80.4 ± 0.46%; p < 0.01) and T₂-weighted magnetic resonance imaging (13.88 ± 3.09% vs. 29.23 ± 6.14%; p < 0.01). Hyaluronidase did not adversely affect blood-brain-barrier-integrity measured by dynamic contrast-enhanced magnetic resonance imaging, nor did hyaluronidase negatively affect functional recovery after controlled cortical impact measured with the rotarod or Morris water maze tasks. Reduction of fixed charge density by hyaluronidase was confirmed in cortical explants in vitro (5.46 ± 1.15 µg/mg vs. 7.76 ± 1.87 µg/mg; p < 0.05). These data demonstrate that targeting the fixed charge density with hyaluronidase reduced edema in an in vivo mouse model of traumatic brain injury.

Softening of the chronic hemi-section spinal cord injury scar parallels dysregulation of cellular and extracellular matrix content

Regeneration following spinal cord injury (SCI) is challenging in part due to the modified tissue composition and organization of the resulting glial and fibrotic scar regions. Inhibitory cell types and biochemical cues present in the scar have received attention as therapeutic targets to promote regeneration. However, altered Young's modulus of the scar as a readout for potential impeding factors for regeneration are not as well-defined, especially in vivo. Although the decreased Young's modulus of surrounding tissue at acute stages post-injury is known, the causation and outcomes at chronic time points remain largely understudied and controversial, which motivates this work. This study assessed the glial and fibrotic scar tissue's Young's modulus and composition (scar morphometry, cell identity, extracellular matrix (ECM) makeup) that contribute to the tissue's stiffness. The spatial Young's modulus of a chronic (~18-wks, post-injury) hemi-section, including the glial and fibrotic regions, were significantly less than naïve tissue (~200 Pa; p < 0.0001). The chronic scar contained cystic cavities dispersed in areas of dense nuclei packing. Abundant CNS cell types such as astrocytes, oligodendrocytes, and neurons were dysregulated in the scar, while epithelial markers such as vimentin were upregulated. The key ECM components in the CNS, namely sulfated proteoglycans (sPGs), were significantly downregulated following injury with concomitant upregulation of unsulfated glycosaminoglycans (GAGs) and hyaluronic acid (HA), likely altering the foundational ECM network that contributes to tissue stiffness. Our results reveal the Young's modulus of the chronic SCI scar as well as quantification of contributing elastic components that can provide a foundation for future study into their role in tissue repair and regeneration.

Inward Tension of Talin and Integrin-related Osmotic Pressure are involved Synergetically in the Invasion and Metastasis of Non-small Cell Lung Cancer

The integrin receptor protein talin plays vital roles in intracellular chemical and mechanical activities, and it is implicated in the high invasion and poor prognosis of non-small cell lung cancer (NSCLC). To better understand the mechanism underlying the function of talin in NSCLC invasion and metastasis, a few newly designed tension probe based on Förster resonance energy transfer was used for real-time observation of tension changes in A549 cells. High NSCLC cell aggressiveness was found to be accompanied with inward talin and outward glial fibrillary acidic protein (GFAP) tensions, which are closely associated with microfilament (MF) force and intracellular osmotic potential. The increased osmotic pressure resulted from the production of intracellular protein nanoparticles and the related ion influx. Furthermore, integrin activation was found to adjust the talin and GFAP tensions. Disruption of the interaction between talin and MFs blocked the mechanical source of talin, reducing both talin tension and osmotic pressure and thus inhibiting NSCLC cell invasion and migration. Consequently, our study demonstrates that talin is involved in NSCLC invasion and migration via its inward tension and that the integrin pathway is correlated closely with protein-nanoparticle-induced outward osmotic pressure.

Influences of sodium and glycosaminoglycans on skin oedema and the potential for ulceration: a finite-element approach

Venous ulcers are chronic transcutaneous wounds common in the lower legs. They are resistant to healing and have a 78% chance of recurrence within 2 years. It is commonly accepted that venous ulcers are caused by the insufficiency of the calf muscle pump, leading to blood pooling in the lower legs, resulting in inflammation, skin oedema, tissue necrosis and eventually skin ulceration. However, the detailed physiological events by which inflammation contributes to wound formation are poorly understood. We therefore sought to develop a model that simulated the inflammation, using it to determine the internal stresses and pressure on the skin that contribute to venous ulcer formation. A three-layer finite-element skin model (epidermis, dermis and hypodermis) was developed to explore the roles in wound formation of two inflammation identifiers: glycosaminoglycans (GAG) and sodium. A series of parametric studies showed that increased GAG and sodium content led to oedema and increased tissue stresses of 1.5 MPa, which was within the reported range of skin tissue ultimate tensile stress (0.1-40 MPa). These results suggested that both the oedema and increased fluid pressure could reach a threshold for tissue damage and eventual ulcer formation. The models presented here provide insights to the pathological events associated with venous insufficiency, including inflammation, oedema and skin ulceration.

Time-resolved quantification of the dynamic extracellular space in the brain: study of cortical spreading depression

Extracellular diffusion in the brain is customarily characterized by two parameters, the extracellular space (ECS) volume fraction α and the diffusion tortuosity λ. How these two parameters are temporarily modified and correlated in a physiological/pathological event remains unclear to date. Using tetramethylammonium (TMA⁺) as an ECS ion tracer in a newly updated iontophoretic sinusoidal method, we studied in this work the dynamic α(t) and λ(t) in rat somatosensory cortex during spreading depression (SD). Temporal variations of α(t) and λ(t), as evoked by SD, were obtained through analyses of the extracellular TMA⁺ diffusion waveform resulting from a sinusoidally modulated point source. Most of the time, cortical SD induced coordinated α(t) decreases and λ(t) increases. In rare occasions, SD induced sole decreases of α(t) with no changes in λ(t). The independent modulation of α(t) and λ(t) was neither associated with cortical anatomy nor with the specific shape of the SD field potential wave. Changes of α(t) and λ(t) often took place acutely at the onset of SD, followed by a more transient modulation. Compared with the prior iontophoretic methods of TMA⁺, the sinusoidal method provides time-resolved quantification of α(t) and λ(t) in relative terms but also raises a higher property requirement on the TMA⁺-selective microelectrode. The sinusoidal method could become a valuable tool in the studies of the dynamic ECS response in various brain events. NEW & NOTEWORTHY An iontophoretic sinusoidal method was applied to study the dynamic changes of two extracellular space parameters, the extracellular volume fraction α(t) and tortuosity λ(t), in the brain during cortical spreading depression. Both parameters showed coordinated (most often) and independent (rarely) modulations in spreading depression. The sinusoidal method is equally applicable to other acute pathological events and a valuable tool to study the functional role of extracellular space in brain events.

Biomechanical simulation of traumatic brain injury in the rat

BACKGROUND

Traumatic brain injury poses an enormous clinical challenge. Rats are the animals most widely used in pre-clinical experiments. Biomechanical simulations of these experiments predict the distribution of mechanical stress and strain across key tissues. It is in theory possible to dramatically increase our understanding of traumatic brain injury pathophysiology by correlating stress and strain with histological and functional injury outcomes. This review summarizes the state of the art in biomechanical simulation of traumatic brain injury in the rat. It also places this body of knowledge in the context of the wider effort to understand traumatic brain injury in rats and in humans.

METHODS

Peer-reviewed research articles on biomechanical simulation of traumatic brain injury in the rat were reviewed and summarized.

FINDINGS

When mathematical models of traumatic brain injury in the rat first emerged, they relied on scant data regarding biomechanical properties. The data on relevant biomechanical properties has increased recently. However, experimental models of traumatic brain injury in the rat have also become less homogeneous. New and modified models have emerged that are biomechanically distinct from traditional models.

INTERPRETATION

Important progress in mathematical modeling and measurement of biomechanical properties has led to credible, predictive simulations of traditional, experimental models of traumatic brain injury in the rat, such as controlled cortical impact. However, recent trends such as the increasing popularity of closed head models and blast models create new biomechanical challenges. Investigators studying rat brain biomechanics must continue to innovate to keep pace with these developments.

Intracellular ion and protein nanoparticle-induced osmotic pressure modify astrocyte swelling and brain edema in response to glutamate stimuli

Intracellular tension activity plays a crucial role in cytotoxic brain edema and astrocyte swelling. Here, a few genetically encoded FRET-based tension probes were designed to detect cytoskeletal structural tension optically, including their magnitude and vectors. The astrocyte swelling resulted in GFAP tension increment, which is associated with the antagonistic effect of inward microfilaments (MFs) and microtubules (MTs) forces. In glutamate-induced astrocyte swelling, GFAP tension rise resulted from outward ion and protein nanoparticle-induced osmotic pressure (PN-OP) increases, where PN-OP could be elicited by MF and MT depolymerization, protein nanoparticle production, and activation of cofilin and stathmin-1. Attenuation of both ion osmotic pressure and PN-OP by drug combinations, together with free-radical scavenger, relieved cerebral edema in vivo. The study suggests that intracellular osmotic pressure (especially PN-OP) has a pivotal role in glutamate-induced astrocyte swelling and brain edema. Recovery of cytoplasmic potential is a promising target to develop new drugs and cure brain edema.

Dynamics of the Hypoxia-Induced Tissue Edema in the Rat Barrel Cortex in vitro

Cerebral edema is a major, life threatening complication of ischemic brain damage. Previous studies using brain slices have revealed that cellular swelling and a concomitant increase in tissue transparency starts within minutes of the onset of metabolic insult in association with collective anoxic spreading depolarization (aSD). However, the dynamics of tissue swelling in brain slices under ischemia-like conditions remain elusive. Here, we explored the dynamics of brain tissue swelling induced by oxygen-glucose deprivation (OGD) in submerged rat barrel cortex slices. Video monitoring of the vertical and horizontal position of fluorescent dye-filled neurons and contrast slice surface imaging revealed elevation of the slice surface and a horizontal displacement of the cortical tissue during OGD. The OGD-induced tissue movement was also associated with an expansion of the slice borders. Tissue swelling started several minutes after aSD and continued during reperfusion with normal solution. Thirty minutes after aSD, slice borders had expanded by ~130 μm and the slice surface had moved up to attain a height of ~70 μm above control levels, which corresponded to a volume increase of ~30%. Hyperosmotic sucrose solution partially reduced the OGD-induced slice swelling. Thus, OGD-induced cortical slice tissue swelling in brain slices in vitro recapitulates many features of ischemic cerebral edema in vivo, its onset is tightly linked to aSD and it develops at a relatively slow pace after aSD. We propose that this model of cerebral edema in vitro could be useful for the exploration of the pathophysiological mechanisms underlying ischemic cerebral edema and in the search for an efficient treatment to this devastating condition.

Diffusion MRI in acute nervous system injury

Diffusion weighted magnetic resonance imaging (DWI) and related techniques such as diffusion tensor imaging (DTI) are uniquely sensitive to the microstructure of the brain and spinal cord. In the acute aftermath of nervous system injury, for example, DWI reveals changes caused by injury that remains invisible on other MRI contrasts such as T₂-weighted imaging. This ability has led to a demonstrated clinical utility in cerebral ischemia. However, despite strong promise in preclinical models and research settings, DWI has not been as readily adopted for other acute injuries such as traumatic spinal cord, brain, or peripheral nerve injury. Furthermore, the precise biophysical mechanisms that underlie DWI and DTI changes are not fully understood. In this report, we review the DWI and DTI changes that occur in acute neurological injury of cerebral ischemia, spinal cord injury, traumatic brain injury, and peripheral nerve injury. Their associations with the underlying biology are examined with an emphasis on the role of acute axon and dendrite beading. Lastly, emerging DWI techniques to overcome the limitations of DTI are discussed as these may offer the needed improvements to translate to clinical settings.

Mathematical modelling of blood-brain barrier failure and oedema

Injuries such as traumatic brain injury and stroke can result in increased blood-brain barrier (BBB) permeability. This increase may lead to water accumulation in the brain tissue resulting in vasogenic oedema. Although the initial injury may be localized, the resulting oedema causes mechanical damage and compression of the vasculature beyond the original injury site. We employ a biphasic mixture model to investigate the consequences of BBB permeability changes within a region of brain tissue and the onset of vasogenic oedema. We find that such localized changes can indeed result in brain tissue swelling and suggest that the type of damage that results (stress damage or strain damage) depends on the ability of the brain to clear oedema fluid.

Experimental measurements and mathematical modeling towards quantification of brain swelling stress

Traumatic brain injury results in brain tissue swelling which can be a life threatening condition due to skull confinement. While previous efforts successfully measured the exhibited volume change in brain tissue swelling, no data exist to provide information about the exhibited stresses. In this study, confined compression mechanical testing was employed to measure swelling stress in murine brain tissue samples by varying the ionic concentration of the bathing solutions. Subsequently, computer simulations of the experimental protocol were employed to confirm a triphasic mathematical model describing the effect and provide insights into the experimental data. We measured the swelling stress to be in the range of 1.2-6.7kPa (9.0-50.2mmHg) depending on the ionic strength of the bathing solution, while a good correspondence was demonstrated among the experimentally measured and simulated responses. Furthermore, the mathematical model featured the osmotic pressure as the primary contributor to the swelling stress, while a parametric analysis showed that the densities of the intracellular fixed charges and of the non-permeable solutes significantly affect the swelling stress.

An overview of multiphase cartilage mechanical modelling and its role in understanding function and pathology

There is a long history of mathematical and computational modelling with the objective of understanding the mechanisms governing cartilage׳s remarkable mechanical performance. Nonetheless, despite sophisticated modelling development, simulations of cartilage have consistently lagged behind structural knowledge and thus the relationship between structure and function in cartilage is not fully understood. However, in the most recent generation of studies, there is an emerging confluence between our structural knowledge and the structure represented in cartilage modelling. This raises the prospect of further refinement in our understanding of cartilage function and also the initiation of an engineering-level understanding for how structural degradation and ageing relates to cartilage dysfunction and pathology, as well as informing the potential design of prospective interventions. Aimed at researchers entering the field of cartilage modelling, we thus review the basic principles of cartilage models, discussing the underlying physics and assumptions in relatively simple settings, whilst presenting the derivation of relatively parsimonious multiphase cartilage models consistent with our discussions. We proceed to consider modern developments that start aligning the structure captured in the models with observed complexities. This emphasises the challenges associated with constitutive relations, boundary conditions, parameter estimation and validation in cartilage modelling programmes. Consequently, we further detail how both experimental interrogations and modelling developments can be utilised to investigate and reduce such difficulties before summarising how cartilage modelling initiatives may improve our understanding of cartilage ageing, pathology and intervention.

Intracerebroventricular administration of chondroitinase ABC reduces acute edema after traumatic brain injury in mice

Background

Brain edema is a significant challenge facing clinicians managing severe traumatic brain injury (TBI) in the acute period. If edema reaches a critical point, it leads to runaway intracranial hypertension that, in turn, leads to severe morbidity or death if left untreated. Clinical data on the efficacy of standard interventions is mixed. The goal of this study was to validate a novel therapeutic strategy for reducing post-traumatic brain edema in a mouse model. Prior in vitro work reported that the brain swells due to coupled electrostatic and osmotic forces generated by large, negatively charged, immobile molecules in the matrix that comprises brain tissue. Chondroitinase ABC (ChABC) digests chondroitin sulfate proteoglycan, a molecule that contributes to this negative charge. Therefore, we administered ChABC by intracerebroventricular (ICV) injection after controlled cortical impact TBI in the mouse and measured associated changes in edema.

Results

Almost half of the edema induced by injury was eliminated by ChABC treatment.

Conclusions

ICV administration of ChABC may be a novel and effective method of treating post-traumatic brain edema in the acute period.

Investigating cerebral oedema using poroelasticity

Cerebral oedema can be classified as the tangible swelling produced by expansion of the interstitial fluid volume. Hydrocephalus can be succinctly described as the abnormal accumulation of cerebrospinal fluid (CSF) within the brain which ultimately leads to oedema within specific sites of parenchymal tissue. Using hydrocephalus as a test bed, one is able to account for the necessary mechanisms involved in the interaction between oedema formation and cerebral fluid production, transport and drainage. The current state of knowledge about integrative cerebral dynamics and transport phenomena indicates that poroelastic theory may provide a suitable framework to better understand various diseases. In this work, Multiple-Network Poroelastic Theory (MPET) is used to develop a novel spatio-temporal model of fluid regulation and tissue displacement within the various scales of the cerebral environment. The model is applied through two formats, a one-dimensional finite difference - Computational Fluid Dynamics (CFD) coupling framework, as well as a two-dimensional Finite Element Method (FEM) formulation. These are used to investigate the role of endoscopic fourth ventriculostomy in alleviating oedema formation due to fourth ventricle outlet obstruction (1D coupled model) in addition to observing the capability of the FEM template in capturing important characteristics allied to oedema formation, like for instance in the periventricular region (2D model).

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.

Brain tissue responses to neural implants impact signal sensitivity and intervention strategies

Implantable biosensors are valuable scientific tools for basic neuroscience research and clinical applications. Neurotechnologies provide direct readouts of neurological signal and neurochemical processes. These tools are generally most valuable when performance capacities extend over months and years to facilitate the study of memory, plasticity, and behavior or to monitor patients’ conditions. These needs have generated a variety of device designs from microelectrodes for fast scan cyclic voltammetry (FSCV) and electrophysiology to microdialysis probes for sampling and detecting various neurochemicals. Regardless of the technology used, the breaching of the blood–brain barrier (BBB) to insert devices triggers a cascade of biochemical pathways resulting in complex molecular and cellular responses to implanted devices. Molecular and cellular changes in the microenvironment surrounding an implant include the introduction of mechanical strain, activation of glial cells, loss of perfusion, secondary metabolic injury, and neuronal degeneration. Changes to the tissue microenvironment surrounding the device can dramatically impact electrochemical and electrophysiological signal sensitivity and stability over time. This review summarizes the magnitude, variability, and time course of the dynamic molecular and cellular level neural tissue responses induced by state-of-the-art implantable devices. Studies show that insertion injuries and foreign body response can impact signal quality across all implanted central nervous system (CNS) sensors to varying degrees over both acute (seconds to minutes) and chronic periods (weeks to months). Understanding the underlying biological processes behind the brain tissue response to the devices at the cellular and molecular level leads to a variety of intervention strategies for improving signal sensitivity and longevity.

Effects of caspase-1 knockout on chronic neural recording quality and longevity: insight into cellular and molecular mechanisms of the reactive tissue response

Chronic implantation of microelectrodes into the cortex has been shown to lead to inflammatory gliosis and neuronal loss in the microenvironment immediately surrounding the probe, a hypothesized cause of neural recording failure. Caspase-1 (aka Interleukin 1β converting enzyme) is known to play a key role in both inflammation and programmed cell death, particularly in stroke and neurodegenerative diseases. Caspase-1 knockout (KO) mice are resistant to apoptosis and these mice have preserved neurologic function by reducing ischemia-induced brain injury in stroke models. Local ischemic injury can occur following neural probe insertion and thus in this study we investigated the hypothesis that caspase-1 KO mice would have less ischemic injury surrounding the neural probe. In this study, caspase-1 KO mice were implanted with chronic single shank 3 mm Michigan probes into V1m cortex. Electrophysiology recording showed significantly improved single-unit recording performance (yield and signal to noise ratio) of caspase-1 KO mice compared to wild type C57B6 (WT) mice over the course of up to 6 months for the majority of the depth. The higher yield is supported by the improved neuronal survival in the caspase-1 KO mice. Impedance fluctuates over time but appears to be steadier in the caspase-1 KO especially at longer time points, suggesting milder glia scarring. These findings show that caspase-1 is a promising target for pharmacologic interventions.

Is the Donnan effect sufficient to explain swelling in brain tissue slices?

Brain tissue swelling is a dangerous consequence of traumatic injury and is associated with raised intracranial pressure and restricted blood flow. We consider the mechanical effects that drive swelling of brain tissue slices in an ionic solution bath, motivated by recent experimental results that showed that the volume change of tissue slices depends on the ionic concentration of the bathing solution. This result was attributed to the presence of large charged molecules that induce ion concentration gradients to ensure electroneutrality (the Donnan effect), leading to osmotic pressures and water accumulation. We use a mathematical triphasic model for soft tissue to characterize the underlying processes that could lead to the volume changes observed experimentally. We suggest that swelling is caused by an osmotic pressure increase driven by both non-permeating solutes released by necrotic cells, in addition to the Donnan effect. Both effects are necessary to explain the dependence of the tissue slice volume on the ionic bath concentration that was observed experimentally.

Multiphasic finite element framework for modeling hydrated mixtures with multiple neutral and charged solutes

Computational tools are often needed to model the complex behavior of biological tissues and cells when they are represented as mixtures of multiple neutral or charged constituents. This study presents the formulation of a finite element modeling framework for describing multiphasic materials in the open-source finite element software febio.1 Multiphasic materials may consist of a charged porous solid matrix, a solvent, and any number of neutral or charged solutes. This formulation proposes novel approaches for addressing several challenges posed by the finite element analysis of such complex materials: The exclusion of solutes from a fraction of the pore space due to steric volume and short-range electrostatic effects is modeled by a solubility factor, whose dependence on solid matrix deformation and solute concentrations may be described by user-defined constitutive relations. These solute exclusion mechanisms combine with long-range electrostatic interactions into a partition coefficient for each solute whose value is dependent upon the evaluation of the electric potential from the electroneutrality condition. It is shown that this electroneutrality condition reduces to a polynomial equation with only one valid root for the electric potential, regardless of the number and valence of charged solutes in the mixture. The equation of charge conservation is enforced as a constraint within the equation of mass balance for each solute, producing a natural boundary condition for solute fluxes that facilitates the prescription of electric current density on a boundary. It is also shown that electrical grounding is necessary to produce numerical stability in analyses where all the boundaries of a multiphasic material are impermeable to ions. Several verification problems are presented that demonstrate the ability of the code to reproduce known or newly derived solutions: (1) the Kedem-Katchalsky model for osmotic loading of a cell; (2) Donnan osmotic swelling of a charged hydrated tissue; and (3) current flow in an electrolyte. Furthermore, the code is used to generate novel theoretical predictions of known experimental findings in biological tissues: (1) current-generated stress in articular cartilage and (2) the influence of salt cation charge number on the cartilage creep response. This generalized finite element framework for multiphasic materials makes it possible to model the mechanoelectrochemical behavior of biological tissues and cells and sets the stage for the future analysis of reactive mixtures to account for growth and remodeling.

Possible causes of apoptotic volume decrease: an attempt at quantitative review

Cell shrinkage and dehydration are essential characteristics of apoptosis, and loss of as much as half of the initial cell volume is not uncommon. This phenomenon is usually explained by efflux of K+and Cl−. We reexamine this hypothesis on the basis of the available data for ion concentrations and the requirements for osmotic equilibrium and electroneutrality. In addition to ion loss, we discuss the possible impacts of several other processes: efflux of low-molecular-weight osmolytes, acidification of the cytosol, effects of water channels and pumps, heterogeneity of intracellular water, and dissociation of apoptotic bodies. We conclude that most mammalian cells are theoretically capable of reducing their volume by 15–20% through ion loss or a decrease in cytosolic pH, although, in reality, the contribution of these mechanisms to apoptotic shrinkage may be smaller. Transitions between osmotically active and inactive water pools might influence cell volume as well; these mechanisms are poorly understood but are amenable to experimental study. Dissociation of apoptotic bodies is a separate mechanism of volume reduction and should be monitored closely; this can be best achieved by measurement of intracellular water, rather than cell volume.

Cervical collagen network remodeling in normal pregnancy and disrupted parturition in Antxr2 deficient mice

The remodeling of the cervix from a rigid barrier into a compliant structure, which dilates to allow for delivery, is a critical process for a successful pregnancy. Changes in the mechanical properties of cervical tissue during remodeling are hypothesized to be related to the types of collagen crosslinks within the tissue. To further understand normal and abnormal cervical remodeling, we quantify the material properties and collagen crosslink density of cervical tissue throughout pregnancy from normal wild-type and Anthrax Toxin Receptor 2 knockout (Antxr2-/-) mice. Antxr2-/- females are known to have a parturition defect, in part, due to an excessive accumulation of extracellular matrix proteins in the cervix, particularly collagen. In this study, we determined the mechanical properties in gestation-timed cervical samples by osmotic loading and measured the density of mature collagen crosslink, pyridinoline (PYD), by liquid chromatography tandem mass spectrometry (LC-MSMS). The equilibrium material response of the tissue to loading was investigated using a hyperelastic material model where the stresses in the material are balanced by the osmotic swelling tendencies of the glycosaminoglycans and the tensile restoring forces of a randomly-oriented crosslinked collagen fiber network. This study shows that the swelling response of the cervical tissue increased with decreasing PYD density in normal remodeling. In the Antxr2-/- mice, there was no significant increase in swelling volume or significant decrease in crosslink density with advancing gestation. By comparing the ECM-mechanical response relationships in normal and disrupted parturition mouse models this study shows that a reduction of collagen crosslink density is related to cervical softening and contributes to the cervical remodeling process.

Regulation of cell volume by glycosaminoglycans

Cell volume is regulated by a delicate balance between ion distribution across the plasma membrane and the osmotic properties of intra- and extracellular components. Using a fluorescent calcein indicator, we analysed the effects of glycosaminoglycans on the cell volume of hyaluronan producing fibroblasts and hyaluronan deficient HEK cells over a time period of 30 h. Exogenous glycosaminoglycans induced cell blebbing after 2 min and swelling of fibroblasts to about 110% of untreated cell volume at low concentrations which decreased at higher concentrations. HEK cells did not show cell blebbing and responded by shrinking to 65% of untreated cell volume. Heparin induced swelling of both fibroblasts and HEK cells. Hyaluronidase treatment or inhibition of hyaluronan export led to cell shrinkage indicating that the hyaluronan coat maintained fibroblasts in a swollen state. These observations were explained by the combined action of the Donnan effect and molecular crowding.