Computer modeling of ischemic stroke

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Curator: William W Lytton



A stroke, also called a cerebrovascular accident (CVA), is a sudden event due to pathology of or within blood vessels to the brain. Stroke results in damage to brain tissue, causing deficits such as paralysis or loss of language. These deficits can be small, or can be devastating and long-term, depending on the brain territory involved and the extent of damage. Stroke can be divided into two main categories: hemorrhagic and ischemic. Hemorrhagic stroke, about 20% of stroke cases, results from bleeding from an arterio-venous malformation or aneurysm, or as a result of severe hypertension. Ischemic stroke, about 80% of cases, results from a blockage of blood flow in an artery due to a thrombus or embolus. This produces a sudden reduction of blood flow - the meaning of ischemia - which results in failure of delivery of vital metabolites to the brain. Ischemic stroke is typically associated with atherosclerosis, as well as with other risk factors such as hypertension and diabetes. Stroke is the major cause of brain ischemia, although more chronic ischemic disorders can also occur. In this chapter we will focus on modeling of ischemic stroke.

Localized brain ischemia in stroke produces oxygen and glucose deprivation to brain cells, leading to cell dysfunction and death. Brain cells do not have much metabolic reserve, so loss of blood flow for even a few minutes can lead to irreversible neurological damage and brain infarction. The eventual goal of modeling in stroke is to assist in prevention and therapy. These include the identification of approaches to reduce risk, development of treatments that can protect the brain at the time of stroke, and development of treatments to restore function and improve long-term outcome. The importance of computer models is emphasized by the frequent discrepancies between the results of therapeutic interventions in animal models compared to outcomes for these same interventions in human trials (Fisher et al., 2009; Legos et al., 2008). Although there are many issues in translating animal model data to clinical failures, it is hoped that improved computer models can help bridge these differences to explain why outcomes in animals and humans might differ in particular cases. To encompass these various goals, stroke modeling must cover multiple spatial and temporal scales, from the single cell to local brain circuits to whole brain functioning, and from early, protective acute ischemic stroke interventions (hours) to much later interventions (days to weeks after stroke) that can restore functions lost due to brain injury. Multiscale modeling is the set of techniques used to capture phenomenology across these many scales.

The tissue involved in a stroke can be subdivided into the ischemic core (the central area of severe ischemia) and the surrounding ischemic penumbra (an area of damaged tissue where cells are at risk but not yet dead). This penumbral area is considered the best target for protection in acute stroke intervention and recovery, as these cells still retain some viability. Currently available acute stroke intervention is aimed at restoring blood flow using intravenous tissue plasminogen activator (tPA) to break up a clot that is impeding blood flow. Thrombolysis using tPA is the only approved intervention for ischemic stroke intervention, but it must be applied within the first several hours after stroke. There is additional opportunity to intervene within this very early period with neuroprotective therapies to reduce or reverse some of the many injurious processes occurring in the penumbra. Unfortunately, clinical trials of neuroprotective drugs have not been successful, despite using the same agents successfully employed in animal trials.

Most computer modeling has been done to look at the early post-stroke period. During this time, and up to 12 to 24 hours post-stroke, a large number of pathophysiological events occur that can be opportunities for intervention to improve outcomes. Protection of the penumbra will involve understanding the interactions of multiple cell types and factors: peripheral circulating leukocytes and lymphocytes, microglia, oligodendroglia and astroglial cellular mechanisms, angiogenesis, neurogenesis, synaptic and myelin reorganization, and many intracellular and extracellular signaling processes (Barone, 2009; Barone, 2010). Although knowledge is currently evolving to help distinguish the roles of these many actors for computer modeling, only a few of the factors are currently being considered in models. During later post-stroke periods, the damage is considered largely fixed. However, rehabilitation is still valuable to assist brain restoration, since plasticity in areas adjacent to the infarction and in the contralateral hemisphere and the rest of the brain can improve patient outcome (e.g., learning to write with the non-affected hand). Models of recovery have been developed and will be mentioned briefly below.

In the future, multiscale modeling of stroke pathology will require a great deal of modeling beyond the effects of ischemia on neurons. This will include modeling of blood vessels (and the neurovascular unit), modeling of changes in glia cells, and perhaps even mechanical modeling of brain parenchyma. In particular, blood and blood vessel dynamics is an enormous topic that will require use of computational fluid dynamics, together with endothelial cell genomic and proteomic modeling and clotting and thrombosis mechanisms. It is important to note here that the focus in the computational neuroscience of ischemia differs greatly from most traditional computational neuroscience approaches which generally focus on cell connectivity via synaptic coupling. In stroke modeling, there is a large variety of intercellular processes occurring, with synaptic coupling being relatively less important than other processes.

In current practice, ischemia is primarily modeled at just two spatial scales: cellular scale (submillimeter) and tissue scale (millimeters to centimeters). The cellular scale focuses on understanding of ionic, neurotransmitter, electrophysiological and ion channel changes in both neurons and glial cells. Tissue level (multicellular) models typically look at the two major regions of interest: 1. the ischemic core which is the central area whose cells are deprived of oxygen and glucose and will die rapidly, and 2. the penumbra that surrounds the core, where blood flow is low but cells can be saved if blood flow is reintroduced or if cells in this area can be protected. Although some of the same pathological processes pertain to both penumbral and core zones, the ongoing additional pathological processes in the penumbra eventually results in infarct expansion into what was initially the penumbra area.

Cellular scale modeling

Intracellular models allow us to develop an understanding of the ischemic cascade and the signaling decision points for cell death. These decision points help determine whether a cell will go through one of several death pathways, or proceed to recovery. Identifying these decision points can assist in developing methods to prevent cell damage. Ischemia sets in motion a cascade of pathological changes including loss of energy, inability to regulate membrane potential, release of excitatory transmitters, calcium-induced activation of enzymes, vascular changes, and altered gene and protein expression. These changes occur across multiple time scales, from milliseconds to days, across multiple spatial scales, and in changing combinations over time. Some ischemic insults will cause immediate cell death via cytotoxicity and necrosis, whereas other levels will engage prolonged programmed cell death. Still others will leave cells in various types of limbo between life and death, as the cell attempts a prolonged recovery. The many pathways suggest the possibility of many different points of possible therapeutic intervention at different temporal stages and in different parts of the ischemic tissue (Barone and Feuerstein, 1999; Legos et al., 2002; Lipton, 1999).

Initial insults

Understanding the systemic effects of ischemia-induced stroke requires an overview of oxygen in cellular metabolism and activity. Cells require oxygen as the final electron acceptor of the electron transport chain in cellular respiration, which generates adenosine triphosphate (ATP), the primary sources of energy for the cell. A decrease in available oxygen creates a shortage of ATP with a variety of subsequent outcomes. Although some cells have secondary energy storages (e.g., creatine phosphate in skeletal muscle), neurons and glial cells do not contain much reserve. Within minutes of oxygen deprivation, ATP will fall to about 20% of normal in brain tissue. This then goes on to produce partial or complete failure of ATP-dependent ion transport pumps. Failure of the critical Na+/K+-ATPase pump leads to loss of the membrane batteries which maintain resting membrane potential, and allow generation of action potentials.

The alteration of K+ pumping produces extracellular K+ accumulation, which causes membrane depolarization, which triggers the influx of Na+ and Ca++ into neurons through voltage-dependent ion channels. Water then flows into the cell following these ions. Calcium entry also causes synaptic vesicle release with subsequent of glutamate, the excitatory neurotransmitter. Then, the accumulation of extracellular glutamate activates ionotropic synaptic channels creating further increases in depolarization, as well as increases of intracellular Ca++ and Na+ . This creates a damaging positive feedback cycle called excitotoxicity.

Augmentation of calcium also initiates other pathological pathways. Calcium entry from the extracellular space is augmented by the signaled release of Ca++ from the endoplasmic reticulum (ER) and mitochondria through calcium-induced calcium release (CICR). Ca++ increase is also caused by failure of the Na+ /Ca++ pump, due to lack of ATP. Overall, Ca++ increase significantly contribute to cellular regulation failure, and potential for cell death (Barone and Feuerstein, 1999; Lipton, 1999). Due to its widespread effects, calcium has been at the center of much reaction-diffusion simulation research in both neurons and muscle. Although most of these calcium studies are not directed at understanding ischemia, they can make important contributions to ischemia modeling.

Cytotoxic Edema

The cellular swelling due to water influx from ionic shifts creates cytotoxic edema: accumulation of excess water within tissue. This cellular edema is caused by the many ongoing pathological processes that disregulate membrane functioning. In the case of ischemia, water accumulates inside the cells due to the pump failures. Cytotoxic edema, measured by diffusion-weighted MRI, is one of the earliest post-stroke imaging biomarkers.

A model of cytotoxic edema by Dronne et al. (2004) included concentrations of Na+ , K+ , Ca++ , Cl- , and glutamate, and compared compartmental volumes altered due to ionic gradients and equilibrium disturbances. The output of the model was used to measure cerebral blood flow, oxygen extraction factor, oxygen consumption, and measures related to water diffusion (detectable by MRI). Ischemic onset produced a decrease in cerebral blood flow, followed by compensatory vasodilation. Oxygen extraction factor increased to partially maintain oxidative metabolism and create ATP. The model produced a 50% shift of water from extracellular to intracellular spaces: the cytotoxic edema. Astrocytes were included and were fundamental to the ischemic cascade, since also vulnerable to ionic concentration alterations. The model showed evolution to necrosis due to a combination of changes in the ions and in glutamate. This study also made a therapeutic suggestion, showing that treatments that would increase activity of the delayed rectifier K+ channel could reduce cytotoxic edema and reduce overall damage.

Recently, Diekman et al. (2013) developed a model exploring how IP3-mediated Ca++ release in astrocytes may protect against their involvement in cytotoxic edema. The model looked at state variables for Ca++ ATP, ADP, pH, NADH in the cytosolic, ER, and mitochondrial compartments. Ischemia was simulated by reducing glucose and O2 by a constant percentage at a given time. This caused the astrocytes to lose the ability to maintain electrochemical gradients due to loss of energy sources. The two metabolites were tested individually and together and similar results were found in several measures: increased cell volume, depolarization, and reductions in ATP, NADH, and Ca++ . Therapeutically, addition of IP3 caused mitochondrial Ca++ to return to a higher level, improving ATP production during a short initial period of ischemia. In another set of simulations, a mitochondrial KATP channel was included and also had a protective effect. These results suggested that loss of mitochondrial Ca++ homeostasis is destabilizing, such that restoration of Ca++ levels could reduce pathological progression.

Cell death

If the damage caused by the ischemic event is beyond repair, cell death will occur. Major defined pathways of cell death include necrosis, primarily contributing to brain infarction, and delayed cell death, including apoptosis, leading to more diffuse cell loss later after stroke. Necrosis is uncontrolled, so that toxic cell contents are spilled out and can create further damage (Velier et al., 1999; Puyal et al., 2013), whereas during apoptosis, a cell is broken down systematically and no intracellular components are released into the extracellular space. Cytochrome oxidase and Ca++ are both signaling agents which are linked to apoptosis initiation. A major component of apoptosis signaling is a family of proteases called caspases. The caspase mechanism of action is predominantly based on their ability to cleave enzymes at specific amino acid residues. Research and modeling continue to attempt to provide more details about the complex caspase cascades. Pre-caspases can be activated from cell stress, cell damage or cell-to-cell signaling. In the model created by Fussenegger et al. (2000), the caspase cascade included FAS surface death receptor (a member of the tumor necrosis factor family), procaspase-8, and a cytoplasmic sequence called the death domain, in addition to related proteins. Activation of apoptotic signaling cascade is dependent on the binding of FADD protein in series with a number of subsequent proteins. The initial sequence created protein clusters which recruited additional adapter proteins, leading to cleavage of proteins associated with cell survival and initiation of apoptosis.

Other models of apoptosis have been developed in other brain conditions and in other tissues that have implications for ischemic brain disease. Thamattoor (2012) modeled cell death proliferation as a result of an initial brain lesion. The study suggested that if the apoptosis pathway could be blocked at certain key points, then damage might be halted after initiation. Another model by Mai and Liu (2009) showed protein interactions during programmed cell death using a 40-node Boolean model with pro- and anti-apoptotic mechanisms. They also explored where interventions could be used to block apoptosis progression.

Reactive Oxygen Species (ROS) and Nitric Oxide (NO)

Reactive oxygen species (ROS) are key mediators in ischemic stroke brain injury (Rodrigo et al., 2013). ROS are free radicals, highly reactive (hence damaging) chemicals with an oxygen that has a single free electron, instead of the usual stable pair. Low concentrations of ROS are produced during normal respiration and are eliminated using scavenging enzymes and uncoupling proteins. As their names suggest, scavenger proteins absorb toxic species, while uncouplers disconnect elements of the electron transport chain to reduce ROS production. Excess ROS, exceeding the capacity of scavenging, is produced in the mitochondria when the electron transport chain fails. The single electron on the oxygen changes its molecular interaction and can be dangerous to the cell because it can cohere with cell membranes, protein or DNA. ROS also damages organelles, particularly mitochondria and the nucleus, and induces apoptosis (Pradeep et al., 2012). Oxidative stress, sometimes referred to as cell stress, refers to the imbalance between the production of ROS and the ability to break them down. In ischemia, the shortage of oxygen and ATP allows ROSs to accumulate in the ischemic core and then spread out into the penumbra. This extracellular accumulation is then also a major trigger for the intracellular apoptotic cascade.

Huett and Periwal (2010) modeled ROS accumulation as a function of glucose and oxygen availability in mitochondria (in a pancreatic beta cell model). This model of uncontrolled ROS accumulation included ATP concentration, ATPase and ATP flux, and scavenger and uncoupling proteins. They measured ROS-induced suspension of electron transport, with associated inability of the proton pump to adequately pump H+ ions across the inner mitochondrial membrane. This model assumed a constant mitochondrial volume. ROS production was due to failure of electrons to be passed along the electron acceptor chain, instead being passed to a free oxygen molecule. The research suggested several cellular mechanisms that would hinder ROS accumulation, including uncoupling proteins and manipulation of mitochondrial membrane potential.

The cellular changes that are induced by ischemia will also increase the accumulation of nitric oxide (NO), a gaseous neurotransmitter which can pass through membranes causing widespread effects. NO serves a homeostatic effect in that it increases blood flow by relaxing arterioles. However, NO also contributes to oxidative stress through its chemical reactivity and is also a trigger of apoptosis (Lipton, 1999). NO was modeled by Alam et al. (2013) in relation to its effects on oxidative stress and metabolic dysfunction. Here again, calcium is a major culprit, triggering a rise of NO production via its synthases and then producing a feedback oscillation of apoptotic control proteins. Meanwhile, NO, since a gas, could diffuse rapidly, moving directly through membranes to have widespread effects on other cells. Various levels of calcium were tested in this model for their effect on the oscillation dynamics of calcium with two cascade proteins: Mdm2 and p53. Two regimes were identified which depended on the rate of calcium production: 1. a stable regime where Mdm2-p53 oscillations yielded apoptosis; and 2. a partly stabilized regime with a damped oscillation. The results suggested how calcium diffusion could induce widespread changes in p53 activity across the cell, so that independent Mdm2-p53 domains in different regions could be simultaneously activated. An analysis of stochastic effects revealed that noise could partially mask the effects of calcium on the Mdm2-p53 population when system size was small. This study suggested an important stochastic element in network regulation of apoptosis, with the level of randomness correlating with system stability.

Tissue scale and systems interactions

Computational neuroscience mostly looks at synaptic interactions and neuronal networks at the tissue scale. Chemical synapses are typically handled as events that are triggered presynaptically and are then received postsynaptically as a conductance change. It remains unclear to what extent these major physiological signalling mechanisms play a role in stroke. In any case, it is clear that these signals are overshadowed by the pathological signals that travel between cells as a result of alterations in extracellular composition of ions and other agents. These pathological interactions include the aforementioned NO and ROS zipping through tissue, cellular and intercellular (vasogenic) edema, cortical spreading depression, upregulation of inflammatory mediators, cells that interfere with blood flow, cell margination into brain tissue, microvascular flow changes due to release of vasoactive agents, mechanical tissue changes, and others. To date, only a few of these have been included in computer models of stroke.

Cerebral Blood Flow and Vasoconstriction

Changes in cerebral blood flow results in ischemia which decreases tissue oxygen and increases carbon dioxide. These changes then feed back to produce a variety of effects on cerebral blood flow, through increases in vasoactive molecules (molecules that change blood vessel caliber). The release of vasoconstrictors due to brain ischemia can exacerbate ischemic brain injury by reducing the degree of penumbral blood flow, contributing to the evolution of the ischemic infarct into the penumbra (Legos et al., 2008; Dawson et al., 1999).

A model by Ursino and Magosso (2001) included cerebral blood flow, intracranial pressure and various vascular compartments. The model was based on a lumped activation factor assumed to be regulated by several factors that play a role in cerebrovascular autoregulation, simulating cerebral blood flow under different levels of hypoxia and hypercapnea (high CO2 ), with different levels of intracerebral pressure change. As expected, they showed that increase in arterial CO2 caused vasodilation. However, the model suggested that these CO2 mechanisms did not directly affect regulatory responses, which were instead indirectly based on changes in oxygen level. It was also concluded that other unidentified mechanisms must also play a role in vasodilation.

Core and penumbra

As noted above, the penumbra is the region of affected neuronal tissue outside of the ischemic core. While the ischemic core is doomed, tissue in the penumbra retains a chance of being salvaged. Parts of the penumbra may retain some neural function, while other parts are still alive, but no longer have the metabolic resources needed to maintain specialized neuronal functions. The penumbra is sustained mainly by collateral blood flow that remains functioning after stroke. It is also negatively affected by proximity to toxic mediators and vasoactive molecules coming out of the core. The balance of these positive and negative influences will determine the relative injury, and viability, of penumbral tissue. Persistence of penumbral blood flow is most important because most tissue damage comes from ischemia itself - the loss of substrates for energy production. Hence, severity of ischemic damage will vary enormously depending on whether or not a region is served by anastomotic connections from neighboring blood supplies. In order to quantify the degree of ischemia, penumbra areas can be classified by combining changes in oxygen extraction factor, cerebral blood flow, and cellular metabolism. One of the key challenges in modeling the many areas of penumbra is to create clearly defined subregion parameters. Ideally a model could then segment the penumbra based on tissue prognosis and degree of cytotoxic edema measured by diffusion weighted-MRI, reflecting current infarction compared to the low but sustained flow to the penumbra considered the area at risk of injury (Legos et al., 2008). These changes reflect the degree of vascular changes that can result in vasogenic edema (blood vessel leakage) that contributes further to the evolution of infarction (Rosenberg et al., 1996; Romanic et al., 1998).

Duval et al. (2002) modeled the cellular consequences of changes in cerebral blood flow and highlighted how extracellular nutrient parameters would affect the penumbral regions, noting what types of edematous tissue might be salvageable. This model added a survival delay variable to quantify the trajectory of tissue in the penumbra from functional, through salvageable, and then to cell death or to restoration of cell health. The model looked at cerebral blood flow, rate of oxygen extraction from blood, metabolic rate of oxygen use by tissue, and the apparent diffusion coefficient of water. Results yielded information about the spatial dynamics of penumbral subregions, changes in distribution, sizes and shapes. Penumbra regions with altered cellular metabolism were generally not salvageable, whereas edematous penumbra tissue retained greater recovery potential. This model clarified ways in which extracellular nutrient parameters might effect the generation of different penumbral regions.

Cortical Spreading Depression

Cortical spreading depression (CSD) is a chemical wave in the neocortex, involving the spread of elevated extracellular potassium and other factors released during cell damage. CSD is a regenerative wave that moves across cortex at about 3.4 mm/second. CSD can be identified physiologically by the local reduction in EEG power associated with temporary reduction in spike generation due to the depolarization associated with high external K+ . CSD has been demonstrated in a wide variety of pathologies including stroke, migraine, post-seizure, and traumatic brain injury. Although the association with stroke both clinically and through in vivo research has been somewhat inconsistent, it is believed that a transient wave of CSD may be an important component of the neuronal responses following stroke.

Revett et al. (1998) modeled the relationship between CSD, penumbra, infarction and reversibility of the penumbra. In this model, the cortex was represented by a hexagonal array of elements, each of which represented a single cell and contained state variables for intracellular and extracellular ionic concentrations, levels of blood flow, and levels of metabolites. Impairment and intactness indices were measures that reflected levels of dysfunction. This model included discrete spatial zones, allowing exploration of how relative damage depended on the ratio of core infarct to penumbra. The model suggested a linear relationship between the amplitude of the CSD wave and the size of the penumbra region with both increasing over time. The study also noted the importance of K+ re-uptake, blood flow rate, and timing for predicting tissue salvageability and damage reversal. A similar model by Wei et al. (2014) produced CSD as a response to energy failure with reduction of Na+ /K+ pump activity. This model also included oxygen concentration as an additional state variable. The results suggested that CSD could contribute to abnormal functioning of the neurons and exacerbate the damage due to the original ischemia. Models by Ruppin and colleagues (Ruppin and Reggia, 2001; Revett et al., 1998; Ruppin et al., 1999) focused on the role of CSD in stroke, contrasting with non-wave mechanisms such as the more rapid free radical and nitric oxide spread, and slower leukocyte-induced toxicity. This model separated out dendritic processes, cell bodies, vascular bed, and glia, all associated with the ion channels involved in the CSD wave. CSD was shown to exacerbate damage in the penumbra and change the shape and size of the damage from the original ischemic incident. The range and shape of damaged tissue produced by the CSD was shown to be significantly different then that due to the non-wave phenomenology, providing testable predictions about stroke consequences.

In the model of Chapuisat et al. (2008) CSD was shown to contribute to determining whether tissue would proceed to apoptosis or necrosis. CSD in this model arose as a consequence of the ischemic event. Results demonstrated the relationship of CSD to underlying alterations in Ca++ and ATP concentrations, in addition to potassium. If insufficient energy was available for cell recovery, a neuron or astrocyte would undergo cell death, the speed of which was dependent on the severity of metabolite deprivation. The model suggested novel therapeutic approaches, with opportunities for brain protection through prevention of CSD by differential blocking of particular channels.

These several CSD models suggest an important additional factor at an intermediate spatial scale between cellular and local processes and the scale of the entire infarct. Due to the origin of CSD through cellular processes (depolarization), the waves are likely to arise from multiple sites and can then interact in complex ways with the other phenomenology of the different penumbra subregions.

Inflammatory mechanisms

Inflammation occurs after any bodily injury and is most familiar to us as the consequences of a sprained ankle or other peripheral injury. Similar mechanisms occur in the brain after traumatic brain injury or after stroke. A major part of the inflammatory response is tissue invasion by leukocytes (white blood cells), due to ischemia-induced upregulation of inflammatory cytokines, vascular adhesion molecules and chemokines that control the migration of leukocytes into the injured brain. Inflammation plays roles in healing as well as in scarring and in clearing away dead tissue. These several roles makes inflammation both good and bad. Immediately after the stroke, it is useful to reduce inflammation. At later times, inflammation is important for brain remodeling and restoration (Barone and Feuerstein, 1999; Ahmad et al., 2014).

A model by Di Russo et al. (2010) was used to evaluate the contribution of inflammatory processes to the further development of edema in the penumbra. The model used proportional densities of healthy, dying, and dead cells, as well as leukocytic cells, to evaluate how diffusion of inflammatory chemokines and cytokines would react with local cells to modify the ischemic insult. Partial differential equations were used to describe how these molecular factors altered the densities of dead, dying and healthy cells over time. The mass change in necrotic tissue was measured by noting proportions among healthy cells, dying cells, and phagocytized cells (those being mopped up by white blood cells) at a given time-step. This study showed that the initial ratio of necrotic to apoptotic cells was critical in determining the brain response to inflammatory events. A higher percentage of initially necrotic cells caused a larger inflammatory response, which then augmented apoptosis in the surrounding region. Depending on the size of the infarct, the inflammatory response could have either negative or protective effects.

Functional effects of stroke

The area of stroke modeling that draws most from traditional computational neuroscience is the study of effects on brain function. Acutely, a large stroke will alter the functioning of untouched remote brain tissue. Over the long term, during a period of stroke recovery and rehabilitation, synaptic plasticity, together with angiogenesis, neurogenesis and other factors alter the functioning of the remaining brain through a series of changes that are similar to those seen during development (Hermann and Chopp, 2012; Carmichael, 2008; Barone, 2010).

One immediate effect of stroke is diaschisis, activity abnormalities in intact brain areas secondary to loss of input signals that originally came from the damaged area (Reggia, 2004). Diaschisis has been primarily explored as occurring when a large stroke on one side disrupts activity on the other side, with loss of signals across the corpus callosum. These and other projections between brain areas not only communicate information, but also provide basal and oscillatory levels of ongoing activation (Kerr et al., 2012). Neuroprosthetic therapeutic interventions could involve restoring activity with electric current provided intra- or extra-cranially (i.e., direct transcranial stimulation) so as to restore the level of activation (Lytton et al., 2014).

A related approach is the direct use of brain models to repair damaged brain through brain-machine interface (BMI). In these systems, remaining active brain regions can be monitored via electrodes and decoded through either biomimetic simulation models or low-dimensional models to establish patient volition (Sanchez et al., 2012). Signals relating to a desired movement can then be fed into another model (or another part of the model) to produce signals for movement of an arm or a robot arm. Such a system can be greatly improved by providing haptic feedback to the system to close the sensorimotor loop. One interesting aspect of BMI is the occurrence of co-adaptation when a plastic artificial system must keep adapting to a brain which is itself adapting as it learns to use the artificial system (Digiovanna et al., 2010; Li et al., 2015).

A micro version of diaschisis is also predicted to occur locally (Lytton et al., 1999). Loss of local excitatory inputs to cells neighboring an area of damage will be accompanied by loss of local inhibitory inputs as well. As a result, minor stimuli that did not previously activate a cell are now able to provide activation, resulting a broadening of receptive fields for remaining cells. Modeling of this situation suggested how this receptive field broadening might provide a filling in of a sensory deficit so that a region of lost sensation would not be as large, or the degree of sensory loss not as severe (Lytton et al., 1999).

Poststroke neuroplasticity has been explored by high-level dynamic causal modeling of functional MRI data (Rehme et al., 2011; Grefkes et al., 2010). These studies showed evidence that contralateral activation and projections back to the damaged hemisphere may play a role over time in providing improved function of an affected limb. Restoration of connectivity among areas on the damaged side also appeared to be a major factor in recovery.

Model Limitations

A model has got to know its limitations. This problem of model limitations is of course a major one that for reasons of practicality is never sufficiently addressed. We mentioned above the limitations of experimental models in the context of clinical neuroprotection trials that failed to confirm results from successful animal studies. The users of animal models are often unable to understand the limitations of their models because these limitations are hidden among many unknown biological details. One advantage of computational modeling is that at least some of the limitations are transparent and accessible. However, there also remain many unknown unknowns.

Here we will mention a few major limitations in ischemia modeling. As noted above, these models do not generally include blood vessels or their contents in any detail, and therefore exclude the proximate causes of stroke. There are specific blood and blood vessel models that do include this, but these remain to be linked together with the ischemia models discussed here. Additionally, the models we have presented generally only include grey matter, whereas stroke will affect both grey and white matter. Although many components, channels, carriers and osmotic regulatory agents are included in these models, many more are not either because they are not known, or not known to be relevant.

This latter point brings up a general problem of detailed biological modeling - many of these models have so many parameters that their dynamics are hard or impossible to interpret. There is a great need for developing data-mining of complex simulations, and developing simplified models of complex models. Such models of models are needed to permit understanding of high-dimensional systems where causality is multi-component and indirect.


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Acknowledgements: Supported by NIH R01MH086638

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