Transient localized wave patterns and their application to migraine

Transient dynamics is pervasive in the human brain and poses challenging problems both in mathematical tractability and clinical observability. We investigate statistical properties of transient cortical wave patterns with characteristic forms (shape, size, duration) in a canonical reaction-diffusion model with mean field inhibition. The patterns are formed by a ghost near a saddle-node bifurcation in which a stable traveling wave (node) collides with its critical nucleation mass (saddle). Similar patterns have been observed with fMRI in migraine. Our results support the controversial idea that waves of cortical spreading depression (SD) have a causal relationship with the headache phase in migraine and therefore occur not only in migraine with aura (MA) but also in migraine without aura (MO), i.e., in the two major migraine subforms. We suggest a congruence between the prevalence of MO and MA with the statistical properties of the traveling waves' forms, according to which (i) activation of nociceptive mechanisms relevant for headache is dependent upon a sufficiently large instantaneous affected cortical area anti-correlated to both SD duration and total affected cortical area such that headache would be less severe in MA than in MO (ii) the incidence of MA is reflected in the distance to the saddle-node bifurcation, and (iii) the contested notion of MO attacks with silent aura is resolved. We briefly discuss model-based control and means by which neuromodulation techniques may affect pathways of pain formation.Comment: 14 pages, 11 figure

Doctor of Philosophy

dissertationThe blood-brain barrier (BBB) limits entry of most molecules into the brain and complicates the development of brain-targeting compounds, necessitating novel BBB models. This dissertation describes the first microfluidic BBB model allowing the study of BBB properties in relation to various chemical compounds by enabling tunable wall shear stress (WSS) via dynamic fluid flow, cell-cell interaction through a thin co-culture membrane, time-dependent delivery of test compounds, and integration of sensors into the system, resulting in significant reduction of reagents and cells required and shorter cell seeding time. Use of parallel channels first enabled simultaneous monitoring of multiple cell populations under a wide range (~x15) of WSS. The microfluidic model formed the BBB by incorporating brain endothelial (b.End3) and glial (C6/C8D1A) cells at the intersection of two crossing microchannels, respectively representing luminal and abluminal sides, fabricated in a transparent polydimethylsiloxane (PDMS) substrate utilizing high-precision soft lithography techniques. The utilized cells were adopted from immortalized cells for high consistency over repeated passages and pure and proliferative culture. The developed microfluidic BBB model was validated by (1) expression of tight junction protein ZO-1 and glial protein GFAP by fluorescence imaging, and P-gp activity by Calcein AM, confirming key BBB proteins; (2) high trans-endothelial electrical resistance (TEER) of co-cultures exceeding 250Ωcm2 confirming sufficiently contiguous cell layer formation; (3) chemically-induced barrier modulation, with transient TEER loss by 150μM histamine (~50% for 8-15min), and increase in permeability at elevated pH (10.0); (4) size-dependent (668-70,000Da) compound permeability mimicking in vivo trends; and (5) highly linear correlation (R2>0.85) of clearance rates of seven selected neural drugs with in vivo brain/plasma ratios. We demonstrated the effects of WSS (0-86dyn/cm2) on bEnd.3 properties under increasing WSS, including increase in (6) TEER, (7) cell re-alignment toward flow direction, and (8) protein expression of ZO-1/P-gp, and (9) decrease in tracer permeability. The developed in vitro microfluidic BBB model provides distinct advantages for monitoring and modulating barrier functions and prediction of compound permeability. Thus, it would provide an innovative platform to study mechanisms and pathology of barrier function as well as to assess novel pharmaceuticals early in development for their BBB clearance capabilities

Coronary Smooth Muscle Cell Calcium Dynamics: Effects of Bifurcation Angle on Atheroprone Conditions

This work investigates the effect of arterial bifurcation angulation on atherosclerosis development through in-silico simulations of coupled cell dynamics. The computational model presented here combines cellular pathways, fluid dynamics, and physiologically-realistic vessel geometries as observed in the human vasculature. The coupled cells model includes endothelial cells (ECs) and smooth muscle cells (SMCs) with ion dynamics, hetero and homotypic coupling, as well as electro-diffusive coupling. Three arterial bifurcation surface models were used in the coupled cells simulations. All three simulations showed propagating waves of Ca2+ in both the SMC and EC layers, following the introduction of a luminal agonist, in this case ATP. Immediately following the introduction of ATP concentration Ca2+ waves propagate from the area of high ATP toward the areas of low ATP concentration, forming complex patterns where waves interact with eachother, collide and fade. These dynamic phenomena are repeated with a series of waves of slower velocity. The underlying motivation of this research was to examine the macro-scale phenomena, given that the characteristic length scales of atherosclerotic plaques are much larger than a single cell. The micro-scale dynamics were modeled on macro-scale arterial bifurcation surfaces containing over one million cells. The results of the simulations presented here suggest that susceptibility to atherosclerosis development depends on the bifurcation angulation. In conjunction with findings reported in the literature, the simulation results demonstrate that arterial bifurcations containing wider angles have a more prominent influence on the coupled cells pathways associated with the development of atherosclerosis, by means of disturbed flow and lower SMC Ca2+ concentrations. The discussion of the results considers the findings of this research within the context of the potential link between information transport through frequency encoding of Ca2+ wave dynamics and development of atheroprone conditions

Autoregulation of the Human Cerebrovasculature by Neurovascular Coupling

Functional hyperaemia is an important mechanism by which increased neuronal activity is matched by a rapid and regional increase in blood supply. This mechanism is facilitated by a process known as “neurovascular coupling” – the orchestrated communication system involving the cells that comprise the neurovascular unit (neurons, astrocytes and the smooth muscle and endothelial cells lining arterioles). Blood flow regulation and neurovascular coupling are altered in several pathological states including hypertension, diabetes, Alzheimer’s disease, cortical spreading depression and stroke. By adapting and extending other models found in the literature, we create, for the first time, a mathematical model of the entire neurovascular unit that is capable of simulating two separate neurovascular coupling mechanisms: a potassium- and EET-based and a NO-based mechanism. These models successfully account for several observations seen in experiment. The potassium/EET-based mechanism can achieve arteriolar dilations similar in magnitude (3%) to those observed during a 60-second neuronal activation (modelled as a release of potassium and glutamate into the synaptic cleft). This model also successfully emulates the paradoxical experimental finding that vasoconstriction follows vasodilation when the astrocytic calcium concentration (or perivascular potassium concentration) is increased further. We suggest that the interaction of the changing smooth muscle cell membrane potential and the changing potassium-dependent resting potential of the inwardly rectifying potassium channel are responsible for this effect. Furthermore, our simulations demonstrate that the arteriolar behaviour is profoundly affected by depolarization of the astrocytic cell membrane, and by changes in the rate of perivascular potassium clearance or the volume ratio between the perivascular space and astrocyte. In the modelled NO-based neurovascular coupling mechanism, NO exerts its vasodilatory effects via neuronal and endothelial cell sources. With both sources included, the model achieves a 1% dilation due to a 60-second neuronal activation. When the endothelial contribution to NO production is omitted, the arteriole is more constricted at baseline. Without the endothelial NO contribution, the arteriolar change in diameter during neuronal activity is greater (6%). We hypothesize that NO has a dual purpose in neurovascular coupling: 1) it dixxxvi rectly mediates neurovascular coupling through release by neuronal sources, and 2) it indirectly modulates the size of the neurovascular coupling response by determining the baseline tone. Our physiological models of neurovascular coupling have allowed us to replicate, and explain, some of the phenomena seen in both neurovascular coupling-oriented and clinicallyoriented experimental research. This project highlights the fact that physiological modelling can be used as a tool to understand biological processes in a way that physical experiment cannot always do, and most importantly, can help to elucidate the cellular processes that induce or accompany our most debilitating diseases

The Scientific Case for Brain Simulators

A key element of the European Union’s Human Brain Project (HBP) and other large-scale brain research projects is the simulation of large-scale model networks of neurons. Here, we argue why such simulations will likely be indispensable for bridging the scales between the neuron and system levels in the brain, and why a set of brain simulators based on neuron models at different levels of biological detail should therefore be developed. To allow for systematic refinement of candidate network models by comparison with experiments, the simulations should be multimodal in the sense that they should predict not only action potentials, but also electric, magnetic, and optical signals measured at the population and system levels

Modelling the transport of nanoparticles across the blood-brain barrier using an agent-based approach

Diseases affecting the Central Nervous System (CNS), consisting of the brain and spinal cord, will account for an estimated 11.84% of all deaths by 2015, with few effective treatment options. This is partly a consequence of poor penetrance of blood-borne molecules, including almost all therapeutics, into the CNS. This is due to the existence of a blood-brain barrier, severely limiting potential therapeutic intervention. Nanoparticles are diverse nanoscale particles that have recently been demonstrated to be able to improve drug penetrance across the blood-brain barrier, by targeting endogenous transport systems. However, further methods to improve their general delivery to the CNS and specific delivery to different regions of the CNS are required. Here, agent-based modelling has been utilised to simulate blood flow in a capillary at the blood-brain barrier. This modelling approach has demonstrated the importance of a number of biological, physiological and physical factors that affect nanoparticle uptake to the CNS. This model was used to demonstrate how the fluid dynamics in capillaries enhances nanoparticle distribution to the vessel wall interface. These simulations have demonstrated that by tuning nanoparticle properties, including ligand density, receptor-ligand affinity and size, general delivery by transcytosis can be improved. Moreover, particular nanoparticle formulations can target high levels, but not low levels, of receptor expression at the blood-brain barrier thus providing a method to improve specific delivery into particularly CNS regions. Furthermore, nanoparticles can be formulated to stabilise nanoparticle binding under different flow conditions. In particular during regional blood flow increases, called functional hyperaemia, which aid access of nutrients to that region of the CNS. It is predicted from these simulations that this could be harnessed to further improve specificity of delivery. Finally, chemotactic nanoparticles are shown to have an improved distribution to the vessel wall interface and penetration through the CNS tissue

Optimization, Validation, and Acceleration of Magnetic Resonance Vascular Fingerprinting to Measure Cerebrovascular Function

Vascular contributions to cognitive impairment and dementia (VCID) are the second leading cause of dementia and increasing in prevalence as lifespans increase. Clinical MRI traditionally relies on structural abnormalities to identify this vascular dysfunction but lacks microstructure and functional information that could be critical for early identification and assessment of disease. Cerebrovascular dysfunction is one of the only contributors to dementia that can currently be treated, and therefore, earlier identification and subsequent intervention could prevent irreversible structural changes that lead to cognitive decline.Magnetic resonance fingerprinting (MRF) is a novel approach to MRI acquisition and reconstruction using biophysical modeling in parallel to image acquisition for the simultaneous collection of quantitative, multiparametric brain maps. MRF can be adapted to specifically measure cerebrovascular parameters via MR vascular fingerprinting (MRvF), which produces quantitative cerebral blood volume (CBV), microvascular vessel radius (R), and tissue oxygen saturation (SO2) maps of the whole brain. This dissertation aims to advance MRvF for contrast-free, dynamic mapping of cerebrovascular function. First, we compare MRvF to another quantitative MRI method, quantitative blood oxygen level dependent (BOLD) imaging, and show consistency between the techniques, reliable oxygen extraction fraction (OEF) measurements, and expected changes in OEF in response to hypoxia and hyperoxia. Next, we describe a new MRvF pattern-matching algorithm developed for improved mapping without contrast agents, investigate the tradeoffs between SNR, sensitivity, and temporal resolution, and optimize an accelerated spin- and gradient-echo (SAGE) sequence for dynamic MRvF. We show adequate SNR with the SAGE sequence from just one repetition for robust whole-brain vascular parameter mapping every 4.5 seconds. Following this, we demonstrate a novel protocol in which this optimized SAGE sequence allows for dynamic and simultaneous acquisition of MRvF and BOLD measures. By combining this with a tailored hypercapnic (5% CO2) breathing paradigm, we show parameter consistency over time and regional changes in BOLD, CBV, R, and SO2 in response to this stimulus, enabling the calculation of cerebrovascular reactivity (CVR). Finally, we use this newly developed imaging paradigm to compare differences in MRvF-derived CVR measurements in healthy young and healthy old adults. We juxtapose these CVR results against more commonly utilized techniques of measuring CVR to compare and validate our MRvF metrics. Collectively, we demonstrate the development of dynamic MRvF in an ongoing effort toward new quantitative functional imaging biomarkers of cerebrovascular dysfunction with the potential to enable better understanding and earlier diagnoses of diseases like VCID

Dynamic Thermal Imaging for Intraoperative Monitoring of Neuronal Activity and Cortical Perfusion

Neurosurgery is a demanding medical discipline that requires a complex interplay of several neuroimaging techniques. This allows structural as well as functional information to be recovered and then visualized to the surgeon. In the case of tumor resections this approach allows more fine-grained differentiation of healthy and pathological tissue which positively influences the postoperative outcome as well as the patient's quality of life. In this work, we will discuss several approaches to establish thermal imaging as a novel neuroimaging technique to primarily visualize neural activity and perfusion state in case of ischaemic stroke. Both applications require novel methods for data-preprocessing, visualization, pattern recognition as well as regression analysis of intraoperative thermal imaging. Online multimodal integration of preoperative and intraoperative data is accomplished by a 2D-3D image registration and image fusion framework with an average accuracy of 2.46 mm. In navigated surgeries, the proposed framework generally provides all necessary tools to project intraoperative 2D imaging data onto preoperative 3D volumetric datasets like 3D MR or CT imaging. Additionally, a fast machine learning framework for the recognition of cortical NaCl rinsings will be discussed throughout this thesis. Hereby, the standardized quantification of tissue perfusion by means of an approximated heating model can be achieved. Classifying the parameters of these models yields a map of connected areas, for which we have shown that these areas correlate with the demarcation caused by an ischaemic stroke segmented in postoperative CT datasets. Finally, a semiparametric regression model has been developed for intraoperative neural activity monitoring of the somatosensory cortex by somatosensory evoked potentials. These results were correlated with neural activity of optical imaging. We found that thermal imaging yields comparable results, yet doesn't share the limitations of optical imaging. In this thesis we would like to emphasize that thermal imaging depicts a novel and valid tool for both intraoperative functional and structural neuroimaging

Personalized computational models of deep brain stimulation

University of Minnesota Ph.D. dissertation. December 2016. Major: Biomedical Engineering. Advisor: Matthew Johnson. 1 computer file (PDF); xii, 138 pages.Deep brain stimulation (DBS) therapy is used for managing symptoms associated with a growing number of neurological disorders. One of the primary challenges with delivering this therapy, however, continues to be accurate neurosurgical targeting of the DBS lead electrodes and post-operative programming of the stimulation settings. Two approaches for addressing targeting have been advanced in recent years. These include novel DBS lead designs with more electrodes and computational models that can predict cellular modulation during DBS. Here, we developed a personalized computational modeling framework to (1) thoroughly investigate the electrode design parameter space for current and future DBS array designs, (2) generate and evaluate machine learning feature sets for semi-automated programming of DBS arrays, (3) study the influence of model parameters in predicting behavioral and electrophysiological outcomes of DBS in a preclinical animal model of Parkinson’s disease, and (4) evaluate feasibility of a novel endovascular targeting approach to delivering DBS therapy in humans. These studies show how independent current controlled stimulation with advanced machine learning algorithms can negate the need for highly dense electrode arrays to shift, steer, and sculpt regions of modulation within the brain. Additionally, these studies show that while advanced and personalized computational models of DBS can predict many of the behavioral and electrophysiological outcomes of DBS, there are remaining inconsistencies that suggest there are additional physiological mechanisms of DBS that are not yet well understood. Finally, the results show how computational models can be beneficial for prospective development of novel approaches to neuromodulation prior to large-scale preclinical and clinical studies