A Continuum Neuronal Model for the Instigation and Propagation of Cortical Spreading Depression

Cortical spreading depression (CSD) waves can occur in the cortices of various brain structures and are associated with the spread of depression of the electroencephalogram signal. In this paper, we present a continuum neuronal model for the instigation and spreading of CSD. Our model assumes that the brain-cell microenvironment can be treated as a porous medium consisting of extra- and intracellular compartments. The main mechanisms in our model for the transport of ions into and out of neurons are cross-membrane ionic currents and (active) pumps, coupled with diffusion in the extracellular space. To demonstrate the applicability of our model, we have carried out extensive numerical simulations under different initial conditions and inclusion of various mechanisms. Our results show that CSD waves can be instigated by injecting cross-membrane ionic currents or by applying KCl in the extracellular space. Furthermore, the estimated speeds of CSD waves are within the experimentally observed range. Effects of specific ion channels, background ion concentrations, extracellular volume fractions, and cell swelling on the propagation speed of CSD are also investigated.     

A Mathematical Model of the Human Metabolic System and Metabolic Flexibility

In healthy subjects some tissues in the human body display metabolic flexibility, by this we mean the ability for the tissue to switch its fuel source between predominantly carbohydrates in the postprandial state and predominantly fats in the fasted state. Many of the pathways involved with human metabolism are controlled by insulin and insulin-resistant states such as obesity and type-2 diabetes are characterised by a loss or impairment of metabolic flexibility. In this paper we derive a system of 12 first-order coupled differential equations that describe the transport between and storage in different tissues of the human body. We find steady state solutions to these equations and use these results to nondimensionalise the model. We then solve the model numerically to simulate a healthy balanced meal and a high fat meal and we discuss and compare these results. Our numerical results show good agreement with experimental data where we have data available to us and the results show behaviour that agrees with intuition where we currently have no data with which to compare.     

Refractory Period Modulates the Spatiotemporal Evolution of Cortical Spreading Depression: A Computational Study

Cortical spreading depression (CSD) is a pathophysiological phenomenon, which underlies some neurological disorders, such as migraine and stroke, but its mechanisms are still not completely understood. One of the striking facts is that the spatiotemporal evolution of CSD wave is varying. Observations in experiments reveal that a CSD wave may propagate through the entire cortex, or just bypass some areas of the cortex. In this paper, we have applied a 2D reaction-diffusion equation with recovery term to study the spatiotemporal evolution of CSD. By modulating the recovery rate from CSD in the modeled cortex, CSD waves with different spatiotemporal evolutions, either bypassing some areas or propagating slowly in these areas, were present. Moreover, spiral CSD waves could also be induced in case of the transiently altered recovery rate, i.e. block release from the absolute refractory period. These results suggest that the refractory period contributes to the different propagation patterns of CSD, which may help to interpret the mechanisms of CSD propagation.     

Influence of Ovarian Hormones on Cortical Spreading Depression and Its Suppression by L-kynurenine in Rat

Migraine is sexually dimorphic and associated in 20–30% of patients with an aura most likely caused by cortical spreading depression (CSD). We have previously shown that systemic L-kynurenine (L-KYN), the precursor of kynurenic acid, suppresses CSD and that this effect depends on the stage of the estrous cycle in female rats. The objectives here are to determine the influence of ovarian hormones on KCl-induced CSD and its suppression after L-KYN by directly modulating estradiol or progesterone levels in ovariectomized rats. Adult female rats were ovariectomized and subcutaneously implanted with silastic capsules filled with progesterone or 17β-estradiol mixed with cholesterol, with cholesterol only or left empty. Two weeks after the ovariectomy/capsule implantation, the animals received an i.p. injection of L-KYN (300 mg/kg) or NaCl as control. Thirty minutes later CSDs were elicited by applying KCl over the occipital cortex and recorded by DC electrocorticogram for 1 hour. The results show that both estradiol and progesterone increase CSD frequency after ovariectomy. The suppressive effect of L-KYN on CSD frequency, previously reported in normal cycling females, is not found anymore after ovariectomy, but reappears after progesterone replacement therapy. Taken together, these results emphasize the complex role of sex hormones on cortical excitability. The CSD increase by estradiol and, more surprisingly, progesterone may explain why clinically migraine with aura appears or worsens during pregnancy or with combined hormonal treatments.     

格列本脲对大鼠皮层扩散性抑制中脑血管的调节作用

皮层扩散性抑制(corticalspreadingdepression,CSD)是研究偏头痛、脑梗塞等疾病的重要病理模型.已有研究表明,在普遍被观察到的CSD过程中软脑膜动脉血管大幅度舒张之前,还存在一个较小幅度的软脑膜动脉扩张和收缩.但其中的脑血管调节机制尚不清楚.采用550nm的内源信号光学成像(opticalintrinsicsignalimaging,OISI)监测ATP敏感钾离子通道(ATP-sensitivepotassiumchannels,KATP)的阻断剂格列本脲(glibenclamide,glyb),对针刺诱导的大鼠CSD过程中软脑膜动脉血管舒缩过程的影响.实验中观测到软脑膜血管的初始小收缩(initialslightconstriction,ISC)相对于对照组显著减弱,其中应用10μmol/Lglyb时,74.5%的ISC被完全抑制,100μmol/Lglyb时则有96.2%的ISC完全消失.相对于CSD发生前,软脑膜动脉血管大幅舒张(largedilation,LD)的峰值也分别显著增强了(53.8±19.3)%和(59.8±19.6)%.结果表明,可能是神经元上的KATP在CSD过程中被glyb阻断从而抑制了软脑膜动脉血管的收缩.     

Osmotic Forces and Gap Junctions in Spreading Depression: A Computational Model

In a computational model of spreading depression (SD), ionic movement through a neuronal syncytium of cells connected by gap junctions is described electrodiffusively. Simulations predict that SD will not occur unless cells are allowed to expand in response to osmotic pressure gradients and K⁺ is allowed to move through gap junctions. SD waves of [K⁺]_out 25 to 60 mM moving at 2 to 18 mm/min are predicted over the range of parametric values reported in gray matter, with extracellular space decreasing up to 50%. Predicted waveform shape is qualitatively similar to laboratory reports. The delayed-rectifier, NMDA, BK, and Na⁺ currents are predicted to facilitate SD, while SK and A-type K⁺ currents and glial activity impede SD. These predictions are consonant with recent findings that gap junction poisons block SD and support the theories that cytosolic diffusion via gap junctions and osmotic forces are important mechanisms underlying SD.     

大鼠皮层扩散性抑制过程的在体内源光信号成像

皮层扩散性抑制(cortical spreading depression,CSD)是研究偏头痛、脑梗塞等疾病的一种重要病理模型.而CSD过程中伴随发生的皮层血液动力学变化目前尚不完全清楚.利用高分辨的内源光信号成像技术,在体观测了大鼠CSD产生和发展过程中540 nm及660 nm波长皮层反射内源光信号变化的时空动力学特征,分析讨论了引起这一内源光信号变化可能的内在生理机制.实验结果显示,CSD诱发的内源光信号变化呈现多时相的特点,其传播由刺激中心以同心圆的样式向周围扩散,速度约为(3.7±0.4) mm/min.对于540 nm,CSD引起了皮层反射光强的降低［幅度(－2.1±1.2)%, 持续时程(16.2±3.8)s］,升高 ［幅度(2.9±1.6)%, 持续时程(13.8±2.2)s］,再降低 ［幅度(－14.2±4.5)%, 持续时程(40.6±8.4)s］和再升高持续时程［(146.2±40.3)s］,同时观测到软脑膜动脉的大幅度舒张,血管管径变化峰值增大了(69.2±26.1)%.而对于660 nm, 内源光信号变化的时间特性在皮质区主要表现为反射光强的增大［幅度(3.8±0.6)%, 持续时程(17.9±5.1)s］,减小［幅度(－3.0±1.7)%, 持续时程(43.3±6.4)s］和稍后持续缓慢的光强增加.     

大鼠局灶性脑缺血后KCl诱导皮层扩散性抑制的体光学成像

采用线栓法制备大鼠大脑中动脉栓塞(middle cerebral artery occlusion,MCAO)模型,在额叶皮层用KCl诱导产生皮层扩散性抑制(cortical spreadingdepression,CSD).MCA04 h后,利用550 nm内源信号光学成像(optical intrinsic signalimaging,OISI)监测局灶性脑缺血后大鼠顶-枕叶皮层内源光信号变化.成像1 h内观测到一系列诱导CSD波(14±3次),CSD波局限于顶-枕叶皮层中央区域扩展,以光强的显著下降为特征;而旁侧区域光强无明显改变,不具备CSD波特征,表明CSD波未传播到该区域.随后TIC染色证明上述旁侧区域已经梗死.实验表明:MCAO后4h,皮层区域旁侧部分会梗死;CSD波的0IS变化可用来区分缺血梗死区和外周供血较为完整区域(未梗死区).     

Chemically Based Mathematical Model for Development of Cerebral Cortical Folding Patterns

The mechanism for cortical folding pattern formation is not fully understood. Current models represent scenarios that describe pattern formation through local interactions, and one recent model is the intermediate progenitor model. The intermediate progenitor (IP) model describes a local chemically driven scenario, where an increase in intermediate progenitor cells in the subventricular zone correlates to gyral formation. Here we present a mathematical model that uses features of the IP model and further captures global characteristics of cortical pattern formation. A prolate spheroidal surface is used to approximate the ventricular zone. Prolate spheroidal harmonics are applied to a Turing reaction-diffusion system, providing a chemically based framework for cortical folding. Our model reveals a direct correlation between pattern formation and the size and shape of the lateral ventricle. Additionally, placement and directionality of sulci and the relationship between domain scaling and cortical pattern elaboration are explained. The significance of this model is that it elucidates the consistency of cortical patterns among individuals within a species and addresses inter-species variability based on global characteristics and provides a critical piece to the puzzle of cortical pattern formation.     

Cortical Metabolic Deficits in a Rat Model of Cholinergic Basal Forebrain Degeneration

Evidence indicates that the degeneration of basal forebrain cholinergic neurons may represent an important factor underlying the progressive cognitive decline characterizing Alzheimer’s disease (AD). However, the nature of the relationship between cholinergic depletion and AD is not fully elucidated. This study aimed at clarifying some aspects of the relation existing between deficits in cerebral energy metabolism and degeneration of cholinergic system in AD, by investigating the neuronal metabolic activity of several cortical areas after depletion of basal forebrain cholinergic neurons. In cholinergically depleted rats, we evaluated the neuronal metabolic activity by assaying cytochrome oxidase (CO) activity in frontal, parietal and posterior parietal cortices at four different time-points after unilateral injection of 192 IgG-saporin in the nucleus basalis magnocellularis. Unilateral depletion of cholinergic cells in the basal forebrain induced a bilateral decrease of metabolic activity in all the analyzed areas. Frontal and parietal cortices showed decreased metabolic activity even 3 days after the lesion, when the cholinergic degeneration was still incomplete. In posterior parietal cortex metabolic activity decreased only 7 days after the lesion. The possible molecular mechanisms underlying these findings were also investigated. Real-time PCR showed an increase of CO mRNA levels at 3, 7 and 15 days after the lesion both in frontal and parietal cortices, followed by normalization at 30 days. Western Blot analysis did not show any change in CO protein levels at any time-point after the lesion. Our findings support a link between metabolic deficit and cholinergic hypofunctionality characterizing AD pathology. The present model of cholinergic hypofunctionality provides a useful means to study the complex mechanisms linking two fundamental and interrelated phenomena characterizing AD from the early stages.     

The Gray Mouse Lemur:A Model for Studies of Primate Metabolic Rate Depression

<正>The use of daily torpor and/or of multi-day torpor bouts during a hibernation season are energy-saving survival strategies that have been well-studied for many years,particularly for small mammals living in seasonally-cold environments.Both phenomena are characterized by a regulated suppression of metabolic rate,a slowing of many physiological processes     

A Mathematical Model of Cell Cycle Effects in Gastric Cancer Chemotherapy

A mathematical model is presented to investigate the relationship between drug order and treatment response in gastric cancer chemotherapy involving a taxane (either paclitaxel or docetaxel) coupled with flavopiridol. To model treatment effects, we simulate treatment by bolus injection and employ a pulsing condition to indicate cell kill as well as instantaneous changes to the cell’s transition rates. Cell population growth is described using an ordinary differential equation model whereby we examine the treatment effects upon cells in various stages of the cell cycle. Ultimately, the results generated support prior clinical investigations which indicate that for an enhanced synergistic effect, flavopiridol must be administered following taxane therapy.     

A Dynamical Model of Fast Cortical Reorganization

In this work we study the connection between some dynamic effects at the synaptic level and fast reorganization of cortical sensory maps. By using a biologically plausible computational model of the primary somatosensory system we obtained simulation results that can be used to relate the dynamics of the interactions of excitatory and inhibitory neurons to the process of somatotopic map reorganization immediately after peripheral lesion. The model consists of three regions integrated into a single structure: tactile receptors representing the glabrous surface of the hand, ventral posterior lateral nucleus of the thalamus and area 3b of the primary somatosensory cortex, reproducing the main aspects of the connectivity of these regions. By applying informational measures to the simulation results of the dynamic behavior of AMPA, NMDA and GABA synaptic conductances we draw some conjectures about how the several neuronal synaptic elements are related to the initial stage of the digit-induced reorganization of the hand map in the somatosensory cortex.     

A Mathematical Model of the Tuberculosis Epidemic

Acta Biotheoretica - Tuberculosis has continued to retain its title as “the captain among these men of death”. This is evident as it is the leading cause of death globally from a single...     

Towards a Mathematical Theory of Cortical Micro-circuits

The theoretical setting of hierarchical Bayesian inference is gaining acceptance as a framework for understanding cortical computation. In this paper, we describe how Bayesian belief propagation in a spatio-temporal hierarchical model, called Hierarchical Temporal Memory (HTM), can lead to a mathematical model for cortical circuits. An HTM node is abstracted using a coincidence detector and a mixture of Markov chains. Bayesian belief propagation equations for such an HTM node define a set of functional constraints for a neuronal implementation. Anatomical data provide a contrasting set of organizational constraints. The combination of these two constraints suggests a theoretically derived interpretation for many anatomical and physiological features and predicts several others. We describe the pattern recognition capabilities of HTM networks and demonstrate the application of the derived circuits for modeling the subjective contour effect. We also discuss how the theory and the circuit can be extended to explain cortical features that are not explained by the current model and describe testable predictions that can be derived from the model.     

大鼠局灶性脑缺血后KCl诱导皮层扩散性抑制的体光学成像

采用线栓法制备大鼠大脑中动脉栓塞(middlecerebralarteryocclusion,MCAO)模型,在额叶皮层用KCl诱导产生皮层扩散性抑制(corticalspreadingdepression,CSD)。MCAO4h后,利用550nm内源信号光学成像(opticalintrin-sicsignalimaging,OISI)监测局灶性脑缺血后大鼠顶-枕叶皮层内源光信号变化。成像1h内观测到一系列诱导CSD波(14±3次),CSD波局限于顶-枕叶皮层中央区域扩展,以光强的显著下降为特征;而旁侧区域光强无明显改变,不具备CSD波特征,表明CSD波未传播到该区域。随后TTC染色证明上述旁侧区域已经梗死。实验表明:MCAO后4h,皮层区域旁侧部分会梗死;CSD波的OIS变化可用来区分缺血梗死区和外周供血较为完整区域(未梗死区)。