Quantitative relations between transient BOLD responses, cortical energetics, and impulse firing in different cortical regions.

The blood oxygen level-dependent (BOLD) functional magnetic resonance imaging signal arises as a consequence of changes in blood flow (cerebral blood flow) and oxygen usage (cerebral metabolic rate of oxygen) that in turn are modulated by changes in neuronal activity. Much attention has been given to both theoretical and experimental aspects of the energetics but not to the neuronal activity. Here we use our previous theory relating the steady-state BOLD signal to neuronal activity and amalgamate it with the standard dynamic causal model (DCM, Friston) theory to produce a quantitative model relating the time-dependent BOLD signal to the underlying neuronal activity. Unlike existing treatments, this new theory incorporates a nonzero baseline activity in a completely consistent way and is thus able to account for both positive and negative BOLD signals. It can reproduce a wide variety of experimental BOLD signals reported in the literature solely by adjusting the neuronal input activity. In this way it provides support for the claim that the main features of the signals, including poststimulus undershoot and overshoot, are principally a result of changes in neuronal activity.NEW & NOTEWORTHY A previous model relating the steady-state blood oxygen level-dependent (BOLD) signal to neuronal activity, both above and below baseline, is extended to account for transient BOLD signals. This allows for a detailed investigation of the role neuronal activity can play in such signals and also encompasses poststimulus undershoot and overshoot. A wide variety of experimental BOLD signals are reproduced solely by adjusting the neuronal input activity, including recent results regarding the BOLD signal in patients with schizophrenia.

Quantitative relations between BOLD responses, cortical energetics, and impulse firing.

The blood oxygen level-dependent (BOLD) functional magnetic resonance imaging signal arises as a consequence of changes in blood flow and oxygen usage that in turn are modulated by changes in neural activity. Much attention has been given to both theoretical and experimental aspects of the energetics but not to the neural activity. Here we identify the best energetic theory for the steady-state BOLD signal on the basis of correct predictions of experimental observations. This theory is then used, together with the recently determined relationship between energetics and neural activity, to predict how the BOLD signal changes with activity. Unlike existing treatments, this new theory incorporates a nonzero baseline activity in a completely consistent way and is thus able to account for both sustained positive and negative BOLD signals. We also show that the increase in BOLD signal for a given increase in activity is significantly smaller the larger the baseline activity, as is experimentally observed. Furthermore, the decline of the positive BOLD signal arising from deeper cortical laminae in response to an increase in neural firing is shown to arise as a consequence of the larger baseline activity in deeper laminae. Finally, we provide quantitative relations integrating BOLD responses, energetics, and impulse firing, which among other predictions give the same results as existing theories when the baseline activity is zero. NEW & NOTEWORTHY We use a recently established relation between energetics and neural activity to give a quantitative account of BOLD dependence on neural activity. The incorporation of a nonzero baseline neural activity accounts for positive and negative BOLD signals, shows that changes in neural activity give BOLD changes that are smaller the larger the baseline, and provides a basis for the observed inverse relation between BOLD responses and the depth of cortical laminae giving rise to them.

Origins of the BOLD changes due to synaptic activity at astrocytes abutting arteriolar smooth muscle.

We have recently provided a detailed model that links glutamatergic synaptic activity to volume and blood flow changes in nearby arterioles [Bennett, M.R., Farnell, L., Gibson, W.G., 2008. Origin of blood volume change due to glutamatergic synaptic activity at astrocytes abutting on arteriolar smooth muscle cells. J. Theor. Biol. 250, 172-185]. This neurovascular coupling model is used in the present work to predict changes in deoxyhemoglobin (Hbr) in capillaries, arterioles, venules and veins due to glutamatergic synaptic activity and hence the changes in the blood oxygen level dependent (BOLD) signals recorded by functional magnetic resonance imaging. The model provides a quantitative account of Hbr changes observed in each of the vascular compartments following stimulation of somatosensory cortex and visual cortex and of the BOLD signal following stimulation of motor and visual cortex.

On the origin of skewed distributions of spontaneous synaptic potentials in autonomic ganglia.

The histograms of spontaneous synaptic potentials at synapses in autonomic ganglia are described by distributions consisting of mixtures of Gaussians, rather than by single Gaussian distributions. The possible origin of these mixed distributions is investigated, using Monte-Carlo simulations of the action of spontaneously released units of transmitter. A single unit of acetylcholine of fixed size, released from an active zone with receptor patches both beneath and adjacent to the zone, does not give rise to the observed histograms. But if the unit is of variable size, consisting of integer multiples of smaller units, and release is from an active zone onto either the receptor patch beneath, or in addition onto adjacent patches, then the histogram is well described by a mixture of Gaussians. However, this explanation is unlikely to be correct as present evidence suggests that in most cases the released unit of transmitter saturates the postsynaptic receptor patch beneath the active zone. The final case considered is where a unit of transmitter is spontaneously released from an active zone, simultaneously with a unit in an adjacent zone less than one micron away. The histogram of potentials then conforms to those observed even when there are differences in the sizes of the receptor patches. It is suggested that this kind of release could provide an explanation for distributions of spontaneous potentials that are mixtures of Gaussians.

Stress analysis of vasoconstriction at arterial branch sites.

The object of the research was to estimate wall stresses caused by vasoconstriction at arterial branches. The basic procedure was a combination of experimental strain measurement and analytical stress analysis. Segments of canine renal arteries were perfused and stimulated to constrict with dopamine hydrochloride and norepinephrine. Surface wall deformation was measured with a stereo-photographic technique. A plane stress finite element analysis was used to calculate wall stresses based on the experimentally derived deformations. The major result of the study was to demonstrate tensile stresses, and in some cases biaxial tension, in contracting vessels. Peak stresses in the apex of the acute angle of the branches were approximately three times unpenetrated hoop stress in the parent vessels. The results imply that constriction at a branch site may be capable of generating sufficient wall tension to tear arterial tissue, and that smooth muscle reactivity is important with respect to the etiology of cerebral aneurysms and the clinical management of acute branch site pathology.

Principles and design feasibility of a Doppler ultrasound intravascular volumetric flowmeter.

A new Doppler ultrasound intravascular method is described for the measurement of volumetric flow. Based on the principles described by Hottinger and Meindl [15], it uses a novel semispherical transducer mounted at the tip of a catheter, which generates sample volumes in the form of a thin semispherical shell. Volumetric flow is calculated by using the average velocity determined from the received Doppler spectrum and the area of intersection of a sample volume that completely intersects flow across the vessel. Although a catheter-size transducer was not developed, a larger version was tested using an in vitro steady flow model. Maximum average flow error was limited to 9% for steady flows of 2 to 7 L/min. This error is believed to be a result of the nonuniform intensity generated by the prototype transducer, as well as slight variations in the received power, rather than any fundamental limitations of the flow measurement method itself. Since this study has verified the design principles and feasibility of this new approach, we believe that more detailed experimental investigations are warranted.

Neuronal cell death, nerve growth factor and neurotrophic models: 50 years on.

Viktor Hamburger has just died at the age of 100. It is 50 years since he and Rita Levi-Montalcini laid the foundations for the study of naturally occurring cell death and of neurotrophic factors in the nervous system. In a period of less than 10 years, from 1949 to 1958, Hamburger and Levi-Montalcini made the following seminal discoveries: that neuron cell death occurs in dorsal root ganglia, sympathetic ganglia and the cervical column of motoneurons; that the predictions arising from this observation, namely that survival is dependent on the supply of a trophic factor, could be substantiated by studying the effects of a sarcoma on the proliferation of ganglionic processes both in vivo and in vitro; and that the proliferation of these processes could be used as an assay system to isolate the factor. This work provides a short review mostly of the early history of this subject in the context of the Hamburger/Levi-Montalcini paradigm. This acts as an introduction to a consideration of models that have been proposed to account for how the different sources of growth factors provide for the survival of neurons during development. It is suggested that what has been called the 'social-control' model provides the most parsimonious quantitative description of the contribution of trophic factors to neuronal survival, a concept for which we are in debt to Viktor Hamburger and Rita Levi-Montalcini.

Multiple coronary artery dissections in old age. A unique case.

A 70-year-old man died of alcoholic cirrhosis and long-standing pulmonary emphysema. Multiple independent dissecting aneurysms involved the distal epicardial branches of the right and left coronary arteries, but spared their proximal trunks. These dissections extended distally from vascular branch points in association with acute and chronic medionecrosis. Iatrogenic trauma superimposed on preexisting medial weakness may have accounted for what is, to our knowledge, a unique presentation of a rare condition.

Origins of blood volume change due to glutamatergic synaptic activity at astrocytes abutting on arteriolar smooth muscle cells.

The cellular mechanisms that couple activity of glutamatergic synapses with changes in blood flow, measured by a variety of techniques including the BOLD signal, have not previously been modelled. Here we provide such a model, that successfully accounts for the main observed changes in blood flow in both visual cortex and somatosensory cortex following their stimulation by high-contrast drifting grating or by single whisker stimulation, respectively. Coupling from glutamatergic synapses to smooth muscle cells of arterioles is effected by astrocytes releasing epoxyeicosatrienoic acids (EETs) onto them, following glutamate stimulation of the astrocyte. Coupling of EETs to the smooth muscle of arterioles is by means of potassium channels in their membranes, leading to hyperpolarization, relaxation and hence an increase in blood flow. This model predicts a linear increase in blood flow with increasing numbers of activated astrocytes, but a non-linear increase with increasing glutamate release.

Mechanisms of calcium sequestration during facilitation at active zones of an amphibian neuromuscular junction.

The calcium transients (Delta[Ca(2+)](i)) at active zones of amphibian (Bufo marinus) motor-nerve terminals that accompany impulses, visualized using a low-affinity calcium indicator injected into the terminal, are described and the pathways of subsequent sequestration of the residual calcium determined, allowing development of a quantitative model of the sequestering processes. Blocking the endoplasmic reticulum calcium pump with thapsigargin did not affect Delta[Ca(2+)](i) for a single impulse but increased its amplitude during short trains. Blocking the uptake of calcium by mitochondria with CCCP had little effect on Delta[Ca(2+)](i) of a single impulse but greatly increased its amplitude during short trains. This present compartmental model is compatible with our previous Monte Carlo diffusion model of Ca(2+) sequestration during facilitation [Bennett, M.R., Farnell, L., Gibson, W.G., 2004. The facilitated probability of quantal secretion within an array of calcium channels of an active zone at the amphibian neuromuscular junction. Biophys. J. 86(5), 2674-2690], with the single plasmalemma pump in that model now replaced by separate pumps for the plasmalemma and endoplasmic reticulum, as well as the introduction of a mitochondrial uniporter.

A quantitative description of the contraction of blood vessels following the release of noradrenaline from sympathetic varicosities.

A model is presented that highlights the principal factors determining the form and extent of contraction in arteries upon stimulation of their sympathetic nerve supply. This model incorporates a previous quantitative model of the process of noradrenaline (NAd) diffusion into the vascular media and reuptake into sympathetic varicosities during nerve stimulation (J. Theor. Biol. 226 (2004) 359). It is also dependent on a model of how the subsequent activation of metabotropic receptors initiates a G-protein cascade, resulting in the production of inositol trisphosphate (IP3) and an increase in intracellular calcium concentration, [Ca2+]i, in the smooth muscle cells (J. Theor. Biol. 223 (2003) 93). In the present work we couple this rise in [Ca2+]i to the increase in phosphorylated myosin bound to actin in the cells and hence determine the force development in arteries due to nerve stimulation. The model accounts for force development as a function of [Ca2+]i and for the rate of change of force as a function of the rate of change of [Ca2+]i in single smooth muscle cells. It also accounts for the characteristic time course of the force developed by the media of the rat-tail artery upon nerve stimulation. This consists of a rapid rise to a transient peak followed by a sustained plateau of contraction during the stimulation period, after which the contraction slowly decays back to baseline at a rate dependent on the strength of the stimulation. The model indicates that the transient peak is primarily due to the partial block of the IP3 receptor by the rise in [Ca2+]i and that the main determinant of the equilibrium condition indicated by the plateau phase is the rate of pumping of calcium into the sarcoplasmic reticulum. The relatively slow decline of contraction at the end of nerve stimulation is primarily a consequence of the slow rates of removal of NAd from the media by diffusion and reuptake into the sympathetic varicosities. The model thus provides a quantitative account of vascular smooth muscle contraction upon sympathetic nerve stimulation.

A quantitative model of purinergic junctional transmission of calcium waves in astrocyte networks.

A principal means of transmitting intracellular calcium (Ca2+) waves at junctions between astrocytes involves the release of the chemical transmitter adenosine triphosphate (ATP). A model of this process is presented in which activation of purinergic P2Y receptors by ATP triggers the release of ATP, in an autocrine manner, as well as concomitantly increasing intracellular Ca2+. The dependence of the temporal characteristics of the Ca2+ wave are shown to critically depend on the dissociation constant (K(R)) for ATP binding to the P2Y receptor type. Incorporating this model astrocyte into networks of these cells successfully accounts for many of the properties of propagating Ca2+ waves, such as the dependence of velocity on the type of P2Y receptor and the time-lag of the Ca2+ wave behind the ATP wave. In addition, the conditions under which Ca2+ waves may jump from one set of astrocytes across an astrocyte-free lane to another set of astrocytes are quantitatively accounted for by the model. The properties of purinergic transmission at astrocyte junctions may determine many of the characteristics of Ca2+ propagation in networks of these cells.

Calcium mobilization and spontaneous transient outward current characteristics upon agonist activation of P2Y2 receptors in smooth muscle cells.

A quantitative model is provided that links the process of metabotropic receptor activation and sequestration to the generation of inositol 1,4,5-trisphosphate, the subsequent release of calcium from the central sarcoplasmic reticulum, and the consequent release of calcium from subsarcolemma sarcoplasmic reticulum that acts on large-conductance potassium channels to generate spontaneous transient outward currents (STOCs). This model is applied to the case of STOC generation in vascular A7r5 smooth muscle cells that have been transfected with a chimera of the P2Y(2) metabotropic receptor and green fluorescent protein (P2Y(2)-GFP) and exposed to the P2Y(2) receptor agonist uridine 5'-triphosphate. The extent of P2Y(2)-GFP sequestration from the membrane on exposure to uridine 5'-triphosphate, the ensuing changes in cytosolic calcium concentration, as well as the interval between STOCs that are subsequently generated, are used to determine parameter values in the model. With these values, the model gives a good quantitative prediction of the dynamic changes in STOC amplitude observed upon activation of metabotropic P2Y(2) receptors in the vascular smooth muscle cell line.

On the contribution of quantal secretion from close-contact and loose-contact varicosities to the synaptic potentials in the vas deferens.

A bidomain model of the smooth muscle syncytium has been used to analyse the sources of transmitter secretion that give rise to the excitatory junction potential (EJP) in the guinea-pig vas deferens. The timecourse of the spontaneous excitatory junction potential (SEJP) has been taken to be the same as the time course of action of a quantum of transmitter. The amplitude of the SEJP is dependent on both the size of the quantum secreted and the distance away of the source of the quantum from the muscle cells. Two such sources are considered, one identified as the close-contact varicosities (CCVS) about 50 nm from the muscle and the other as loose-contact varicosities (LCVS) at greater distances. It is shown that in order for the syncytium to reach equipotential by the time the EJP has declined to about 80% of its peak, each muscle cell must receive a quantum of transmitter. The relatively low density of innervation of muscle cells by CCVS so far reported, together with the extremely low probability for secretion from these, indicates that many LCVS surrounding each muscle cell contribute to the EJP. The rising phase of the EJP contains components that indicate the sources of the transmitter responsible for its generation, and these components have been made explicit by differentiating the EJP to give the DEJP. This always has a smooth and relatively slow component that lasts for about 80 to 100 ms and occasionally has fast components superimposed on it. These latter are shown to be almost certainly due to secretion of quanta from the CCVS. It is known that there is a distribution of action potential velocities in the sympathetic nerves to the vas deferens. To account for this, the secretion of quanta from different CCVS on a set of muscle cells in the syncytium were given different delays so that the DEJP consisted of a slow wave form that extended over 80 ms, composed of clearly discernible components arising from the CCVS. This wave form could be smoothed by allowing each cell in the syncytium to receive a quantum of transmitter from a CCV, a condition that did not then allow for the appearance of fast components in the DEJP. A model that generated both the non-intermittent slow component of the DEJP and the intermittent fast component consisted of each cell in the syncytium receiving an innervation from a single CCV as well as from a large number of LCVS. In this case, all the varicosities could secrete a quantum of transmitter with a particular probability after a delay characteristic for that varicosity.(ABSTRACT TRUNCATED AT 400 WORDS)

Electrotonic coupling between two CA3 hippocampal pyramidal neurons: a distributed cable model with somatic gap-junction.

A model of a pair of electrotonically coupled CA3 hippocampal pyramidal neurons is presented. Each neuron is represented by a tapered equivalent cable attached to an isopotential soma. The synaptic potential in a neuron soma is determined as a consequence of electrical coupling to another soma that receives a synaptic input on its dendritic tree. Estimates of the coupling resistances, soma input resistances and soma-to-dendritic tree conductance ratio show that a substantial current may arise in a neuron as a consequence of synaptic activity in a neuron coupled to it. The small increase in decay time due to coupling in the model indicates that actual coupling is between more than just pairs of neurons.

The facilitated probability of quantal secretion within an array of calcium channels of an active zone at the amphibian neuromuscular junction.

A Monte Carlo analysis has been made of the phenomenon of facilitation, whereby a conditioning impulse leaves nerve terminals in a state of heightened release of quanta by a subsequent test impulse, this state persisting for periods of hundreds of milliseconds. It is shown that a quantitative account of facilitation at the amphibian neuromuscular junction can be given if the exocytosis is triggered by the combined action of a low-affinity calcium-binding molecule at the site of exocytosis and a high-affinity calcium-binding molecule some distance away. The kinetic properties and spatial distribution of these molecules at the amphibian neuromuscular junction are arrived at by considering the appropriate values that the relevant parameters must take to successfully account for the experimentally observed amplitude and time course of decline of F1 and F2 facilitation after a conditioning impulse, as well as the growth of facilitation during short trains of impulses. This model of facilitation correctly predicts the effects on facilitation of exogenous buffers such as BAPTA during short trains of impulses. In addition, it accounts for the relative invariance of the kinetics of quantal release due to test-conditioning sequences of impulses as well as due to change in the extent of calcium influx during an impulse.

Probabilistic secretion of quanta: spontaneous release at active zones of varicosities, boutons, and endplates.

The amplitude-frequency histogram of spontaneous miniature endplate potentials follows a Gaussian distribution at mature endplates. This distribution gives the mean and variance of the quantum of transmitter. According to the vesicle hypothesis, this quantum is due to exocytosis of the contents of a single synaptic vesicle. Multimodal amplitude-frequency histograms are observed in varying degrees at developing endplates and at peripheral and central synapses, each of which has a specific active zone structure. These multimodal histograms may be due to the near synchronous exocytosis of more than one vesicle. In the present work, a theoretical treatment is given of the rise of intraterminal calcium after the stochastic opening of a calcium channel within a particular active zone geometry. The stochastic interaction of this calcium with the vesicle-associated proteins involved in exocytosis is then used to calculate the probability of quantal secretions from one or several vesicles at each active zone type. It is shown that this procedure can account for multiquantal spontaneous release that may occur at varicosities and boutons, compared with that at the active zones of motor nerve terminals.

Extracellular current flow and potential during quantal transmission from varicosities in a smooth muscle syncytium.

A discrete model has been developed that describes the extracellular current that flows in a smooth muscle syncytium upon the secretion of a quantum of transmitter onto a smooth muscle cell in the syncytium. This allows a description to be given of the current (called the excitatory junctional current (EJC)) recorded by an electrode of given diameter placed on the surface of the muscle, during synaptic transmission from a varicosity situated anywhere in the muscle. The EJC is of maximum negative amplitude when the varicosity is at the surface of the muscle near the inside rim of the electrode and decreases as the varicosity moves to the centre of the electrode. It is of maximum positive amplitude when the varicosity is at the surface near the outside rim of the electrode and declines rapidly in amplitude as the varicosity is removed further from the outside rim. Smaller diameter electrodes give larger EJCs than larger diameter electrodes for most positions of the varicosity on the surface of the muscle. The EJC amplitude declines for varicosities beneath the electrode that are not on the surface of the muscle, but deep in the tissue. The rate of this decline is greater the smaller the diameter of the electrode. The time-course of the EJC is largely invariant under changes in the position of the varicosity with respect to the recording electrode. Changes in the polarity of the current flow during a single EJC can occur, however, if two varicosities secrete transmitter simultaneously, one inside the electrode and one outside, and the time-course of the currents due to the individual varicosities is either the same or slightly different. This theoretical work has been used to interpret a number of recent experimental studies of extracellular current flow during autonomic neuromuscular transmission.

Probabilistic secretion of quanta and the synaptosecretosome hypothesis: evoked release at active zones of varicosities, boutons, and endplates.

A quantum of transmitter may be released upon the arrival of a nerve impulse if the influx of calcium ions through a nearby voltage-dependent calcium channel is sufficient to activate the vesicle-associated calcium sensor protein that triggers exocytosis. A synaptic vesicle, together with its calcium sensor protein, is often found complexed with the calcium channel in active zones to form what will be called a "synaptosecretosome." In the present work, a stochastic analysis is given of the conditions under which a quantum is released from the synaptosecretosome by a nerve impulse. The theoretical treatment considers the rise of calcium at the synaptosecretosome after the stochastic opening of a calcium channel at some time during the impulse, followed by the stochastic binding of calcium to the vesicle-associated protein and the probability of this leading to exocytosis. This allows determination of the probabilities that an impulse will release 0, 1, 2,... quanta from an active zone, whether this is in a varicosity, a bouton, or a motor endplate. A number of experimental observations of the release of transmitter at the active zones of sympathetic varicosities and boutons as well as somatic motor endplates are described by this analysis. These include the likelihood of the secretion of only one quantum at an active zone of endplates and of more than one quantum at an active zone of a sympathetic varicosity. The fourth-power relationship between the probability of transmitter release at the active zones of sympathetic varicosities and motor endplates and the external calcium concentration is also explained by this approach. So, too, is the fact that the time course of the increased rate of quantal secretion from a somatic active zone after an impulse is invariant with changes in the amount of calcium that enters through its calcium channel, whether due to changes consequent on the actions of autoreceptor agents such as adenosine or to facilitation. The increased probability of quantal release that occurs during F1 facilitation at the active zones of motor endplates and sympathetic boutons is predicted by the residual binding of calcium to a high-affinity site on the vesicle-associated protein. The concept of the stochastic operation of a synaptosecretosome can accommodate most phenomena involving the release of transmitter quanta at these synapses.

Quantal transmitter release at somatic motor-nerve terminals: stochastic analysis of the subunit hypothesis.

Here we analyze the problem of determining whether experimentally measured spontaneous miniature end-plate currents (MEPCs) indicate that quanta are composed of subunits. The properties of MEPCs at end plates with or without secondary clefts at the neuromuscular junction are investigated, using both stochastic and deterministic models of the action of a quantum of transmitter. It is shown that as the amount of transmitter in a quantum is increased above about 4000 acetylcholine (ACh) molecules there is a linear increase in the size of the MEPC. It is possible to then use amplitude-frequency histograms of such MEPCs to detect a subunit structure, as there is little potentiation effect above 4000 ACh molecules. Autocorrelation and power spectral analyses of such histograms establish that their subunit structure can be detected if the coefficient of variation of the subunit size is less than about 0.12 or, if electrical noise is added, about 0.1. Positive gradients relate the rise time and half-decay times of MEPCs to their amplitude, even in the absence of potentiating effects; these gradients are shallower at motor nerve terminals that possess secondary clefts. The effect of asynchronous release of subunits is also investigated. The criteria determined by this analysis for identifying a subunit composition in the quantum are applied to an amplitude-frequency histogram of MEPCs recorded from a small group of active zones at a visualized amphibian motor-nerve terminal. This did not provide evidence for a subunit structure.