David Cai

Outflow Boundary Conditions for Blood Flow in Arterial Trees

In the modeling of the pulse wave in the systemic arterial tree, it is necessary to truncate small arterial crowns representing the networks of small arteries and arterioles. Appropriate boundary conditions at the truncation points are required to represent wave reflection effects of the truncated arterial crowns. In this work, we provide a systematic method to extract parameters of the three-element Windkessel model from the impedance of a truncated arterial tree or from experimental measurements of the blood pressure and flow rate at the inlet of the truncated arterial crown. In addition, we propose an improved three-element Windkessel model with a complex capacitance to accurately capture the fundamental-frequency time lag of the reflection wave with respect to the incident wave. Through our numerical simulations of blood flow in a single artery and in a large arterial tree, together with the analysis of the modeling error of the pulse wave in large arteries, we show that both a small truncation radius and the complex capacitance in the improved Windkessel model play an important role in reducing the modeling error, defined as the difference in dynamics induced by the structured tree model and the Windkessel models.

Phenomenological Incorporation of Nonlinear Dendritic Integration Using Integrate-and-Fire Neuronal Frameworks

It has been discovered recently in experiments that the dendritic integration of excitatory glutamatergic inputs and inhibitory GABAergic inputs in hippocampus CA1 pyramidal neurons obeys a simple arithmetic rule as , where , and are the respective voltage values of the summed somatic potential, the excitatory postsynaptic potential (EPSP) and the inhibitory postsynaptic potential measured at the time when the EPSP reaches its peak value. Moreover, the shunting coefficient in this rule only depends on the spatial location but not the amplitude of the excitatory or inhibitory input on the dendrite. In this work, we address the theoretical issue of how much the above dendritic integration rule can be accounted for using subthreshold membrane potential dynamics in the soma as characterized by the conductance-based integrate-and-fire (I&F) model. Then, we propose a simple I&F neuron model that incorporates the spatial dependence of the shunting coefficient by a phenomenological parametrization. Our analytical and numerical results show that this dendritic-integration-rule-based I&F (DIF) model is able to capture many experimental observations and it also yields predictions that can be used to verify the validity of the DIF model experimentally. In addition, the DIF model incorporates the dendritic integration effects dynamically and is applicable to more general situations than those in experiments in which excitatory and inhibitory inputs occur simultaneously in time. Finally, we generalize the DIF neuronal model to incorporate multiple inputs and obtain a similar dendritic integration rule that is consistent with the results obtained by using a realistic neuronal model with multiple compartments. This generalized DIF model can potentially be used to study network dynamics that may involve effects arising from dendritic integrations.

Bilinearity in Spatiotemporal Integration of Synaptic Inputs

Neurons process information via integration of synaptic inputs from dendrites. Many experimental results demonstrate dendritic integration could be highly nonlinear, yet few theoretical analyses have been performed to obtain a precise quantitative characterization analytically. Based on asymptotic analysis of a two-compartment passive cable model, given a pair of time-dependent synaptic conductance inputs, we derive a bilinear spatiotemporal dendritic integration rule. The summed somatic potential can be well approximated by the linear summation of the two postsynaptic potentials elicited separately, plus a third additional bilinear term proportional to their product with a proportionality coefficient . The rule is valid for a pair of synaptic inputs of all types, including excitation-inhibition, excitation-excitation, and inhibition-inhibition. In addition, the rule is valid during the whole dendritic integration process for a pair of synaptic inputs with arbitrary input time differences and input locations. The coefficient is demonstrated to be nearly independent of the input strengths but is dependent on input times and input locations. This rule is then verified through simulation of a realistic pyramidal neuron model and in electrophysiological experiments of rat hippocampal CA1 neurons. The rule is further generalized to describe the spatiotemporal dendritic integration of multiple excitatory and inhibitory synaptic inputs. The integration of multiple inputs can be decomposed into the sum of all possible pairwise integration, where each paired integration obeys the bilinear rule. This decomposition leads to a graph representation of dendritic integration, which can be viewed as functionally sparse.

The characterization of hippocampal theta-driving neurons — a time-delayed mutual information approach

Interneurons are important for computation in the brain, in particular, in the information processing involving the generation of theta oscillations in the hippocampus. Yet the functional role of interneurons in the theta generation remains to be elucidated. Here we use time-delayed mutual information to investigate information flow related to a special class of interneurons—theta-driving neurons in the hippocampal CA1 region of the mouse—to characterize the interactions between theta-driving neurons and theta oscillations. For freely behaving mice, our results show that information flows from the activity of theta-driving neurons to the theta wave, and the firing activity of theta-driving neurons shares a substantial amount of information with the theta wave regardless of behavioral states. Via realistic simulations of a CA1 pyramidal neuron, we further demonstrate that theta-driving neurons possess the characteristics of the cholecystokinin-expressing basket cells (CCK-BC). Our results suggest that it is important to take into account the role of CCK-BC in the generation and information processing of theta oscillations.

Efficient image processing via compressive sensing of integrate-and-fire neuronal network dynamics

Integrate-and-fire (I&F) neuronal networks are ubiquitous in diverse image processing applications, including image segmentation and visual perception. While conventional I&F network image processing requires the number of nodes composing the network to be equal to the number of image pixels driving the network, we determine whether I&F dynamics can accurately transmit image information when there are significantly fewer nodes than network input-signal components. Although compressive sensing (CS) theory facilitates the recovery of images using very few samples through linear signal processing, it does not address whether similar signal recovery techniques facilitate reconstructions through measurement of the nonlinear dynamics of an I&F network. In this paper, we present a new framework for recovering sparse inputs of nonlinear neuronal networks via compressive sensing. By recovering both one-dimensional inputs and two-dimensional images, resembling natural stimuli, we demonstrate that input information can be well-preserved through nonlinear I&F network dynamics even when the number of network-output measurements is significantly smaller than the number of input-signal components. This work suggests an important extension of CS theory potentially useful in improving the processing of medical or natural images through I&F network dynamics and understanding the transmission of stimulus information across the visual system.

A Novel Characterization of Amalgamated Networks in Natural Systems

Densely-connected networks are prominent among natural systems, exhibiting structural characteristics often optimized for biological function. To reveal such features in highly-connected networks, we introduce a new network characterization determined by a decomposition of network-connectivity into low-rank and sparse components. Based on these components, we discover a new class of networks we define as amalgamated networks, which exhibit large functional groups and dense connectivity. Analyzing recent experimental findings on cerebral cortex, food-web, and gene regulatory networks, we establish the unique importance of amalgamated networks in fostering biologically advantageous properties, including rapid communication among nodes, structural stability under attacks, and separation of network activity into distinct functional modules. We further observe that our network characterization is scalable with network size and connectivity, thereby identifying robust features significant to diverse physical systems, which are typically undetectable by conventional characterizations of connectivity. We expect that studying the amalgamation properties of biological networks may offer new insights into understanding their structure-function relationships.