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A nonlinear multi-scale model for blood circulation in a realistic vascular system.

ABSTRACT: In the last decade, numerical models have become an increasingly important tool in biological and medical science. Numerical simulations contribute to a deeper understanding of physiology and are a powerful tool for better diagnostics and treatment. In this paper, a nonlinear multi-scale model framework is developed for blood flow distribution in the full vascular system of an organ. We couple a quasi one-dimensional vascular graph model to represent blood flow in larger vessels and a porous media model to describe flow in smaller vessels and capillary bed. The vascular model is based on Poiseuille's Law, with pressure correction by elasticity and pressure drop estimation at vessels' junctions. The porous capillary bed is modelled as a two-compartment domain (artery and venous) using Darcy's Law. The fluid exchange between the artery and venous capillary bed compartments is defined as blood perfusion. The numerical experiments show that the proposed model for blood circulation: (i) is closely dependent on the structure and parameters of both the larger vessels and of the capillary bed, and (ii) provides a realistic blood circulation in the organ. The advantage of the proposed model is that it is complex enough to reliably capture the main underlying physiological function, yet highly flexible as it offers the possibility of incorporating various local effects. Furthermore, the numerical implementation of the model is straightforward and allows for simulations on a regular desktop computer.

SUBMITTER: Qohar UNA

PROVIDER: S-EPMC8633777 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:In synapses, calcium is required for modulating synaptic transmission, plasticity, synaptogenesis, and synaptic pruning. The regulation of calcium dynamics within neurons involves cellular mechanisms such as synaptically activated channels and pumps, calcium buffers, and calcium sequestrating organelles. Many experimental studies tend to focus on only one or a small number of these mechanisms, as technical limitations make it difficult to observe all features at once. Computational modeling enables incorporation of many of these properties together, allowing for more complete and integrated studies. However, the scale of existing detailed models is often limited to synaptic and dendritic compartments as the computational burden rapidly increases when these models are integrated in cellular or network level simulations. In this article we present a computational model of calcium dynamics at the postsynaptic spine of a CA1 pyramidal neuron, as well as a methodology that enables its implementation in multi-scale, large-scale simulations. We first present a mechanistic model that includes individually validated models of various components involved in the regulation of calcium at the spine. We validated our mechanistic model by comparing simulated calcium levels to experimental data found in the literature. We performed additional simulations with the mechanistic model to determine how the simulated calcium activity varies with respect to presynaptic-postsynaptic stimulation intervals and spine distance from the soma. We then developed an input-output (IO) model that complements the mechanistic calcium model and provide a computationally efficient representation for use in larger scale modeling studies; we show the performance of the IO model compared to the mechanistic model in terms of accuracy and speed. The models presented here help achieve two objectives. First, the mechanistic model provides a comprehensive platform to describe spine calcium dynamics based on individual contributing factors. Second, the IO model is trained on the main dynamical features of the mechanistic model and enables nonlinear spine calcium modeling on the cell and network level simulation scales. Utilizing both model representations provide a multi-level perspective on calcium dynamics, originating from the molecular interactions at spines and propagating the effects to higher levels of activity involved in network behavior.

Project description:BackgroundTranscranial direct current stimulation (tDCS) is a non-invasive brain stimulation modality that can alter cortical excitability. However, it remains unclear how the subcellular elements of different neuron types are polarized by specific electric field (E-field) distributions.ObjectiveTo quantify neuronal polarization generated by tDCS in a multi-scale computational model.MethodsWe embedded layer-specific, morphologically-realistic cortical neuron models in a finite element model of the E-field in a human head and simulated steady-state polarization generated by conventional primary-motor-cortex-supraorbital (M1-SO) and 4 × 1 high-definition (HD) tDCS. We quantified somatic, axonal, and dendritic polarization of excitatory pyramidal cells in layers 2/3, 5, and 6, as well as inhibitory interneurons in layers 1 and 4 of the hand knob.ResultsAxonal and dendritic terminals were polarized more than the soma in all neurons, with peak axonal and dendritic polarization of 0.92 mV and 0.21 mV, respectively, compared to peak somatic polarization of 0.07 mV for 1.8 mA M1-SO stimulation. Both montages generated regions of depolarization and hyperpolarization beneath the M1 anode; M1-SO produced slightly stronger, more diffuse polarization peaking in the central sulcus, while 4 × 1 HD produced higher peak polarization in the gyral crown. The E-field component normal to the cortical surface correlated strongly with pyramidal neuron somatic polarization (R2>0.9), but exhibited weaker correlations with peak pyramidal axonal and dendritic polarization (R2:0.5-0.9) and peak polarization in all subcellular regions of interneurons (R2:0.3-0.6). Simulating polarization by uniform local E-field extracted at the soma approximated the spatial distribution of tDCS polarization but produced large errors in some regions (median absolute percent error: 7.9 %).ConclusionsPolarization of pre- and postsynaptic compartments of excitatory and inhibitory cortical neurons may play a significant role in tDCS neuromodulation. These effects cannot be predicted from the E-field distribution alone but rather require calculation of the neuronal response.

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A nonlinear multi-scale model for blood circulation in a realistic vascular system.

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