ComprehensiveIn SituAnalysis of Arteriolar Network Geometry and Topology in Rat Gluteus Maximus Muscle

A constrained constructive optimization model of branching arteriolar networks in rat skeletal muscle

Blood flow regulation within the microvasculature reflects a complex interaction of regulatory mechanisms and varies spatially and temporally according to conditions such as metabolism, growth, injury, and disease. Understanding the role of microvascular flow distributions across conditions is of interest to investigators spanning multiple disciplines; however, data collection within networks can be labor-intensive and challenging due to limited resolution. To overcome these experimental challenges, computational network models that can accurately simulate vascular behavior are highly beneficial. Constrained constructive optimization (CCO) is a commonly used algorithm for vascular simulation, particularly well known for its adaptability toward vascular modeling across tissues. The present work demonstrates an implementation of CCO aimed to simulate a branching arteriolar microvasculature in healthy skeletal muscle, validated against literature including comprehensive rat gluteus maximus vasculature datasets, and reviews a list of user-specified adjustable model parameters to understand how their variability affects the simulated networks. Network geometric properties, including mean element diameters, lengths, and numbers of bifurcations per order, Horton's law ratios, and fractal dimension, demonstrate good validation once model parameters are adjusted to experimental data. This model successfully demonstrates hemodynamic properties such as Murray's law and the network Fahraeus effect. Application of centrifugal and Strahler ordering schemes results in divergent descriptions of identical simulated networks. This work introduces a novel CCO-based model focused on generating branching skeletal muscle microvascular arteriolar networks based on adjustable model parameters, thus making it a valuable tool for investigations into skeletal muscle microvascular structure and tissue perfusion.NEW & NOTEWORTHY The present work introduces a CCO-based algorithm for generating branching arteriolar networks, with adjustable model parameters to enable modeling in varying skeletal muscle tissues. The geometric and hemodynamic parameters of the generated networks have been comprehensively validated using experimental data collected previously in-house and from literature. This is one of few validated CCO-based models to specialize in skeletal muscle microvasculature and acts as a beneficial tool for investigating the microvasculature for hypothesis testing and validation.

Steady-State Tissue Oxygen Distributions Calculated by a Green's Function Method and a Finite Difference Method: A Comparison

Simulations that are meant to determine the steady-state distribution of a diffusible solute such as oxygen in tissues have typically used finite difference methods to solve the diffusion equation. Finite difference methods require a tissue mesh with enough points to resolve oxygen gradients near and between discrete blood vessels. The large number of points that are typically required can make these calculations very slow. In this paper, we investigate a numerical method known as the Green's function method which is not bound by the same constraint. The Green's function method is expected to yield an accurate oxygen distribution more quickly by requiring fewer mesh points. Both methods were applied to calculate the steady state oxygen distribution in a model simulation region. When the Green's function calculation used meshes with 1/2, 1/4 and, 1/8 of the resolution required for the finite-difference mesh, there was good agreement with the finite difference calculation in all cases. When the volume of the domain was increased 8-fold the Green's function method was able to calculate the O₂ field in 22 minutes, whereas the finite difference calculation is expected to take approximately 1 week. The number of steps required for the Green's function calculation increases quadratically with the number of points in the tissue mesh. As a result, small meshes are calculated very quickly using Green's functions, while for larger mesh sizes this method experiences a significant decrease in efficiency.

A healthy dose of chaos: Using fractal frameworks for engineering higher-fidelity biomedical systems

Optimal levels of chaos and fractality are distinctly associated with physiological health and function in natural systems. Chaos is a type of nonlinear dynamics that tends to exhibit seemingly random structures, whereas fractality is a measure of the extent of organization underlying such structures. Growing bodies of work are demonstrating both the importance of chaotic dynamics for proper function of natural systems, as well as the suitability of fractal mathematics for characterizing these systems. Here, we review how measures of fractality that quantify the dose of chaos may reflect the state of health across various biological systems, including: brain, skeletal muscle, eyes and vision, lungs, kidneys, tumours, cell regulation, skin and wound repair, bone, vasculature, and the heart. We compare how reports of either too little or too much chaos and fractal complexity can be damaging to normal biological function, and suggest that aiming for the healthy dose of chaos may be an effective strategy for various biomedical applications. We also discuss rising examples of the implementation of fractal theory in designing novel materials, biomedical devices, diagnostics, and clinical therapies. Finally, we explain important mathematical concepts of fractals and chaos, such as fractal dimension, criticality, bifurcation, and iteration, and how they are related to biology. Overall, we promote the effectiveness of fractals in characterizing natural systems, and suggest moving towards using fractal frameworks as a basis for the research and development of better tools for the future of biomedical engineering.

Estimating blood flow in skeletal muscle arteriolar trees reconstructed from in vivo data using the Fry approach

OBJECTIVE

To develop a computational method to accurately predict blood flow in skeletal muscle arteriolar trees in the absence of complete boundary data.

METHODS

We used arteriolar trees in the rat GM muscle that were reconstructed from montages obtained via IVVM, and incorporated a recently published method for approximating unknown b.c.'s into our existing two-phase, steady-state blood flow model. For varying numbers of unknown b.c.'s, we used the new flow model and GM geometry to approximately match RBC flows corresponding to experimental measurements.

RESULTS

We showed this method gives errors that decrease as the number of unknown b.c.'s decreases. We also showed that specifying total blood flow decreases the mean RBC flow error and its variability. By varying required target values of intravascular pressure and wall shear stress, we showed results are less sensitive to target pressure. Finally, we developed and validated a method for determining target values, so that network hemodynamics and resistance can be accurately calculated based only on measured or estimated total blood flow.

CONCLUSIONS

We have developed and validated a computational method that can accurately estimate RBC flow distribution in skeletal muscle arteriolar trees in the absence of complete boundary data.