Formation of vascular-like structures using a chemotaxis-driven multiphase model.

We propose a continuum model for pattern formation, based on the multiphase model framework, to explore in vitro cell patterning within an extracellular matrix (ECM). We demonstrate that, within this framework, chemotaxis-driven cell migration can lead to the formation of cell clusters and vascular-like structures in 1D and 2D respectively. The influence on pattern formation of additional mechanisms commonly included in multiphase tissue models, including cell-matrix traction, contact inhibition, and cell-cell aggregation, are also investigated. Using sensitivity analysis, the relative impact of each model parameter on the simulation outcomes is assessed to identify the key parameters involved. Chemoattractant-matrix binding is further included, motivated by previous experimental studies, and found to reduce the spatial scale of patterning to within a biologically plausible range for capillary structures. Key findings from the in-depth parameter analysis of the 1D models, both with and without chemoattractant-matrix binding, are demonstrated to translate well to the 2D model, obtaining vascular-like cell patterning for multiple parameter regimes. Overall, we demonstrate a biologically-motivated multiphase model capable of generating long-term pattern formation on a biologically plausible spatial scale both in 1D and 2D, with applications for modelling in vitro vascular network formation.

A variable heart rate multi-compartmental coupled model of the cardiovascular and respiratory systems.

Current mathematical models of the cardiovascular system that are based on systems of ordinary differential equations are limited in their ability to mimic important features of measured patient data, such as variable heart rates (HR). Such limitations present a significant obstacle in the use of such models for clinical decision-making, as it is the variations in vital signs such as HR and systolic and diastolic blood pressure that are monitored and recorded in typical critical care bedside monitoring systems. In this paper, novel extensions to well-established multi-compartmental models of the cardiovascular and respiratory systems are proposed that permit the simulation of variable HR. Furthermore, a correction to current models is also proposed to stabilize the respiratory behaviour and enable realistic simulation of vital signs over the longer time scales required for clinical management. The results of the extended model developed here show better agreement with measured bio-signals, and these extensions provide an important first step towards estimating model parameters from patient data, using methods such as neural ordinary differential equations. The approach presented is generalizable to many other similar multi-compartmental models of the cardiovascular and respiratory systems.

Symmetric arrangement of mitochondria:plasma membrane contacts between adjacent photoreceptor cells regulated by Opa1.

Mitochondria are known to play an essential role in photoreceptor function and survival that enables normal vision. Within photoreceptors, mitochondria are elongated and extend most of the inner-segment length, where they supply energy for protein synthesis and the phototransduction machinery in the outer segment, as well as acting as a calcium store. Here, we examined the arrangement of the mitochondria within the inner segment in detail using three-dimensional (3D) electron microscopy techniques and show they are tethered to the plasma membrane in a highly specialized arrangement. Remarkably, mitochondria and their cristae openings align with those of neighboring inner segments. The pathway by which photoreceptors meet their high energy demands is not fully understood. We propose this to be a mechanism to share metabolites and assist in maintaining homeostasis across the photoreceptor cell layer. In the extracellular space between photoreceptors, Müller glial processes were identified. Due to the often close proximity to the inner-segment mitochondria, they may, too, play a role in the inner-segment mitochondrial arrangement as well as metabolite shuttling. OPA1 is an important factor in mitochondrial homeostasis, including cristae remodeling; therefore, we examined the photoreceptors of a heterozygous Opa1 knockout mouse model. The cristae structure in the Opa1+/- photoreceptors was not greatly affected, but the mitochondria were enlarged and had reduced alignment to neighboring inner-segment mitochondria. This indicates the importance of key regulators in maintaining this specialized photoreceptor mitochondrial arrangement.

Ultrasound propagation through dilute polydisperse microbubble suspensions.

In a fully nonlinear model of wave propagation through bubbly media, computational complexity arises when the medium contains a polydisperse bubble population. This is because a nonlinear ordinary differential equation governing the bubble response must be solved for the current radius of each bubble size present at every spatial location and at every time step. In biomedical ultrasound imaging, commercial contrast agents typically possess a wide range of bubble sizes that exhibit a variety of differing behaviours at ultrasound frequencies of clinical interest. Despite the advent of supercomputing resources, the simulation of ultrasound propagation through microbubble populations still represents a formidable numerical task. Consequently, efficient computational algorithms that have the potential to be implemented in real time on clinical scanners remain highly desirable. In this work, a numerical approach is investigated that computes only a single ordinary differential equation at each spatial location which can potentially reduce significantly the computational effort. It is demonstrated that, under certain parameter regimes, the approach replicates the fully nonlinear model of an incident ultrasound pulse propagating through a polydisperse population of bubbles with a high degree of accuracy.

Finding optimal geometries for noise barrier tops using scaled experiments.

Scaled acoustic laboratory experiments are used to develop a methodology for obtaining the acoustic characteristics of different barrier top designs and for identifying geometries that may have advantages over the traditional thin vertical screen. The idea is to use a short impulsive spherical sound pulse possessing a broad frequency spectrum. If the duration of the pulse is sufficiently short, the entire primary signal, which travels by the shortest direct route diffracting at the top of the barrier, arrives at the receiver much earlier than any secondary signals reflected from the surroundings. Secondary signals may therefore be ignored and only the information from the primary signal can be analyzed. When the typical frequency band of the sound pulse is about an order of magnitude higher than typical traffic noise spectra, then scaled acoustic modeling using the same scaling factor for lengths and distances is possible. The results of such experiments are reported here for barriers with six different geometries. Using spectral analysis, insertion losses as functions of frequency were calculated for different source-receiver positions and barrier tops. The results were then rescaled for full-size traffic barriers and, using a typical traffic noise spectrum, single number ratings of barrier performance were obtained.

Quantifying the Frictional Forces between Skin and Nonwoven Fabrics.

When a compliant sheet of material is dragged over a curved surface of a body, the frictional forces generated can be many times greater than they would be for a planar interface. This phenomenon is known to contribute to the abrasion damage to skin often suffered by wearers of incontinence pads and bed/chairbound people susceptible to pressure sores. Experiments that attempt to quantify these forces often use a simple capstan-type equation to obtain a characteristic coefficient of friction. In general, the capstan approach assumes the ratio of applied tensions depends only on the arc of contact and the coefficient of friction, and ignores other geometric and physical considerations; this approach makes it straightforward to obtain explicitly a coefficient of friction from the tensions measured. In this paper, two mathematical models are presented that compute the material displacements and surface forces generated by, firstly, a membrane under tension in moving contact with a rigid obstacle and, secondly, a shell-membrane under tension in contact with a deformable substrate. The results show that, while the use of a capstan equation remains fairly robust in some cases, effects such as the curvature and flaccidness of the underlying body, and the mass density of the fabric can lead to significant variations in stresses generated in the contact region. Thus, the coefficient of friction determined by a capstan model may not be an accurate reflection of the true frictional behavior of the contact region.

Vortices and flow reversal due to suction slots.

Suction into small two- or three-dimensional surface slots inside an otherwise planar boundary-layer is examined theoretically through a combined analytical and computational approach. Increasing suction strength leads to enhanced nonlinear structures with flow reversals or trailing vortices.