Fluid-Dynamic Modeling of Flow in Embryonic Tissue Indicates That Lymphatic Valve Location Is Not Consistently Determined by the Local Fluid Shear or Its Gradient.

OBJECTIVE: Intravascular lymphatic valves often occur in proximity to vessel junctions. It is commonly held that disturbed flow at junctions is responsible for accumulation of valve-forming cells (VFCs) at these locations as the initial step in valve creation, and the one which explains the association with these sites. However, evidence in favor is largely limited to cell culture experiments. METHODS: We acquired images of embryonic lymphatic vascular networks from day E16.5, when VFC accumulation has started but the developing valve has not yet altered the local vessel geometry, stained for Prox1, which co-localizes with Foxc2. Using finite-element computational fluid mechanics, we simulated the flow through the networks, under conditions appropriate to this early development stage. Then we correlated the Prox1 distributions with the distributions of simulated fluid shear and shear stress gradient. RESULTS: Across a total of 16 image sets, no consistent correlation was found between Prox1 distribution and the local magnitude of fluid shear, or its positive or negative gradient. CONCLUSIONS: This, the first direct semi-empirical test of the localization hypothesis to interrogate the tissue from in vivo at the critical moment of development, does not support the idea that a feature of the local flow determines valve localization.

A dual-clock-driven model of lymphatic muscle cell pacemaking to emulate knock-out of Ano1 or IP3R.

Lymphatic system defects are involved in a wide range of diseases, including obesity, cardiovascular disease, and neurological disorders, such as Alzheimer's disease. Fluid return through the lymphatic vascular system is primarily provided by contractions of muscle cells in the walls of lymphatic vessels, which are in turn driven by electrochemical oscillations that cause rhythmic action potentials and associated surges in intracellular calcium ion concentration. There is an incomplete understanding of the mechanisms involved in these repeated events, restricting the development of pharmacological treatments for dysfunction. Previously, we proposed a model where autonomous oscillations in the membrane potential (M-clock) drove passive oscillations in the calcium concentration (C-clock). In this paper, to model more accurately what is known about the underlying physiology, we extend this model to the case where the M-clock and the C-clock oscillators are both active but coupled together, thus both driving the action potentials. This extension results from modifications to the model's description of the IP3 receptor, a key C-clock mechanism. The synchronised dual-driving clock behaviour enables the model to match IP3 receptor knock-out data, thus resolving an issue with previous models. We also use phase-plane analysis to explain the mechanisms of coupling of the dual clocks. The model has the potential to help determine mechanisms and find targets for pharmacological treatment of some causes of lymphoedema.

Modeling flow in embryonic lymphatic vasculature: what is its role in valve development?

A majority of lymphatic valves tend to form in proximity to vessel junctions, and it is often proposed that disturbed flow at junctions creates oscillating shear stress that leads to accumulation of transcription factors which bring about valvogenesis at these sites. In images of networks of dorsal skin lymphatics from embryonic mice (day E16), we compared simulated fluid flow patterns and observed distributions of the transcription factor Prox1, which is implicated in valve formation. Because of creeping-flow conditions, flow across vessel junctions was not 'disturbed', and within a given vessel, shear stress varied inversely with local conduit width. Prox1 concentration was indeed localised to vessel end-regions, but over three networks was not consistently correlated with the vessel normalised-distance distribution of either fluid shear stress or shear-stress axial gradient. These findings do not support the presently accepted mechanism for the role of flow in valve localisation.

A multiphase model of growth factor-regulated atherosclerotic cap formation.

Atherosclerosis is characterised by the growth of fatty plaques in the inner artery wall. In mature plaques, vascular smooth muscle cells (SMCs) are recruited from adjacent tissue to deposit a collagenous cap over the fatty plaque core. This cap isolates the thrombogenic plaque content from the bloodstream and prevents the clotting cascade that leads to myocardial infarction or stroke. Despite the protective role of the cap, the mechanisms that regulate cap formation and maintenance are not well understood. It remains unclear why some caps become stable, while others become vulnerable to rupture. We develop a multiphase PDE model with non-standard boundary conditions to investigate collagen cap formation by SMCs in response to diffusible growth factor signals from the endothelium. Platelet-derived growth factor stimulates SMC migration, proliferation and collagen degradation, while transforming growth factor (TGF)-[Formula: see text] stimulates SMC collagen synthesis and inhibits collagen degradation. The model SMCs respond haptotactically to gradients in the collagen phase and have reduced rates of migration and proliferation in dense collagenous tissue. The model, which is parameterised using in vivo and in vitro experimental data, reproduces several observations from plaque growth in mice. Numerical and analytical results demonstrate that a stable cap can be formed by a relatively small SMC population and emphasise the critical role of TGF-[Formula: see text] in effective cap formation. These findings provide unique insight into the mechanisms that may lead to plaque destabilisation and rupture. This work represents an important step towards the development of a comprehensive in silico plaque model.

A two-phase model of early fibrous cap formation in atherosclerosis.

Atherosclerotic plaque growth is characterised by chronic, non-resolving inflammation that promotes the accumulation of cellular debris and extracellular fat in the inner artery wall. This material is highly thrombogenic, and plaque rupture can lead to the formation of blood clots that occlude major arteries and cause myocardial infarction or stroke. In advanced plaques, vascular smooth muscle cells (SMCs) are recruited from deeper in the artery wall to synthesise a cap of fibrous tissue that stabilises the plaque and sequesters the thrombogenic plaque content from the bloodstream. The fibrous cap provides crucial protection against the clinical consequences of atherosclerosis, but the mechanisms of cap formation are poorly understood. In particular, it is unclear why certain plaques become stable and robust while others become fragile and dangerously vulnerable to rupture. We develop a multiphase model with non-standard boundary conditions to investigate early fibrous cap formation in the atherosclerotic plaque. The model is parameterised using data from a range of in vitro and in vivo studies, and includes highly nonlinear mechanisms of SMC proliferation and migration in response to an endothelium-derived chemical signal. We demonstrate that the model SMC population naturally evolves towards a steady-state, and predict a rate of cap formation and a final plaque SMC content consistent with experimental observations in mice. Parameter sensitivity simulations show that SMC proliferation makes a limited contribution to cap formation, and demonstrate that stable cap formation relies primarily on a critical balance between the rates of SMC recruitment to the plaque, chemotactic SMC migration within the plaque and SMC loss by apoptosis or phenotype change. This model represents the first detailed in silico study of fibrous cap formation in atherosclerosis, and establishes a multiphase modelling framework that can be readily extended to investigate many other aspects of plaque development.

Consequences of intravascular lymphatic valve properties: a study of contraction timing in a multi-lymphangion model.

The observed properties of valves in collecting lymphatic vessels include transmural pressure-dependent bias to the open state and hysteresis. The bias may reduce resistance to flow when the vessel is functioning as a conduit. However, lymphatic pumping implies a streamwise increase in mean pressure across each valve, suggesting that the bias is then potentially unhelpful. Lymph pumping by a model of several collecting lymphatic vessel segments (lymphangions) in series, which incorporated these properties, was investigated under conditions of adverse pressure difference while varying the refractory period between active muscular contractions and the inter-lymphangion contraction delay. It was found that many combinations of the timing parameters and the adverse pressure difference led to one or more intermediate valves remaining open instead of switching between open and closed states during repetitive contraction cycles. Cyclic valve switching was reliably indicated if the mean pressure in a lymphangion over a cycle was higher than that in the lymphangion upstream, but either lack of or very brief valve closure could cause mean pressure to be lower downstream. Widely separated combinations of refractory period and delay time were found to produce the greatest flow-rate for a given pressure difference. The efficiency of pumping was always maximized by a long refractory period and lymphangion contraction starting when the contraction of the lymphangion immediately upstream was peaking. By means of an ex vivo experiment, it was verified that intermediate valves in a chain of pumping lymphangions can remain open, while the lymphangions on either side of the open valve continue to execute contractions.

The acoustic field in biomedical tissue with midscale inhomogeneities.

Biomedical ultrasound is often used for investigations within and close to tissue inhomogeneities, such as lesions and plaques, that are midsized compared with the ultrasound wavelength. The scaled wavenumber is typically in the range 1 to 100. Even with small (less than 10%) sound speed variations, such objects are associated with very complicated diffractive field magnitude modulations. The corresponding phase modulations are much more regular, and this observation is the basis for the method described in this paper. The acoustic field can be expressed in terms of a scattering integral. For biomedical parameters, calculations with the widely used Born approximation give accurate results in only very limited circumstances. In this paper we demonstrate the importance of the initial phase estimate, and introduce the Phase Corrected Scattering Integral (PCSI) method. We show that remarkably accurate results for the acoustic field can be obtained from a single evaluation of the scattering integral if this incorporates an initial estimate of the phase modulation imposed by the inhomogeneity. A simple ray model can be used to find the phase correction. The PCSI method deals very effectively with scattering due to small changes in sound speed and irregular geometry, both characteristic of biomedical problems.

Acoustic intensity for a long vessel with noncircular cross section.

The acoustic intensity distribution around and within long vessels of noncircular cross section was investigated for parameters typical of biomedical ultrasound and blood vessels. We have developed a collocation method for finding the acoustic field when a uniform plane wave is obliquely incident on a long, not necessarily cylindrical, impedance interface. Results are presented for vessels of noncircular cross section and for vessels with thick walls of nonuniform thickness. The intensity in the vicinity of the vessel, throughout the lumen, and in the wall, is calculated for intermediate length scales, i.e., vessel radius and wall thickness in the range 1 to 10 wavelengths. The intensity distribution is an interference pattern, with complicated regions of increased and decreased intensity. These results are compared with approximate intensity obtained using ray theory. Effects not predicted by ray theory and intensity variations that will be significant in any close ultrasonic investigation of these vessels are revealed.