Mathematical model of blood and interstitial flow and lymph production in the liver.

We present a mathematical model of blood and interstitial flow in the liver. The liver is treated as a lattice of hexagonal \u2018classic\u2019 lobules, which are assumed to be long enough that end effects may be neglected and a two-dimensional problem considered. Since sinusoids and lymphatic vessels are numerous and small compared to the lobule, we use a homogenized approach, describing the sinusoidal and interstitial spaces as porous media. We model plasma filtration from sinusoids to the interstitium, lymph uptake by lymphatic ducts, and lymph outflow from the liver surface. Our results show that the effect of the liver surface only penetrates a depth of a few lobules\u2019 thickness into the tissue. Thus, we separately consider a single lobule lying sufficiently far from all external boundaries that we may regard it as being in an infinite lattice, and also a model of the region near the liver surface. The model predicts that slightly more lymph is produced by interstitial fluid flowing through the liver surface than that taken up by the lymphatic vessels in the liver and that the on-peritonealized region of the surface of the liver results in the total lymph production (uptake by lymphatics plus fluid crossing surface) being about 5 % more than if the entire surface were covered by the Glisson\u2013peritoneal membrane. Estimates of lymph outflow through the surface of the liver are in good agreement with experimental data. We also study the effect of non-physiological values of the controlling parameters, particularly focusing on the conditions of portal hypertension and ascites. To our knowledge, this is the first attempt to model lymph production in the liver. The model provides clinically relevant information about lymph outflow pathways and predicts the systemic response to pathological variations

Phakic iris-fixated intraocular lens placement in the anterior chamber: effects on aqueous flow

Phakic intraocular lenses (pIOLs) are used for correcting vision; in this paper we investigate the fluid dynamical effects of an iris-fixated lens in the anterior chamber. In particular, we focus on changes in the wall shear stress (WSS) on the cornea and iris, which could be responsible for endothelial and pigment cell loss, respectively, and also on the possible increase of the intraocular pressure, which is known to correlate with the incidence of secondary glaucoma

Intracellular flow in optic-nerve axons: a mechanism for cell death in glaucoma

PURPOSE. In glaucoma, elevated intraocular pressure causes a progressive loss of retinal ganglion cells and results in optic neuropathy. The authors propose a potential mechanism for cell death, whereby elevated intraocular pressure causes fluid to permeate axonal membranes, creating a passive intracellular fluid flow within the axons. It is hypothesized that this intracellular flow locally depletes the adenosine triphosphate (ATP) concentration, disrupting axonal transport and leading to cell death.METHODS. A mathematical model was developed that takes into account the biomechanical principles underpinning the proposed hypothesis, and was solved to determine the implications of the mechanism.RESULTS. The model suggests that the raised intraocular pressures present in glaucoma are adequate to produce significant intracellular fluid flow. In the periphery of the optic nerve head, this flow may be sufficient to disrupt the diffusion of ATP and hence interrupt active axonal transport.CONCLUSIONS. The mathematical model demonstrates that it is physically plausible that a passive intracellular fluid flow could significantly contribute to the pathophysiology of the retinal ganglion cell axon in glaucoma

Large-amplitude ac voltammetry: Theory for reversible redox reactions in the “slow scan limit approximation”

Analytical solutions for the current response of an ac voltammetric experiment on a reversible redox system have traditionally relied on two approximations: the “slow scan limit approximation” and small ac potential amplitudes. There has been no rigorous analytical investigation of the limits of validity of the solutions derived under the first assumption, and the second assumption only allows for small currents, which restricts the applicability of the method. In this article, we derive a novel analytical solution for the current response, valid for ac potential excitations of any magnitude. We establish rigorous estimates of the error induced by the slow scan limit approximation and discuss in detail how this should influence the choice of experimental parameters. The effects of double-layer capacitance are generally large under the slow scan limit approximation and can cause difficulties in isolating the higher harmonics due to spectral leakage in the power spectrum of the FFT. We demonstrate how the Hann window can be used to overcome this problem in the case of linear capacitance. Finally we show how parameters describing the electrochemical system (including linear capacitance) can be deduced from features of the time-dependent harmonic envelopes and the dc part of the current response, without the need for baseline subtraction

A 3D porous media liver lobule model: the importance of vascular septa and anisotropic permeability for homogeneous perfusion

The hepatic blood circulation is complex, particularly at the microcirculatory level. Previously, 2D liver lobule models using porous media and a 3D model using real sinusoidal geometries have been developed. We extended these models to investigate the role of vascular septa (VS) and anisotropic permeability. The lobule was modelled as a hexagonal prism (with or without VS) and the tissue was treated as a porous medium (isotropic or anisotropic permeability). Models were solved using computational fluid dynamics. VS inclusion resulted in more spatially homogeneous perfusion. Anisotropic permeability resulted in a larger axial velocity component than isotropic permeability. A parameter study revealed that results are most sensitive to the lobule size and radial pressure drop. Our model provides insight into hepatic microhaemodynamics, and suggests that inclusion of VS in the model leads to perfusion patterns that are likely to reflect physiological reality. The model has potential for applications to unphysiological and pathological conditions.peerreview_statement: The publishing and review policy for this title is described in its Aims & Scope. aims_and_scope_url: http://www.tandfonline.com/action/journalInformation?show=aimsScope&journalCode=gcmb20status: publishe