arXiv subjects

Huaxiong Huang

Publications and source records attributed to Huaxiong Huang.

42 records · Page 3Linked to original sources

arXiv2017

Electro-Neutral Models for Dynamic Poisson-Nernst-Planck System

The Poisson-Nernst-Planck (PNP) system is a standard model for describing ion transport. In many applications, e.g., ions in biological tissues, the presence of thin boundary layers poses both modelling and computational challenges. In this paper, we derive simplified electro-neutral (EN) models where the thin boundary layers are replaced by effective boundary conditions. There are two major advantages of EN models. First of all, it is much cheaper to solve them numerically. Secondly, EN models are easier to deal with compared with the original PNP, therefore it is also easier to derive macroscopic models for cellular structures using EN models. Even though the approach is applicable to higher dimensional cases, this paper mainly focuses on the one-dimensional system, including the general multi-ion case. Using systematic asymptotic analysis, we derive a variety of effective boundary conditions directly applicable to EN system for the bulk region. This EN system can be solved directly and efficiently without computing the solution in the boundary layer. The derivation is based on matched asymptotics, and the key idea is to bring back higher order contributions into effective boundary conditions. For Dirichlet boundary conditions, the higher order terms can be neglected and classical results (continuity of electrochemical potential) are recovered. For flux boundary conditions, however, neglecting higher contribution leads to physically incorrect solutions since they account for accumulation of ions in boundary layer. The validity of our EN model is verified by several examples and numerical computation. In particular, our EN model is much more efficient than the original PNP model when applied to the computation of membrane potential.

physics.bio-ph↗

arXiv2013

A mathematical model of the metabolic and perfusion effects on cortical spreading depression

Cortical spreading depression (CSD) is a slow-moving ionic and metabolic disturbance that propagates in cortical brain tissue. In addition to massive cellular depolarization, CSD also involves significant changes in perfusion and metabolism -- aspects of CSD that had not been modeled and are important to traumatic brain injury, subarachnoid hemorrhage, stroke, and migraine. In this study, we develop a mathematical model for CSD where we focus on modeling the features essential to understanding the implications of neurovascular coupling during CSD. In our model, the sodium-potassium--ATPase, mainly responsible for ionic homeostasis and active during CSD, operates at a rate that is dependent on the supply of oxygen. The supply of oxygen is determined by modeling blood flow through a lumped vascular tree with an effective local vessel radius that is controlled by the extracellular potassium concentration. We show that during CSD, the metabolic demands of the cortex exceed the physiological limits placed on oxygen delivery, regardless of vascular constriction or dilation. However, vasoconstriction and vasodilation play important roles in the propagation of CSD and its recovery. Our model replicates the qualitative and quantitative behavior of CSD -- vasoconstriction, oxygen depletion, extracellular potassium elevation, prolonged depolarization -- found in experimental studies. We predict faster, longer duration CSD in vivo than in vitro due to the contribution of the vasculature. Our results also help explain some of the variability of CSD between species and even within the same animal. These results have clinical and translational implications, as they allow for more precise in vitro, in vivo, and in silico exploration of a phenomenon broadly relevant to neurological disease.

q-bio.NC↗

arXiv2012

Valuation and hedging of the ruin-contingent life annuity (RCLA)

This paper analyzes a novel type of mortality contingent-claim called a ruin-contingent life annuity (RCLA). This product fuses together a path-dependent equity put option with a "personal longevity" call option. The annuitant's (i.e. long position) payoff from a generic RCLA is \$1 of income per year for life, akin to a defined benefit pension, but deferred until a pre-specified financial diffusion process hits zero. We derive the PDE and relevant boundary conditions satisfied by the RCLA value (i.e. the hedging cost) assuming a complete market where No Arbitrage is possible. We then describe some efficient numerical techniques and provide estimates of a typical RCLA under a variety of realistic parameters. The motivation for studying the RCLA on a stand-alone basis is two-fold. First, it is implicitly embedded in approximately \$1 trillion worth of U.S. variable annuity (VA) policies; which have recently attracted scrutiny from financial analysts and regulators. Second, the U.S. administration - both Treasury and Department of Labor - have been encouraging Defined Contribution (401k) plans to offer stand-alone longevity insurance to participants, and we believe the RCLA would be an ideal and cost effective candidate for that job.

q-fin.PR↗

arXiv2012

A different perspective on retirement income sustainability: the blueprint for a ruin contingent life annuity (RCLA)

The purpose of this article is twofold. First, we motivate the need for a new type of stand-alone retirement income insurance product that would help individuals protect against personal longevity risk and possible "retirement ruin" in an economically efficient manner. We label this product a ruin-contingent life annuity (RCLA), which we elaborate-on and explain with various numerical examples and a basic pricing model. Second, we argue that with the proper perspective a similar product actually exists, albeit not available on a stand-alone basis. Namely, they are fused and embedded within modern variable annuity (VA) policies with guaranteed living income benefit (GLiB) riders. Indeed, the popularity of GLiB riders on VA policies point towards the potential commercial success of such a stand-alone vehicle.

q-fin.RM↗

arXiv2012

Optimal retirement consumption with a stochastic force of mortality

We extend the lifecycle model (LCM) of consumption over a random horizon (a.k.a. the Yaari model) to a world in which (i.) the force of mortality obeys a diffusion process as opposed to being deterministic, and (ii.) a consumer can adapt their consumption strategy to new information about their mortality rate (a.k.a. health status) as it becomes available. In particular, we derive the optimal consumption rate and focus on the impact of mortality rate uncertainty vs. simple lifetime uncertainty -- assuming the actuarial survival curves are initially identical -- in the retirement phase where this risk plays a greater role. In addition to deriving and numerically solving the PDE for the optimal consumption rate, our main general result is that when utility preferences are logarithmic the initial consumption rates are identical. But, in a CRRA framework in which the coefficient of relative risk aversion is greater (smaller) than one, the consumption rate is higher (lower) and a stochastic force of mortality does make a difference. That said, numerical experiments indicate that even for non-logarithmic preferences, the stochastic mortality effect is relatively minor from the individual's perspective. Our results should be relevant to researchers interested in calibrating the lifecycle model as well as those who provide normative guidance (a.k.a. financial advice) to retirees.

q-fin.RM↗

arXiv2008

The lipid bilayer at the mesoscale: a physical continuum model

We study a continuum model of the lipid bilayer based on minimizing the free energy of a mixture of water and lipid molecules. This paper extends previous work by Blom & Peletier (2004) in the following ways. (a) It formulates a more physical model of the hydrophobic effect to facilitate connections with microscale simulations. (b) It clarifies the meaning of the model parameters. (c) It outlines a method for determining parameter values so that physically-realistic bilayer density profiles can be obtained, for example for use in macroscale simulations. Points (a)-(c) suggest that the model has potential to robustly connect some micro- and macroscale levels of multiscale blood flow simulations. The mathematical modelling in point (a) is based upon a consideration of the underlying physics of inter-molecular forces. The governing equations thus obtained are minimized by gradient flows via a novel numerical approach; this enables point (b). The numerical results are shown to behave physically in terms of the effect of background concentration, in contrast to the earlier model which is shown here to not display the expected behaviour. A "short-tail" approximation of the lipid molecules also gives an analytical tool which yields critical values of some parameters under certain conditions. Point (c) involves the first quantitative comparison of the numerical data with physical experimental results.

cond-mat.soft↗