Modelling of hydrogen diffusion in the retina

A simple mathematical model for diffusion of hydrogen within the retina has been developed. The model consists of three, well-mixed, one dimensional layers that exchange hydrogen via a diffusion process. A Fourier series method is applied to compute the hydrogen concentration. The effect of important parameters is examined and discussed. The results may contribute to an understanding of the hydrogen clearance technique to estimate blood flow. A two dimensional numerical method for the hydrogen diffusion is also presented. It is shown that the predominant features of the process are captured quite well by the simpler model. References V. A. Alder, D. Y. Yu, S. J. Cringle and E. N. Su. Experimental approaches to diabetic retinopathy. Asia-Pac. J. Ophthalmol. 4:20–25, 1992. J. C. Arciero, P. Causin and F. Malgoroli. Mathematical methods for modeling the microcirculation. AIMS Biophys. 4:362–399, 2017. doi:10.3934/biophy.2017.3.362 D. E. Farrow, G. C. Hocking, S. J. Cringle and D.-Y. Yu. Modeling Hydrogen clearance from the retina. ANZIAM J. 59:281–292, 2018. doi:10.1017/S1446181117000426 A. B. Friedland. A mathematical model of transmural transport of oxygen to the retina. Bull. Math. Biol. 40:823–837, 2018; doi:10.1007/BF02460609 D. Goldman. Theoretical models of microvascular oxygen transport to tissue. Microcirculation 15:795–811, 2008. doi:10.1080/10739680801938289 A. C. Hindmarsh. ODEPACK, A Systematized Collection of ODE Solvers. In Scientific Computing, R. S. Stepleman, et al., Eds., pp. 55-64. North-Holland, Amsterdam, 1983. S. S. Kety. The theory and applications of the exchange of inert gas at the lungs and tissues. Pharmacol. Rev. 3:1–41, 1951. http://pharmrev.aspetjournals.org/content/3/1/1 B. P. Leonard. A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comput. Methods Appl. Mech. Eng. 19:59–98, 1979. doi:10.1016/0045-7825(79) 90034-3 S. L. Mitchell. Coupling transport and chemistry: numerics, analysis and applications. PhD thesis, University of Bath, UK, 2003. https://researchportal.bath.ac.uk/en/studentTheses/coupling-transport-and-chemistry-numerics-analysis-and-applicatio G. A. Winchell. Mathematical model of inert gas washout from the retina: evaluation of hydrogen washout as a means of determining retinal blood flow in the cat. Master\textquoteright s Thesis, Northwestern University, Evanston, USA, 1983. https://search.library.northwestern.edu/permalink/f/5c25nc/01NWU_ALMA21563278530002441 D. Y. Yu, V. A. Alder and S. J. Cringle. Measurement of blood flow in rat eyes by hydrogen clearance. Am. J. Physiol. (Heart Circ. Physiol.) 261:H960–H968, 1991. doi:10.1152/ajpheart.1991.261.3.H960 D. Y. Yu, S. J. Cringle, V. A. Alder, E. N. Su, and P. K. Yu, Intraretinal oxygen distribution and choroidal regulation in the avascular retina of guinea pigs. Am. J. Physiol. (Heart Circ. Physiol.) 270:H965-H973, 1996. doi:10.1152/ajpheart.1996.270.3.H965 S. Cringle, D.-Y. Yu, V. Alder, E.-N. Su, and P. Yu. Choroidal regulation of oxygen supply to the guinea pig retina. In A. G. Hudetz, and D. F. Bruley (Eds.), Oxygen Transport to Tissue XX, pp. 385–389. Springer, 1998. doi:10.1007/978-1-4615-4863-8

MODELLING HYDROGEN CLEARANCE FROM THE RETINA

The human retina is supplied by two vascular systems: the highly vascular choroidal, situated behind the retina; and the retinal, which is dependent on the restriction that the light path must be minimally disrupted. Between these two circulations, the avascular retinal layers depend on diffusion of metabolites through the tissue. Oxygen supply to these layers may be threatened by diseases affecting microvasculature, for example diabetes and hypertension, which may ultimately cause loss of sight.An accurate model of retinal blood flow will therefore facilitate the study of retinal oxygen supply and, hence, the complications caused by systemic vascular disease. Here, two simple models of the blood flow and exchange of hydrogen with the retina are presented and compared qualitatively with data obtained from experimental measurements. The models capture some interesting features of the exchange and highlight effects that will need to be considered in a more sophisticated model and in the interpretation of experimental results.

Effect of hypertension and peroxynitrite decomposition with FeTMPyP on CBF and stroke outcome

We investigated the effect of peroxynitrite decomposition catalyst FeTMPyP treatment on perfusion deficit, vascular function and stroke outcome in Wistar ( n = 26) and spontaneously hypertensive rats stroke-prone (SHRSP; n = 26) that underwent tMCAO for 2 h or Sham operation. Peri-infarct CBF was measured by hydrogen clearance in the absence or presence of FeTMPyP (10 mg/kg, i.v.) or vehicle 10 min before reperfusion. Myogenic tone of parenchymal arterioles (PAs) was measured as an indication of small vessel resistance (SVR). Baseline CBF was similar between Wistar and SHRSP (114 ± 12 vs. 132 ± 9 mL/100 g/min); however, MCAO caused greater perfusion deficit in SHRSP (24 ± 6 vs. 7 ± 1 mL/100 g/min; p < 0.05) and increased infarct volume by TTC (12 ± 6 vs. 32 ± 2%; p < 0.05). Reperfusion CBF was decreased from baseline in both SHRSP and Wistar (54 ± 16 and 46 ± 19 mL/100 g/min; p < 0.05), suggesting increased infarction in SHRSP was related to greater perfusion deficit. PAs from SHRSP had increased tone vs. Wistar that was enhanced after tMCAO. FeTMPyP treatment did not affect CBF during ischemia or reperfusion, or tone of PAs, but decreased the incidence of hemorrhage in SHRSP by 50%. Thus, increased tone in PAs from SHRSP could increase perfusion deficit during MCAO that was not alleviated by FeTMPyP.

Optical coherence tomography for the quantitative study of cerebrovascular physiology

Doppler optical coherence tomography (DOCT) and OCT angiography are novel methods to investigate cerebrovascular physiology. In the rodent cortex, DOCT flow displays features characteristic of cerebral blood flow, including conservation along nonbranching vascular segments and at branch points. Moreover, DOCT flow values correlate with hydrogen clearance flow values when both are measured simultaneously. These data validate DOCT as a noninvasive quantitative method to measure tissue perfusion over a physiologic range.