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

Aquaporin-1 shifts the critical transmural pressure to compress the aortic intima and change transmural flow: theory and implications

Transmural-pressure (ΔP)-driven plasma advection carries macromolecules into the vessel wall, the earliest prelesion atherosclerotic event. The wall's hydraulic conductivity, LP, the water flux-to-ΔP ratio, is high at low pressures, rapidly decreases, and remains flat to high pressures (Baldwin AL, Wilson LM. Am J Physiol Heart Circ Physiol 264: H26–H32, 1993; Nguyen T, Toussaint, Xue JD, Raval Y, Cancel CB, Russell LM, Shou S, Sedes Y, Sun O, Yakobov Y, Tarbell JM, Jan KM, Rumschitzki DS. Am J Physiol Heart Circ Physiol 308: H1051–H1064, 2015; Tedgui A, Lever MJ. Am J Physiol Heart Circ Physiol. 247: H784–H791, 1984. Shou Y, Jan KM, Rumschitzki DS. Am J Physiol Heart Circ Physiol 291: H2758–H2771, 2006) due to pressure-induced subendothelial intima (SI) compression that causes endothelial cells to partially block internal elastic laminar fenestrae. Nguyen et al. showed that rat and bovine aortic endothelial cells express the membrane protein aquaporin-1 (AQP1) and transmural water transport is both transcellular and paracellular. They found that LP lowering by AQP1 blocking was perplexingly ΔP dependent. We hypothesize that AQP1 blocking lowers average SI pressure; therefore, a lower ΔP achieves the critical force/area on the endothelium to partially block fenestrae. To test this hypothesis, we improve the approximate model of Huang et al. (Huang Y, Rumschitzki D, Chien S, Weinbaum SS. Am J Physiol Heart Circ Physiol 272: H2023–H2039, 1997) and extend it by including transcellular AQP1 water flow. Results confirm the observation by Nguyen et al.: wall LP and water transport decrease with AQP1 disabling. The model predicts 1) low-pressure LP experiments correctly; 2) AQP1s contribute 30–40% to both the phenomenological endothelial + SI and intrinsic endothelial LP; 3) the force on the endothelium for partial SI decompression with functioning AQP1s at 60 mmHg equals that on the endothelium at ∼43 mmHg with inactive AQP1s; and 4) increasing endothelial AQP1 expression increases wall LP and shifts the ΔP regime where LP drops to significantly higher ΔP than in Huang et al. Thus AQP1 upregulation (elevated wall LP) might dilute and slow low-density lipoprotein binding to SI extracellular matrix, which may be beneficial for early atherogenesis.

Mitochondrial reactive oxygen species: which ROS signals cardioprotection?

Mitochondria are the major effectors of cardioprotection by procedures that open the mitochondrial ATP-sensitive potassium channel (mitoKATP), including ischemic and pharmacological preconditioning. MitoKATP opening leads to increased reactive oxygen species (ROS), which then activate a mitoKATP-associated PKCε, which phosphorylates mitoKATP and leaves it in a persistent open state (Costa AD, Garlid KD. Am J Physiol Heart Circ Physiol 295, H874–H882, 2008). The ROS responsible for this effect is not known. The present study focuses on superoxide (O2·−), hydrogen peroxide (H2O2), and hydroxyl radical (HO˙), each of which has been proposed as the signaling ROS. Feedback activation of mitoKATP provides an ideal setting for studying endogenous ROS signaling. Respiring rat heart mitochondria were preincubated with ATP and diazoxide, together with an agent being tested for interference with this process, either by scavenging ROS or by blocking ROS transformations. The mitochondria were then assayed to determine whether or not the persistent phosphorylated open state was achieved. Dimethylsulfoxide (DMSO), dimethylformamide (DMF), deferoxamine, Trolox, and bromoenol lactone each interfered with formation of the ROS-dependent open state. Catalase did not interfere with this step. We also found that DMF blocked cardioprotection by both ischemic preconditioning and diazoxide. The lack of a catalase effect and the inhibitory effects of agents acting downstream of HO˙ excludes H2O2 as the endogenous signaling ROS. Taken together, the results support the conclusion that the ROS message is carried by a downstream product of HO˙ and that it is probably a product of phospholipid oxidation.

Heart failure with preserved ejection fraction: chronic low-intensity interval exercise training preserves myocardial O2 balance and diastolic function

We have previously reported chronic low-intensity interval exercise training attenuates fibrosis, impaired cardiac mitochondrial function, and coronary vascular dysfunction in miniature swine with left ventricular (LV) hypertrophy (Emter CA, Baines CP. Am J Physiol Heart Circ Physiol 299: H1348–H1356, 2010; Emter CA, et al. Am J Physiol Heart Circ Physiol 301: H1687–H1694, 2011). The purpose of this study was to test two hypotheses: 1) chronic low-intensity interval training preserves normal myocardial oxygen supply/demand balance; and 2) training-dependent attenuation of LV fibrotic remodeling improves diastolic function in aortic-banded sedentary, exercise-trained (HF-TR), and control sedentary male Yucatan miniature swine displaying symptoms of heart failure with preserved ejection fraction. Pressure-volume loops, coronary blood flow, and two-dimensional speckle tracking ultrasound were utilized in vivo under conditions of increasing peripheral mean arterial pressure and β-adrenergic stimulation 6 mo postsurgery to evaluate cardiac function. Normal diastolic function in HF-TR animals was characterized by prevention of increased time constant of isovolumic relaxation, normal LV untwisting rate, and enhanced apical circumferential and radial strain rate. Reduced fibrosis, normal matrix metalloproteinase-2 and tissue inhibitors of metalloproteinase-4 mRNA expression, and increased collagen III isoform mRNA levels ( P < 0.05) accompanied improved diastolic function following chronic training. Exercise-dependent improvements in coronary blood flow for a given myocardial oxygen consumption ( P < 0.05) and cardiac efficiency (stroke work to myocardial oxygen consumption, P < 0.05) were associated with preserved contractile reserve. LV hypertrophy in HF-TR animals was associated with increased activation of Akt and preservation of activated JNK/SAPK. In conclusion, chronic low-intensity interval exercise training attenuates diastolic impairment by promoting compliant extracellular matrix fibrotic components and preserving extracellular matrix regulatory mechanisms, preserves myocardial oxygen balance, and promotes a physiological molecular hypertrophic signaling phenotype in a large animal model resembling heart failure with preserved ejection fraction.

E-wave deceleration time may not provide an accurate determination of LV chamber stiffness if LV relaxation/viscoelasticity is unknown

Average left ventricular (LV) chamber stiffness (ΔPavg/ΔVavg) is an important diastolic function index. An E-wave-based determination of ΔPavg/ΔVavg (Little WC, Ohno M, Kitzman DW, Thomas JD, Cheng CP. Circulation 92: 1933–1939, 1995) predicted that deceleration time (DT) determines stiffness as follows: ΔPavg/ΔVavg = N(π/DT)2 (where N is constant), which implies that if the DTs of two LVs are indistinguishable, their stiffness is indistinguishable as well. We observed that LVs with indistinguishable DTs may have markedly different ΔPavg/ΔVavg values determined by simultaneous echocardiography-catheterization. To elucidate the mechanism by which LVs with indistinguishable DTs manifest distinguishable chamber stiffness, we use a validated, kinematic E-wave model (Kovács SJ, Barzilai B, Perez JE. Am J Physiol Heart Circ Physiol 252: H178–H187, 1987) with stiffness ( k) and relaxation/viscoelasticity ( c) parameters. Because the predicted linear relation between k and ΔPavg/ΔVavg has been validated, we reexpress the DT-stiffness (ΔPavg/ΔVavg) relation of Little et al. as follows: DT k ≈ [Formula: see text]. Using the kinematic model, we derive the general DT-chamber stiffness/viscoelasticity relation as follows: DT k, c = [Formula: see text](where c and k are determined directly from the E-wave), which reduces to DT k when c ≪ k. Validation involved analysis of 400 E-waves by determination of five-beat averaged k and c from 80 subjects undergoing simultaneous echocardiography-catheterization. Clinical E-wave DTs were compared with model-predicted DT k and DT k, c. Clinical DT was better predicted by stiffness and relaxation/viscoelasticity ( r2 = 0.84, DT vs. DT k, c) jointly rather than by stiffness alone ( r2 = 0.60, DT vs. DT k). Thus LVs can have indistinguishable DTs but significantly different ΔPavg/ΔVavg if chamber relaxation/viscoelasticity differs. We conclude that DT is a function of both chamber stiffness and chamber relaxation viscoelasticity. Quantitative diastolic function assessment warrants consideration of simultaneous stiffness and relaxation/viscoelastic effects.

Macromolecular transport in heart valves. III. Experiment and theory for the size distribution of extracellular liposomes in hyperlipidemic rabbits

The heart valve leaflets of 29-day cholesterol-fed rabbits were examined by ultrarapid freezing without conventional chemical fixation/processing, followed by rotary shadow freeze-etching. This procedure images the leaflets' subendothelial extracellular matrix in extraordinary detail, and extracellular lipid liposomes, from 23 to 220 nm in diameter, clearly appear there. These liposomes are linked to matrix filaments and appear in clusters. Their size distribution shows 60.7% with diameters 23–69 nm, 31.7% between 70 and 119 nm, 7.3% between 120 and 169 nm, and 0.3% between 170 and 220 nm (superlarge) and suggests that smaller liposomes can fuse into larger ones. We couple our model from Part II of this series (Zeng Z, Yin Y, Jan KM, Rumschitzki DS. Am J Physiol Heart Circ Physiol 292: H2671–H2686, 2007) for lipid transport into the leaflet to the nucleation-polymerization model hierarchy for liposome formation proposed originally for aortic liposomes to predict liposome formation/growth in heart valves. Simulations show that the simplest such model cannot account for the observed size distribution. However, modifying this model by including liposome fusing/merging, using parameters determined from aortic liposomes, leads to predicted size distributions in excellent agreement with our valve data. Evolutions of both the liposome size distribution and total liposome mass suggest that fusing becomes significant only after 2 wk of high lumen cholesterol. Inclusion of phagocytosis by macrophages limits the otherwise monotonically increasing total liposome mass, while keeping the excellent fit of the liposome size distribution to the data.

Transport in rat vessel walls. I. Hydraulic conductivities of the aorta, pulmonary artery, and inferior vena cava with intact and denuded endothelia

In this study, filtration flows through the walls of the rat aorta, pulmonary artery (PA), and inferior vena cava (IVC), vessels with very different susceptibilities to atherosclerosis, were measured as a function of transmural pressure (ΔP), with intact and denuded endothelium on the same vessel. Aortic hydraulic conductivity ( Lp) is high at 60 mmHg, drops ∼40% by 100 mmHg, and is pressure independent to 140 mmHg. The trends are similar in the PA and IVC, dropping 42% from 10 to 40 mmHg and flat to 100 mmHg (PA) and dropping 33% from 10 to 20 mmHg and essentially flat to 60 mmHg (IVC). Removal of the endothelium renders Lp(ΔP) flat: it increases Lp of the aorta by ∼75%, doubles Lp of the PA, and quadruples Lp of the IVC. Specific resistance (1/ Lp) of the aortic endothelium is ∼47% of total resistance; i.e., the endothelium accounts for ∼47% of the ΔP drop at 100 mmHg. The PA value is 55% at >40 mmHg, and the IVC value is 23% at 10 mmHg. Lp of the intact aorta, PA, and IVC are order 10−8, 10−7, and 5 × 10−7 cm·s−1·mmHg−1, and wall thicknesses are 145.8 μm (SD 9.3), 78.9 μm (SD 3.3), and 66.1 μm (SD 4.1), respectively. These data are consistent with the different wall structures of the three vessels. The rat aortic Lp data are quantitatively consistent with rabbit Lp(ΔP) (Tedgui A and Lever MJ. Am J Physiol Heart Circ Physiol 247: H784–H791, 1984; Baldwin AL and Wilson LM. Am J Physiol Heart Circ Physiol 264: H26–H32, 1993), suggesting that intimal compression under pressure loading may also play a role in Lp(ΔP) in these other vessels. Despite very different driving ΔP, nominal transmural water fluxes of these three vessels are very similar and, therefore, cannot alone account for their differences in disease susceptibility. The different fates of macromolecular tracers convected by these water fluxes into the walls of these vessels may account for this difference.

The Role of Nitric Oxide in Regulation of Red Blood Cell Deformability.

Nitric Oxide (NO) has been suggested to modulate the deformability of red blood cells (RBCs). Bor-Kucukatay (Bor-Kucukatay et al. Am J Physiol Heart Circ Physiol284: H1577, 2003) found that cells incubated with 1 μM of the NO donor sodium nitroprusside lead to a small but significant increase RBC deformability as measured by ektacytometry. However, no significant effect was seen at lower or higher concentrations of sodium nitroprusside or for any concentration of another NO donor, diethylenetriamine NONOate. Kleinbongard (Kleinbongard et al. Blood10; 3992, 2005) found large increases in red cell deformability as a function of added arginine (the substrate for Nitric Oxide Synthase) by measuring the flow rate through filters. On the other hand, using cell aspiration techniques, Bateman (Bateman et al. Am J Physiol Heart Circ Physiol 280; H2848 H2001) found that NO production during sepsis causes a decrease in RBC deformability. Clearly more work is needed to determine the effects of NO on RBC deformability. The present work was undertaken to further investigate the effect of NO on normal and sickle RBC deformability. ProLi NONOate, arginine, and nitrite (which can be reduced to NO by hemoglobin (Hb), were incubated with blood at various concentrations over a period of 2 hours. Nitrosyl Hb and MetHb formed due to the interaction between NO and RBCs were quantified by electron paramagnetic resonance spectroscopy. The deformability was measured using a flow channel laser diffraction similar to ektacytometry (Huang et al. Am J Hematol67; 151, 2001, Biophys J85; 2374, 2003) with a stress range from 0 to 1,000 Pa. Diffraction patterns produced by deformed cells were analyzed by Matlab®. The deformability coefficients were compared to the control (n=6 per experiment condition). Our results suggested that ProLi NONOate did not significantly effect the deformability of normal RBCs. In a single case, ProLi NONOate improved the deformability of poorly deformable sickle red cells and this result is being studied further. Using our flow channel assay, we did not find any significant affects of arginine on RBC deformability. In addition, our studies involving nitrite, performed under both oxygenated and deoxygenated conditions, suggested that nitrite has no significant effect on RBC deformability. In summary, NO didn’t significantly affect the deformability of normal RBCs, and its potential effects on sickle RBCs needs to be further investigated.

Macromolecule permeability of in situ and excised rodent skeletal muscle arterioles and venules

In microvessels, acute inflammation is typified by an increase in leukocyte-endothelial cell interactions, culminating in leukocyte transmigration into the tissue, and increased permeability to water and solutes, resulting in tissue edema. The goal of this study was to establish a method to quantify solute permeability ( Ps) changes in microvessels in intact predominantly blood-perfused networks in which leukocyte transmigratory behavior could be precisely described using established paradigms. We used intravital confocal microscopy to measure solute (BSA) flux across microvessel walls, hence Ps. A quantitative fluorescence approach (Huxley VH, Curry FE, and Adamson RH. Am J Physiol Heart Circ Physiol 252: H188–H197, 1987) was adapted to the imaged confocal tissue slice in which the fluorescent source volume and source surface area of the microvessel were restricted to the region of vessel that was contained within the imaged confocal tissue section. Ps measurements were made in intact cremaster muscle microvasculature of anesthetized mice and compared with measurements of Ps made in isolated rat skeletal muscle microvessels. Mouse arteriolar Ps was 9.9 ± 1.1 × 10−7 cm/s ( n = 16), which was not different from 8.4 ± 1.3 × 10−7 cm/s ( n = 6) in rat arterioles. Values in venules were significantly ( P < 0.05) higher: 44.4 ± 7.9 × 10−7 cm/s ( n = 14) in mice and 25.0 ± 3.7 × 10−7 cm/s in rats. Convective coupling was estimated to contribute <10% to the measured Ps in both microvessel types and both animal models. We conclude that this approach provides an appropriate quantification of Ps in the intact microvasculature and that arteriolar Ps, while lower than in venules, is nevertheless consistent with arterioles being a significant source of interstitial protein.

Cilostazol improves endothelium-derived hyperpolarizing factor-type relaxation in mesenteric arteries from diabetic rats

We previously reported that in mesenteric arteries from streptozotocin (STZ)-induced diabetic rats that 1) endothelium-derived hyperpolarizing factor (EDHF)-type relaxation is impaired, possibly due to a reduced action of cAMP via increased phosphodiesterase 3 (PDE3) activity (Matsumoto T, Kobayashi T, and Kamata K. Am J Physiol Heart Circ Physiol 285: H283–H291, 2003) and that 2) PKA activity is decreased (Matsumoto T, Wakabayashi K, Kobayashi T, and Kamata K. Am J Physiol Heart Circ Physiol 287: H1064–H1071, 2004). Here we investigated whether chronic treatment with cilostazol, a PDE3 inhibitor, improves EDHF-type relaxation in mesenteric arteries isolated from STZ rats. We found that in such arteries 1) cilostazol treatment (2 wk) improved ACh-, A-23187-, and cyclopiazonic acid-induced EDHF-type relaxations; 2) the ACh-induced cAMP accumulation was transient and sustained in arteries from cilostazol-treated STZ rats; 3) the EDHF-type relaxation was significantly decreased by a PKA inhibitor in the cilostazol-treated group, but not in the cilostazol-untreated group; 4) cilostazol treatment improved both the relaxations induced by cAMP analogs and the PKA activity level; and 5) PKA catalytic subunit (Cat-α) protein was significantly decreased, but the regulatory subunit RII-β was increased (and the latter effect was significantly decreased by cilostazol treatment). These results strongly suggest that cilostazol improves EDHF-type relaxations in STZ rats via an increase in cAMP and PKA signaling.