Pre-atherosclerotic flow and oncotically active solute transport across the arterial endothelium.

Atherosclerosis starts with transmural (transwall) pressure-driven advective transport of blood-borne low-density lipoprotein (LDL) cholesterol across rare endothelial cell (EC) monolayer leaks into the arterial subendothelial intima (SI) wall layer where they can spread, bind to extracellular matrix and seed lesions. The local SI LDL concentration, which governs LDL's binding kinetics, depends on the overall diluting transmural liquid flow. Transmural pressures typically compress the SI at physiological pressures, which keeps this flow low. Nguyen et al. (2015) showed that aortic ECs express the water channel protein aquaporin-1 (AQP1) and the transEC (δP) portion of the transmural (ΔP) pressure difference drives, in parallel, water across AQP1s and plasma across interEC junctions. Since the lumen is isotonic, selective AQP1-mediated water flow should quickly render the ECs' lumen side hypertonic and the SI hypotonic; resulting transEC oncotic pressure differences, δπ, should oppose δP and quickly halt transEC flow. Yet Nguyen et al.'s (2015) transAQP1 flows persist for hours. To resolve this paradox, we extend our fluid filtration theory Joshi et al. (2015) to include mass transfer for oncotically active solutes like albumin. This addition nonlinearly couples mass transfer, fluid flow and wall mechanics. We simultaneously solve these problems at steady state. Surprisingly it finds that media layer filtration causes steady SI to exceed EC glycocalyx albumin concentration. Thus δπ reinforces rather than opposes δP, i.e., it sucks water from, rather than pushing water into the lumen from the SI. Endothelial AQP1s raise the overall driving force for flow across the EC above δP, most significantly at pressures too low to compress the SI, and they increase the ΔP needed for SI compression. This suggests the intriguing possibility that increasing EC AQP1 expression can raise this requisite compression pressure to physiological values. That is, increasing EC AQP1 may decompress the SI at physiological pressures, which would significantly increase SI thickness, flow and subsequently SI LDL dilution. This could retard LDL binding and delay preatherosclerotic lesion onset. The model also predicts that glycocalyx-degrading enzymes decrease overall transEC driving forces and thus lower, not raise, transmural water flux.

Chronic hypertension increases aortic endothelial hydraulic conductivity by upregulating endothelial aquaporin-1 expression.

Numerous studies have examined the role of aquaporins in osmotic water transport in various systems, but virtually none have focused on the role of aquaporin in hydrostatically driven water transport involving mammalian cells save for our laboratory's recent study of aortic endothelial cells. Here, we investigated aquaporin-1 expression and function in the aortic endothelium in two high-renin rat models of hypertension, the spontaneously hypertensive genetically altered Wistar-Kyoto rat variant and Sprague-Dawley rats made hypertensive by two-kidney, one-clip Goldblatt surgery. We measured aquaporin-1 expression in aortic endothelial cells from whole rat aortas by quantitative immunohistochemistry and function by measuring the pressure-driven hydraulic conductivities of excised rat aortas with both intact and denuded endothelia on the same vessel. We used them to calculate the effective intimal hydraulic conductivity, which is a combination of endothelial and subendothelial components. We observed well-correlated enhancements in aquaporin-1 expression and function in both hypertensive rat models as well as in aortas from normotensive rats whose expression was upregulated by 2 h of forskolin treatment. Upregulated aquaporin-1 expression and function may be a response to hypertension that critically determines conduit artery vessel wall viability and long-term susceptibility to atherosclerosis.NEW & NOTEWORTHY The aortic endothelia of two high-renin hypertensive rat models express greater than two times the aquaporin-1 and, at low pressures, have greater than two times the endothelial hydraulic conductivity of normotensive rats. Data are consistent with theory predicting that higher endothelial aquaporin-1 expression raises the critical pressure for subendothelial intima compression and for artery wall hydraulic conductivity to drop.

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.

Aquaporin-1 facilitates pressure-driven water flow across the aortic endothelium.

Aquaporin-1, a ubiquitous water channel membrane protein, is a major contributor to cell membrane osmotic water permeability. Arteries are the physiological system where hydrostatic dominates osmotic pressure differences. In the present study, we show that the walls of large conduit arteries constitute the first example where hydrostatic pressure drives aquaporin-1-mediated transcellular/transendothelial flow. We studied cultured aortic endothelial cell monolayers and excised whole aortas of male Sprague-Dawley rats with intact and inhibited aquaporin-1 activity and with normal and knocked down aquaporin-1 expression. We subjected these systems to transmural hydrostatic pressure differences at zero osmotic pressure differences. Impaired aquaporin-1 endothelia consistently showed reduced engineering flow metrics (transendothelial water flux and hydraulic conductivity). In vitro experiments with tracers that only cross the endothelium paracellularly showed that changes in junctional transport cannot explain these reductions. Percent reductions in whole aortic wall hydraulic conductivity with either chemical blocking or knockdown of aquaporin-1 differed at low and high transmural pressures. This observation highlights how aquaporin-1 expression likely directly influences aortic wall mechanics by changing the critical transmural pressure at which its sparse subendothelial intima compresses. Such compression increases transwall flow resistance. Our endothelial and historic erythrocyte membrane aquaporin density estimates were consistent. In conclusion, aquaporin-1 significantly contributes to hydrostatic pressure-driven water transport across aortic endothelial monolayers, both in culture and in whole rat aortas. This transport, and parallel junctional flow, can dilute solutes that entered the wall paracellularly or through endothelial monolayer disruptions. Lower atherogenic precursor solute concentrations may slow their intimal entrainment kinetics.

A theory for water and macromolecular transport in the pulmonary artery wall with a detailed comparison to the aorta.

The pulmonary artery (PA) wall, which has much higher hydraulic conductivity and albumin void space and approximately one-sixth the normal transmural pressure of systemic arteries (e.g, aorta, carotid arteries), is rarely atherosclerotic, except under pulmonary hypertension. This study constructs a detailed, two-dimensional, wall-structure-based filtration and macromolecular transport model for the PA to investigate differences in prelesion transport processes between the disease-susceptible aorta and the relatively resistant PA. The PA and aorta models are similar in wall structure, but very different in parameter values, many of which have been measured (and therefore modified) since the original aorta model of Huang et al. (23). Both PA and aortic model simulations fit experimental data on transwall LDL concentration profiles and on the growth of isolated endothelial (horseradish peroxidase) tracer spots with circulation time very well. They reveal that lipid entering the aorta attains a much higher intima than media concentration but distributes better between these regions in the PA than aorta and that tracer in both regions contributes to observed tracer spots. Solutions show why both the overall transmural water flow and spot growth rates are similar in these vessels despite very different material transport parameters. Since early lipid accumulation occurs in the subendothelial intima and since (matrix binding) reaction kinetics depend on reactant concentrations, the lower intima lipid concentrations in the PA vs. aorta likely lead to slower accumulation of bound lipid in the PA. These findings may be relevant to understanding the different atherosusceptibilities of these vessels.

Representation of time-varying nonlinear systems with time-varying principal dynamic modes.

System identification of nonlinear time-varying (TV) systems has been a daunting task, as the number of parameters required for accurate identification is often larger than the number of data points available, and scales with the number of data points. Further, a 3-D graphical representation of TV second-order nonlinear dynamics without resorting to taking slices along one of the four axes has been a significant challenge to date. In this paper, we present a TV principal dynamic mode (TVPDM) method which overcomes these deficiencies. The TVPDM, by design, reduces one dimension, and by projecting PDM coefficients onto a set of basis functions, both nonstationary and nonlinear dynamics can be characterized. Another significant advantage of the TVPDM is its ability to discriminate the signal from noise dynamics, and provided that signal dynamics are orthogonal to each other, it has the capability to separate them. The efficacy of the proposed method is demonstrated with computer simulation examples comprised of various forms of nonstationarity and nonlinearity. The application of the TVPDM to the human heart rate and arterial blood pressure data during different postures is also presented and the results reveal significant nonstationarity even for short-term data recordings. The newly developed method has the potential to be a very useful tool for characterizing nonlinear TV systems, which has been a significant, challenging problem to date.

Autonomic nervous nonlinear interactions lead to frequency modulation between low- and high-frequency bands of the heart rate variability spectrum.

Cardiac sympathetic and parasympathetic neural activities have been found to interact with each other to efficiently regulate the heart rate and maintain homeostasis. Quantitative and noninvasive methods used to detect the presence of interactions have been lacking, however. This may be because interactions among autonomic nervous systems are nonlinear and nonstationary. The goal of this work was to identify nonlinear interactions between the sympathetic and parasympathetic nervous systems in the form of frequency and amplitude modulations in human heart rate data. To this end, wavelet analysis was performed, followed by frequency analysis of the resultant wavelet decomposed signals in several frequency brackets defined as very low frequency (f < 0.04 Hz), low frequency (LF; 0.04-0.15 Hz), and high frequency (HF; 0.15-0.4 Hz). Our analysis suggests that the HF band is significantly modulated by the LF band in the heart rate data obtained in both supine and upright body positions. The strength of modulations is stronger in the upright than supine position, which is consistent with elevated sympathetic nervous activities in the upright position. Furthermore, significantly stronger frequency modulation than in the control condition was also observed with the cold pressor test. The results with the cold pressor test, as well as the body position experiments, further demonstrate that the frequency modulation between LF and HF is most likely due to sympathetic and parasympathetic nervous interactions during sympathetic activations. The modulation phenomenon suggests that the parasympathetic nervous system is frequency modulated by the sympathetic nervous system. In this study, there was no evidence of amplitude modulation among these frequencies.

Macromolecular transport in heart valves. I. Studies of rat valves with horseradish peroxidase.

The present study aims to experimentally elucidate subtle structural features of the rat valve leaflet and the related nature of macromolecular transport across its endothelium and in its subendothelial space, information necessary to construct a rational theoretical model that can explain observation. After intravenous injection of horseradish peroxidase (HRP), we perfusion-fixed the aortic valve of normal Sprague-Dawley rats and found under light microscopy that HRP leaked through the leaflet's endothelium at very few localized brown spots, rather than uniformly. These spots grew nearly as rapidly with HRP circulation time before euthanasia as aortic spots, particularly when the time axis only included the time the valve was closed. These results suggest that macromolecular transport in heart valves depends not only on the direction normal to, but also parallel to, the endothelial surface and that convection, as well as molecular diffusion, plays an important role in macromolecular transport in heart valves. Transmission electron microscopy of traverse leaflet sections after 4-min HRP circulation showed a very thin ( approximately 150 nm), sparse layer immediately beneath the endothelium where the HRP concentration was much higher than that in the matrix below it. Nievelstein-Post et al.'s (Nievelstein-Post P, Mottino G, Fogelman A, Frank J. Arterioscler Thromb 14: 1151-1161, 1994) ultrarapid freezing/rotary shadow etching of the normal rabbit valve's subendothelial space supports the existence of this very thin, very sparse "valvular subendothelial intima," in analogy to the vascular subendothelial intima.

Transport in rat vessel walls. II. Macromolecular leakage and focal spot size growth in rat arteries and veins.

Transendothelial lipid transport into and spread in the subendothelial intima of large arteries, and subsequent lipid accumulation, appear to start plaque formation. We experimentally examine transendothelial horseradish peroxidase (HRP) transport in vessels that are usually, e.g., pulmonary artery (PA), or almost always, e.g., inferior vena cava (IVC), atherosclerosis resistant vs. disease prone, e.g., aorta, vessels. In these vessels, HRP traverses the endothelium at isolated, focal spots, rather than uniformly, for short circulation times. For femoral vein HRP introduction, PA spots have 30-s radii [ approximately 53.2 microm (SD 10.4); compare aorta: 54.6 microm (SD 8.75)] and grow quickly from 30 s to 1 min (40%, P<0.05) and more slowly afterward (P>0.05). This trend resembles the aorta, suggesting the PA has a similarly sparse intima. With carotid artery (CA) HRP introduction, the 30-s spot (132.86 +/- 37.32 microm) is far larger than the PAs, grows little ( approximately 28%, P<0.05) from 30 to 60 s, and is much flatter than the artery curves. Transverse electron microscopic sections after approximately 10 min HRP circulation show thin, intense staining immediately beneath both vessels' endothelia with an almost step change to diffuse staining beyond. This indicates the existence of a sparse, subendothelial intima, even when there is no internal elastic lamina (IVC). This motivates a simple model that translates growth rates into lower bounds for the flow through focal leaks. The model results and our earlier wall and medial hydraulic conductivity data explain these spot growth curves and point to differences in transport patterns that might be relevant in understanding the immunity of IVC to disease initiation.

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.

Macromolecular transport in heart valves. II. Theoretical models.

This paper proposes a new, two-dimensional convection-diffusion model for macromolecular transport in heart valves based on horseradish peroxidase (HRP) experiments on rats presented in the first of the papers in this series (Part I; Zeng Z, Yin Y, Huang AL, Jan KM, Rumschitzki DS. Am J Physiol Heart Circ Physiol 292: H2664-H2670, 2007). Experiments require two valvular intimae, one underneath each endothelium. Tompkins et al. (Tompkins RG, Schnitzer JJ, Yarmush ML. Circ Res 64: 1213-1223, 1989) found large variations in shape and magnitude in transvalvular (125)I-labeled low-density lipoprotein (LDL) profiles from identical experiments on four squirrel monkeys. Their one-dimensional, uniform-medium diffusion-only model fit three parameters independently for each profile; data variability resulted in large parameter spreads. Our theory aims to explain their data with one parameter set. It uses measured parameters and some aortic values but fits the endothelial mass transfer coefficient (k(a)=k(v)=1.63 x 10(-8) cm/s, where subscripts a and v indicate aortic aspect and ventricular aspect, respectively) and middle layer permeability (K(p(2))=2.28 x 10(-16)cm(2)) and LDL diffusion coefficient [D(2)(LDL)=5.93 x 10(-9) cm(2)/s], using one of Tompkins et al.'s profiles, and fixes them throughout. It accurately predicts Part I's rapid localized HRP leakage spot growth rate in rat leaflets that results from the intima's much sparser structure, dictating its far larger transport parameters [K(p(1))= 1.10 x 10(-12)cm(2), D(1)(LDL/HRP)=1.02/4.09 x 10(-7)cm(2)/s] than the middle layer. This contrasts with large arteries with similarly large HRP spots, since the valve has no internal elastic lamina. The model quantitatively explains all of Tompkins et al.'s monkey profiles with these same parameters. Different numbers and locations of isolated macromolecular leaks on both aspects and different section-leak(s) distances yield all profiles.

Frequency modulation between low- and high-frequency components of the heart rate variability spectrum.

Interactions among physiological mechanisms are abundant in biomedical signals, and they may exist to maintain efficient homeostasis. For example, sympathetic and parasympathetic neural activities interact to either elevate or depress the heart rate to maintain homeostasis. There has been considerable effort devoted to developing algorithms that can detect interactions between various physiological mechanisms. However, methods used to detect the presence of interactions between the sympathetic and parasympathetic nervous systems, to take one example, have had limited success. This may be because interactions in physiological systems are non-linear and non-stationary. The goal of this work was to identify non-linear interactions between the sympathetic and parasympathetic nervous systems in the form of frequency and amplitude modulations in human heart-rate data (n=6). To this end, wavelet analysis was performed, followed by frequency analysis of the resultant wavelet decomposed signals in several frequency brackets we define as: very low frequency (f<0.04 Hz), low frequency (0.04-0.15 Hz) and high frequency (0.15-0.4 Hz). Our analysis suggests that the high-frequency bracket is modulated by the low-frequency bracket in the heart rate data obtained in both upright and sitting positions. However, there was no evidence of amplitude modulation among these frequencies.

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 (DeltaP), with intact and denuded endothelium on the same vessel. Aortic hydraulic conductivity (L(p)) is high at 60 mmHg, drops approximately 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 L(p)(DeltaP) flat: it increases L(p) of the aorta by approximately 75%, doubles L(p) of the PA, and quadruples L(p) of the IVC. Specific resistance (1/L(p)) of the aortic endothelium is approximately 47% of total resistance; i.e., the endothelium accounts for approximately 47% of the DeltaP drop at 100 mmHg. The PA value is 55% at >40 mmHg, and the IVC value is 23% at 10 mmHg. L(p) of the intact aorta, PA, and IVC are order 10(-8), 10(-7), and 5 x 10(-7) cm.s(-1).mmHg(-1), and wall thicknesses are 145.8 microm (SD 9.3), 78.9 microm (SD 3.3), and 66.1 microm (SD 4.1), respectively. These data are consistent with the different wall structures of the three vessels. The rat aortic L(p) data are quantitatively consistent with rabbit L(p)(DeltaP) (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 L(p)(DeltaP) in these other vessels. Despite very different driving DeltaP, 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.

Quantifying cardiac sympathetic and parasympathetic nervous activities using principal dynamic modes analysis of heart rate variability.

The ratio between low-frequency (LF) and high-frequency (HF) spectral power of heart rate has been used as an approximate index for determining the autonomic nervous system (ANS) balance. An accurate assessment of the ANS balance can only be achieved if clear separation of the dynamics of the sympathetic and parasympathetic nervous activities can be obtained, which is a daunting task because they are nonlinear and have overlapping dynamics. In this study, a promising nonlinear method, termed the principal dynamic mode (PDM) method, is used to separate dynamic components of the sympathetic and parasympathetic nervous activities on the basis of ECG signal, and the results are compared with the power spectral approach to assessing the ANS balance. The PDM analysis based on the 28 subjects consistently resulted in a clear separation of the two nervous systems, which have similar frequency characteristics for parasympathetic and sympathetic activities as those reported in the literature. With the application of atropine, in 13 of 15 supine subjects there was an increase in the sympathetic-to-parasympathetic ratio (SPR) due to a greater decrease of parasympathetic than sympathetic activity (P=0.003), and all 13 subjects in the upright position had a decrease in SPR due to a greater decrease of sympathetic than parasympathetic activity (P<0.001) with the application of propranolol. The LF-to-HF ratio calculated by the power spectral density is less accurate than the PDM because it is not able to separate the dynamics of the parasympathetic and sympathetic nervous systems. The culprit is equivalent decreases in both the sympathetic and parasympathetic activities irrespective of the pharmacological blockades. These findings suggest that the PDM shows promise as a noninvasive and quantitative marker of ANS imbalance, which has been shown to be a factor in many cardiac and stress-related diseases.

Frequency modulation between low- and high-frequency components of the heart rate variability spectrum may indicate sympathetic-parasympathetic nonlinear interactions.

Interactions among physiological mechanisms are abundant in biomedical signals, and they may exist to maintain efficient homeostasis. For example, sympathetic and parasympathetic neural activities interact to either elevate or depress the heart rate, to maintain homeostasis. There has been considerable effort devoted to developing algorithms that can detect interactions between various physiological mechanisms. However, methods used to detect the presence of interactions between the sympathetic and parasympathetic nervous systems, to take one example, have had limited success. This may be because interactions in physiological systems are nonlinear and nonstationary. The goal of this work was to identify nonlinear interactions between the sympathetic and parasympathetic nervous systems in the form of frequency and amplitude modulations in human heart rate data. To this end, wavelet analysis was performed, followed by frequency analysis of the resultant wavelet decomposed signals in several frequency brackets we define as: very low frequency (f<0.04 Hz), low frequency (0.04-0.15 Hz) and high frequency (0.15-0.4 Hz). Our analysis suggests that the HF bracket is significantly modulated by the LF bracket in the heart rate data obtained in both supine and upright body positions. Furthermore, the strength of modulations is stronger in the upright than supine position, which is consistent with elevated sympathetic nervous activities in the upright position. However, there was no evidence of amplitude modulation among these frequencies.

Nonlinear analysis of the separate contributions of autonomic nervous systems to heart rate variability using principal dynamic modes.

This paper introduces a modified principal dynamic modes (PDM) method, which is able to separate the dynamics of sympathetic and parasympathetic nervous activities. The PDM is based on the principle that among all possible choices of expansion bases, there are some that require the minimum number of basis functions to achieve a given mean-square approximation of the system output. Such a minimum set of basis functions is termed PDMs of the nonlinear system. We found that the first two dominant PDMs have similar frequency characteristics for parasympathetic and sympathetic activities, as reported in the literature. These results are consistent for all nine of our healthy human subjects using our modified PDM approach. Validation of the purported separation of parasympathetic and sympathetic activities was performed by the application of the autonomic nervous system blocking drugs atropine and propranolol. With separate applications of the respective drugs, we found a significant decrease in the amplitude of the waveforms that correspond to each nervous activity. Furthermore, we observed near complete elimination of these dynamics when both drugs were given to the subjects. Comparison of our method to the conventional low-frequency/high-frequency ratio shows that our proposed approach provides more accurate assessment of the autonomic nervous balance. Our nonlinear PDM approach allows a clear separation of the two autonomic nervous activities, the lack of which has been the main reason why heart rate variability analysis has not had wide clinical acceptance.

Protective effects of dietary potassium chloride on hemodynamics of Dahl salt-sensitive rats in response to chronic administration of sodium chloride.

BACKGROUND: Dietary potassium supplementation decreases blood pressure and prevents strokes in humans, and prevents strokes and renal damage in Dahl salt-sensitive (DSS) rats. OBJECTIVE: To study the effects of various concentrations of dietary potassium chloride (KCl) on the hemodynamics of Dahl salt-resistant (DSR) and DSS rats receiving a 1% sodium chloride (NaCl) diet for 8 months, to determine whether there is an optimal dietary concentration of KCl that minimizes increases in blood pressure and causes least impairment of blood flow in the brain and kidneys. METHODS AND RESULTS: We found a biphasic effect on hemodynamic parameters as a function of dietary KCl in DSS rats of the Rapp strain fed 1% NaCl with increasing dietary KCl (0.7, 2.6, 4 and 8%). After 8 months receiving a diet containing 1% NaCl and 0.7% KCl, DSS rats had mean arterial pressures (MAP), plasma volumes, cardiac outputs and renal and cerebral vascular resistances that were significantly increased compared with those of DSR rats receiving the same diet. With a 2.6% KCl diet, all these parameters were significantly reduced compared with those in DSS rats fed the 0.7% KCl diet and were similar to those in DSR rats fed 2.6% KCl. Total peripheral resistance in DSR and DSS rats was similar on all diets. When KCl was increased to 4 and 8%, MAP, plasma volume, cardiac output and renal vascular resistance progressively increased in DSR and DSS rats, without changing total peripheral resistance. These changes paralleled increases in plasma aldosterone, which resulted from adrenocortical stimulation by the increasing dietary KCl; however, cerebral vascular resistance of DSR and DSS rats decreased significantly with a 4% KCl diet, despite increased aldosterone and sodium retention. Only DSS rats fed a 2.6% KCl diet had hemodynamics similar to those of DSR control rats fed the same diet, and hyperaldosteronism, sodium retention and increased plasma volume did not occur. CONCLUSION: 'Optimal' dietary KCl (2.6%) prevents hypertension and preserves cerebral and renal hemodynamics in DSS rats fed a diet containing 1% NaCl for 8 months, which causes hypertension when dietary KCl is limited or excessive.

Off-pump right atrial thrombectomy for heparin-induced thrombocytopenia with thrombosis.

This report describes a 72-year-old woman with atrial fibrillation who presented with lower extremity ischemia secondary to thromboembolism. After lower extremity thrombectomy, the patient developed heparin-induced thrombocytopenia with thrombosis (HITT). Her postoperative course was complicated by recurrent supraventricular and ventricular tachycardia, secondary to a mobile thrombus in the right atrium extending into the right ventricle. Because administration of heparin was contraindicated, the patient underwent off-pump right atrial thrombectomy during a brief period of inflow occlusion. Postoperatively, she was placed on lepirudin. Her platelet count normalized without any further thrombotic episodes, and she was discharged on warfarin.