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Statistical physics and physiology: monofractal and multifractal approaches.

Even under healthy, basal conditions, physiologic systems show erratic fluctuations resembling those found in dynamical systems driven away from a single equilibrium state. Do such "nonequilibrium" fluctuations simply reflect the fact that physiologic systems are being constantly perturbed by external and intrinsic noise? Or, do these fluctuations actually, contain useful, "hidden" information about the underlying nonequilibrium control mechanisms? We report some recent attempts to understand the dynamics of complex physiologic fluctuations by adapting and extending concepts and methods developed very recently in statistical physics. Specifically, we focus on interbeat interval variability as an important quantity to help elucidate possibly non-homeostatic physiologic variability because (i) the heart rate is under direct neuroautonomic control, (ii) interbeat interval variability is readily measured by noninvasive means, and (iii) analysis of these heart rate dynamics may provide important practical diagnostic and prognostic information not obtainable with current approaches. The analytic tools we discuss may be used on a wider range of physiologic signals. We first review recent progress using two analysis methods--detrended fluctuation analysis and wavelets--sufficient for quantifying monofractual structures. We then describe recent work that quantifies multifractal features of interbeat interval series, and the discovery that the multifractal structure of healthy subjects is different than that of diseased subjects.

Biophysical Phenomena↗

Localization of ischemia in canine hearts using tagged rotated long axis MR images, endocardial surface stretch and wall thickening.

Tagged magnetic resonance imaging allows the noninvasive measurement of regional systolic myocardial deformations and helps localize ischemic regions in the left ventricle (LV). The objective of this study was to evaluate the potential accuracy of localizing ischemic regions in the LV using endocardial and epicardial data obtained from tagged rotated long axis images. Nine canine hearts with acute ischemia induced by coronary artery ligation were imaged along four long axis planes rotated around the LV long axis, at end diastole and end systole. Each plane was tagged by four parallel lines perpendicular to the LV long axis. Tracing the endocardial and epicardial intersection points of the tag lines, 24 myocardial cuboids were reconstructed for each LV at end diastole and end systole. Endocardial surface stretch and transmural systolic thickening were calculated for each cuboid. The functional data were compared to perfusion data obtained from postmortem monastral blue staining of the heart. The ability of each functional index to discriminate between ischemic and non-ischemic regions was assessed using the "t"-statistic. The potential accuracy in localizing ischemia was evaluated by studying the corresponding sensitivity-specificity curves. The results demonstrate that adequate discrimination and localization can be obtained with both functional indices. However, endocardial surface stretch is advantageous as it uses only endocardial data and can save 50% of the post-processing time.

Animals↗

Modeling of diastole.

Modeling methods have been employed to further characterize the physical and physiologic processes of filling and diastolic function. They have led to more detailed understanding of the effect of alteration of physiologic parameters on the Doppler E-wave contour as well as pulmonary vein flow. Depending on the modeling approach, different aspects of the filling process have been considered from AV gradient and net compliance to atrial appendage function to the mechanical suction pump attribute of the heart. The models have been applied for further characterization of diastolic function and elucidation of novel basic physiologic relations. We trust that readers recognize that this article could not serve as a comprehensive and global review of the state-of-the-art in physiologic modeling, but rather as a selective overview, with emphasis on the main modeling principles and options currently in use. Modeling of systems physiology, especially as it relates to the function of the four-chamber heart, remains a fertile area of investigation. Future progress is likely to have profound influence on (noninvasive) diagnosis and quantitation of the effect of therapy and lead to continued discovery of "new" (macroscopic, cellular, and molecular biologic) physiology.

Animals↗

Application of Doppler color flow imaging to determine valve area in mitral stenosis.

This study was undertaken to examine whether Doppler color flow imaging could accurately estimate the valve area in mitral stenosis. Doppler color flow assessments were performed in both an in vitro model and in 30 patients with mitral stenosis undergoing cardiac catheterization. In the experimental Doppler study using a circuit model, color jet width correlated well with actual orifice diameter (r = 0.99). In the clinical Doppler study, the mitral valve orifice was assumed to be elliptic and the mitral valve area was calculated from the following equation: (pi/4) (a x b), where a = color jet width at the mitral valve orifice in the apical long-axis view (short diameter) and b = the width in the 90 degrees rotated view (long diameter). Mitral valve area was also determined by two-dimensional echocardiography and the pressure half-time method, and the results for all three noninvasive methods were compared with those obtained at cardiac catheterization. By Doppler color flow imaging, mitral valve area could be determined in all patients and there was a significant correlation between the Doppler jet and catheterization estimates of mitral valve area (r = 0.93). Valve area determined by two-dimensional echocardiography correlated well with catheterization measurements in 26 patients (r = 0.84). However, the area could not be determined in 4 (13%) of the 30 patients because of technical problems. Although there was a fair correlation between the valve area determined by the pressure half-time method and catheterization (r = 0.79), this method tended to overestimate valve area in patients with aortic regurgitation.(ABSTRACT TRUNCATED AT 250 WORDS)

Blood Flow Velocity↗

Evaluation of antiarrhythmic drug effects with simultaneous analysis of single ventricular premature contractions, couplets and salvos.

To improve the clinical value of ambulatory Holter electrocardiographic (ECG) monitoring as a tool of antiarrhythmic therapy control, a new statistical model was developed. In a patient group at increased risk of sudden cardiac death, the spontaneous variability of ventricular arrhythmias was assessed, with simultaneous consideration of single ventricular premature complexes, couplets and salvos. The study included 100 patients who suffered from coronary heart disease or idiopathic dilated cardiomyopathy and for whom greater than 30 ventricular premature complexes/h and couplets had been demonstrated on the last Holter ECG before the study. Between 3 and 12 Holter recordings were made for each patient in a drug-free state; the mean follow-up period was 260 days (maximum 1,403). The mean hourly values of the ectopic events (EE) were assessed separately for ventricular premature complexes, couplets and salvos. The spontaneous variability (SV) was calculated for single ventricular premature complexes, couplets and salvos as SV = log (EEday 2 + 0.01/EEday 1 + 0.01) and linked in one, two and three dimensions. Compared with the consideration of only one type of arrhythmia (one-dimensional model), the simultaneous use of two or three types of arrhythmia (two- or three-dimensional model) resulted in considerably lower reduction and aggravation rates as sufficient proof of drug effects. With control intervals up to 1 week, the one-dimensional model yielded reduction rates for ventricular premature complexes, couplets and salvos of -63%, -90% and -95%, respectively. In contrast, with the three-dimensional model, the rates were -28%, -72% and -88%. The corresponding aggravation values were +370, +1,114% and +2,189% versus +38%, +256% and +747%.(ABSTRACT TRUNCATED AT 250 WORDS)

Anti-Arrhythmia Agents↗

Influence of angle on wall shear stress distribution for an end-to-side anastomosis.

PURPOSE: The purpose of this article was to study the effects of anastomotic angle on the wall shear stress distribution for end-to-side anastomosis models under pulsatile flow conditions. METHOD: The photochromic tracer technique was used to visualize the flow field and to determine the instantaneous wall shear stress at multiple locations simultaneously. Models with angles of 20, 30, 45, and 60 degrees were examined. RESULTS: For all angles, low shear stress was present at the heel and on the bed opposite the heel of the anastomosis apparently as a result of the complete occlusion of the proximal end of the host vessel. Near the toe, increased flow separation occurred with increasing angle. On the bed across from the toe, increasing the angle led to increased shear stress. In addition, in this region the anastomotic angle significantly altered other properties of the shear stress field such as the mean and peak-to-peak magnitudes and cycle-to-cycle fluctuations. CONCLUSIONS: This study provides quantitative data on the wall shear stress distribution within an end-to-side anastomosis and its relation to the anastomotic angle. The results are discussed in terms of possible roles of shear-induced intimal hyperplasia.

Anastomosis, Surgical↗

In vitro assessment of the hemodynamic effects of a partial occlusion in a vena cava filter.

PURPOSE: Flow fields surrounding a vena cava filter were studied with a noninvasive method of flow visualization to examine the underlying hemodynamic factors that contribute to its function and patency. METHODS: The photochromic technique was used to measure axial velocity profiles and wall shear stress distributions in a 12F titanium Greenfield filter partially occluded with a simulated volume of entrapped thrombi. These results were compared with similar measurements obtained for an unoccluded filter and with a theoretic prediction of the velocity profile and wall shear stress without a vena cava filter. Shear stress distributions were obtained along the vessel wall and for the partially occluded filter along the surface of the simulated clot. RESULTS: The unoccluded filter was observed to have little effect on the flow field. In the case of the partially occluded filter, the results of these measurements show that caval blood flow is preserved by the creation of an annular region of increased flow around the periphery of the clot. Within this region high shear stresses that develop as a result of the increased flow are observed along the vessel wall and along the surface of the simulated clot. No vortices or turbulence were observed with either the unoccluded or the partially occluded filter. CONCLUSIONS: The elevated levels of shear stress may be a factor in the lysis of trapped clots observed in vivo. Although increased shear stress is reported to cause thrombogenesis in an in vivo study in canines, particularly under turbulent flow conditions, the levels of shear measured in this study around the simulated clot were well below such values.

Algorithms↗

Pulsatile pressure affects the disappearance of echocardiographic contrast agents.

The purpose of this study was to determine in an in vitro model the effect of pulsatile pressure on the decay of echocardiographic contrast agents. Use of contrast agents for quantitative assessment of perfusion requires understanding of the factors controlling their rates of disappearance. Prior studies have shown that constant pressure affects the rate of disappearance of these agents. It is not known whether pulsatile pressure influences the rate of decay of contrast agents. In an in vitro chamber, three contrast agents (Albunex, hand-agitated saline solution, and hand-agitated Angiovist) were exposed to pulses of pressure at three rates (30, 60, and 120 pulsations/min), keeping pressure characteristics (peak, nadir, and mean) within a narrow range. Five injections were performed for each agent at each rate. Two-dimensional echocardiographic images of the effects of contrast material were recorded from injection until total disappearance. Videointensity was measured and time-intensity curves were generated. These curves of intensity decay were fitted to an exponential decay function (I = Ae-lambda t) and the velocity of decay (lambda) was used for comparisons. For all agents, intensity of contrast decreased over time. Saline solution and Angiovist, but not Albunex, showed pulsatile decreases in intensity of contrast with each peak pressure and partial recovery of contrast intensity with each nadir pressure. (ABSTRACT TRUNCATED AT 250 WORDS)

Albumins↗

Three-dimensional surface geometry correction is required for calculating flow by the proximal isovelocity surface area technique.

This study addressed the hypothesis that surface geometry must be taken into account in proximal convergence calculations of regurgitant flow rate. In vitro models allowed flow to converge within models designed to test derived angle correction equations. Flow was overestimated by the uncorrected equation for surfaces allowing flow to converge over less than a hemisphere and underestimated if flow converged over more than a hemisphere. The extent of deviation depended on the two-dimensional versus three-dimensional nature of the surface (angled flat surfaces versus conical surfaces). Correcting these estimates according to the derived equation produced good agreement for all geometries.

Blood Flow Velocity↗

Quantitative measurement of volume flow rate (cardiac output) by the multibeam Doppler method.

A new method has been developed for measuring the volume flow rate of blood flowing through large vessels or outflow tracts of the heart. In this article we describe the principle of a method that can reduce the dependence of the Doppler angle of flow measurement by setting the sample points along a line to which every ultrasound beam is perpendicular. To evaluate the accuracy of this method, flow phantom experiments were made for both steady and pulsatile flows. The volume flow rate measured by this method agrees well with that observed by an ultrasound flowmeter (r = 0.99) when the vessel diameter is large (25 mm). However, this method overestimates by 40% when the vessel diameter is small (8 mm). To make this method applicable to small vessels, an improvement in the lateral resolution of Doppler measurement is necessary. It has been concluded that this method can be used to measure the cardiac output or volume flow rates in large vessels.

Algorithms↗

A new method for echocardiographic computerized three-dimensional reconstruction of left ventricular endocardial surface: in vitro accuracy and clinical repeatability of volumes.

This study evaluates the in vitro accuracy and clinical repeatability of volumes derived by a new algorithm for three-dimensional reconstruction of cavity surfaces based on echocardiographic apical images obtained by probe rotation. The accuracy of the method was tested in latex phantoms (true volumes, 32 to 349 cm3) with (n = 9) or without (n = 9) rotational symmetry around the midcavitary long axis. Repeatability of left ventricular volumes was assessed in subjects without (n = 5) or with (n = 10) myocardial disease. Estimated phantom volumes obtained from four (three) imaging planes were close to true volumes with a mean difference +/- SD of 0 +/- 2 (2 +/- 3) cm3 in symmetric and 1 +/- 3 (4 +/- 4) cm3 in asymmetric objects. Biplane and single-plane volume estimates were less accurate. Interobserver and intraobserver repeatability of three-dimensional left ventricular volumes was good for analysis (coefficients of variation: 3.5% to 6.2%) and was lower for recording (coefficients of variation: 7.4% to 10.9%). Hence the present algorithm reproduces volumes of symmetric and deformed in vitro objects accurately over a wide range of size and shape, and it produces repeatable left ventricular volumes in the clinical situation.

Adult↗

Intravascular ultrasound imaging of the Heartmate 1000 IP left ventricular assist device.

Left ventricular assist devices are increasingly used as a bridge to transplantation in patients with end-stage cardiac disease. Potential complications of these devices include thromboembolism and infection. Because conventional cardiac diagnostic techniques cannot be used to obtain an image of the interior of a left ventricular assist device, we assessed the ability of intravascular ultrasonography to obtain an image of the interior of the Heartmate 1000 IP left ventricular assist device. Feasibility of intravascular ultrasound imaging was initially demonstrated in vitro on a left ventricular assist device immersed in water. Five soft rubber masses were then placed in the device intake port adherent to the wall, and their images were obtained by intravascular ultrasonography. Excellent correlation between actual size and size as measured by intravascular ultrasonography was noted (long-axis, r = 0.98, short-axis, r = 0.89). After the device was implanted in two calves, intravascular ultrasound imaging was performed in vivo in the animals. The catheter was easily advanced through the device, and excellent images were obtained. In conclusion, intravascular ultrasonography can easily be used to obtain an image of the left ventricular assist device interior and can accurately assess the presence and size of abnormal masses inside the device. Intravascular ultrasonography may be clinically useful in evaluating cases of thrombus or vegetation related to left ventricular assist devices.

Animals↗

Relation between three-dimensional geometry of the inflow tract to the orifice and the area, shape, and velocity of regurgitant color Doppler jets: an in vitro study.

The relation between three-dimensional geometry of the inflow tract to the orifice and the area, shape, and velocity of regurgitant jets was studied in a pulsatile in vitro color Doppler flow model. A 2.5 MHz transducer connected to a diagnostic ultrasound machine was placed in a water tank facing pulsatile jets (duration, 0.5 second) obtained by a calibrated injector. Flow rate from 6 to 52 ml/sec were tested through a 5 mm diameter circular orifice. Four different three-dimensional inflow tract geometries were compared: (A) sharp-edged, (B) Venturi (funnel), (C) converging conical, and (D) diverging conical. Mean velocities of jets were measured by continuous-wave Doppler echocardiography. Driving pressures were also measured by means of a fluid-filled catheter. Two observers independently digitized contours of maximal color jet areas by computer system from two separate sets of experiments. Results are given as the mean values of the four measurements for each parameter. Jet areas were correlated to flow rate, with no difference from A through D. The shape (eccentricity) of jets was different between A and B (p less than 0.05), between B and D (p less than 0.01), and between C and D (p less than 0.01). The shape of jets was correlated with flow rate, continuous-wave velocity, and pressure gradient in B, C, and D but not in A. Measured pressure gradients and estimated gradients by continuous-wave Doppler echocardiography were similarly correlated from A through D.(ABSTRACT TRUNCATED AT 250 WORDS)

Echocardiography, Doppler↗

Instantaneous cross-sectional flow velocity profiles: a comparative study of two ultrasound Doppler methods applied to an in vitro pulsatile flow model.

Two methods based on different techniques for construction of cross-sectional flow velocity profiles from Doppler ultrasound signals were compared: an intraluminal method using pulsed-wave Doppler echocardiography and an extraluminal method using two-dimensional (color) Doppler ultrasound. The methods were applied to an in vitro pulsatile flow model. With the intraluminal method, pulsed Doppler recordings obtained throughout several flow pulses at different positions across a tube were digitized, and cross-sectional flow velocity profiles were obtained by matching the onset of flow velocity at the various positions. With the extraluminal method, cross-sectional flow velocity profiles were obtained by time interpolation between the digital flow velocity data obtained from several flow velocity maps. The first flow velocity map was recorded at onset of flow and the following maps were incrementally delayed with 20 msec from one flow pulse to the next. The time lag caused by the time needed to update each of the flow velocity maps was compensated for by time interpolation between the sequentially recorded flow velocity maps. The cross-sectional flow velocity profiles obtained with the two methods were compared at identical positions within the tube model at equal flow settings and throughout the pulsatile flow periods. At three different flow settings with peak flow velocity of 0.3, 0.5, and 0.7 m/sec, the difference (mean +/- SD) between the obtained velocities were 0.01 +/- 0.04, -0.01 +/- 0.05, and -0.03 +/- 0.07 m/sec, respectively. The findings suggest that cross-sectional flow velocity profiles from pulsatile flow velocity recordings can be obtained equally well with both methods.

Blood Flow Velocity↗

Doppler color flow mapping of the proximal isovelocity surface area: a new method for measuring volume flow rate across a narrowed orifice.

This manuscript describes a new method, validated in in vitro models, for quantitating volume flow rate across an orifice with Doppler color flow mapping. Flow through a narrowed orifice is characterized by the convergence of radial streamlines proximal to the orifice. In this color Doppler method, one or more isovelocity surface areas (PISA), delineated by blue and red aliasing velocity interfaces, can be identified proximal to the narrowed orifice. Volume flow rate (in milliliters per second) can then be calculated as PISA (in square centimeters) multiplied by the isovelocity of the PISA (in centimeters per second). Doppler color flow mapping was performed in in vitro models of constant and pulsatile flow through an orifice in a wall. The first proximal isovelocity surface area, with an isovelocity corresponding to the aliasing velocity, that is, one half the Nyquist sampling limit, could be identified as a blue and red color interface proximal to the orifice. Over a range of circular orifice diameters from 3 mm to 16 mm and flow rates from 0.5 to 18.7 L/min, the proximal isovelocity surface area could be imaged in two planes. This PISA was best described by a hemielliptic mathematical model with two different radii measured from long-axis and short-axis views. In the constant flow model, volume flow rate calculated from the Doppler PISA correlated well with actual volume flow rate measured simultaneously with a cylinder and stopwatch (r = 0.98, p less than 0.001, standard error of the estimate [SEE] = 0.36 L/min). In the pulsatile flow model, with jet velocities ranging from 2.6 to 7.7 m/sec and flow volume ranging from 1.0 to 10.3 L/min, calculated volume flow rate also demonstrated an excellent correlation with actual volume flow rate (r = 0.99, p less than 0.001, SEE = 0.53 L/min). Findings from these in vitro models suggest that quantification of the proximal isovelocity surface area by Doppler color flow mapping appears to be a promising technique for estimating volume flow rate across a narrowed orifice. This new color Doppler flow method may have advantages over previous Doppler methods in estimating volume flow rate in various clinical situations, for example, valvular regurgitation and shunt lesions.

Blood Flow Velocity↗

Biomechanical factors in abdominal aortic aneurysm rupture.

Hitherto the size of abdominal aortic aneurysms (AAA) has been considered the most important factor in determining the risk of rupture. For this reason most interest has been devoted to physical, echographic and tomographic analyses of the shape of AAA. However, it is known that rupture can also occur in small AAA. Other factors must be considered to have an important role in the natural history of aneurysms. The aim of this study was to characterise the mechanical stress in the wall of an AAA due to pressure in the presence of atherosclerosis, intraluminal thrombus and anatomical restraints. The Finite Elements Method (FEM) was used to determine wall stress distribution. Due to the simplicity of the AAA structure an axisymmetric model has been built. The results of the structural analysis confirms that maximum stress increases with diameter. These effects may be reduced by the presence of intraluminal thrombus, which in the models reduces maximum stress by up to 30%; however this is not the case for dissecting thrombus. On the other hand atherosclerotic plaques cause stress concentration and a significant increase in maximum wall stress. The risk of rupture can increase by about 200%. Finally the investigation shows the FEM is a versatile tool for studying the mechanics of vascular structures. It enables the influence of various parameters on wall stress to be quantified in diagnostic settings, and so could be useful for predicting the rupture of AAA, although at present such predictions are limited by data leakage and by the approximations used in the model.

Aged↗

Cell activation and thrombin generation in heparin bonded cardiopulmonary bypass circuits using a novel in vitro model.

OBJECTIVE: It is generally agreed that when the blood contact surfaces of a cardiopulmonary bypass circuit are treated with a layer of heparin molecules the activation of the humoral pathways is attenuated. However, there is still debate as to whether heparin-bonded circuits reduce thrombin generation. This study aims to examine the effects of immobilized heparin on cell activation and thrombin generation in a novel, well controlled model of cardiopulmonary bypass. METHODS: The model used consisted of a heparin-bonded and a non-bonded cardiopulmonary bypass circuit perfused in tandem with the same unit of fresh heparinized (3.3 U/ml) human blood for a period of 6 h. Samples were taken for analysis from the bag just prior to perfusion and at 30, 60, 120 and 360 min of perfusion. Whole blood was used to analyse platelet and white blood cell count, haematocrit and activated coagulation time. Plasma samples were prepared for batch analysis of the cell activation markers p-selectin, elastase and interleukin-8, and the thrombin generation markers thrombin-antithrombin and prothrombin fragment F1 + 2. A sample of tubing was taken from each circuit at the end of the perfusion and prepared for visualization by scanning electron microscopy. RESULTS: Platelet counts were significantly reduced in the non-bonded circuits compared with the heparin-bonded circuits at 30 (22 versus 200 x 10(9)/L P < 0.01), 60 (26 versus 193 x 10(9)/L P < 0.01) and 120 min (28 versus 193 x 10(9)/L P < 0.01) as were white blood cell counts at 30(1.5 versus 2.7 x 10(9)/L P < 0.01), 60 (0.9 versus 2.4 x 10(9)/L P < 0.01), 120 (0.9 versus 1.8 x 10(9)/L P < 0.01) and 360 min (0.4 versus 0.9 x 10(9)/L P < 0.05). The concentration of p-selectin was found to be significantly higher in the non-bonded circuits than in the heparin-bonded circuits at 30 (37 versus 29 ng/ml P < 0.01), 60 (37 versus 28 ng/ml P < 0.01). 120 (42 versus 27 ng/ml P < 0.01) and at 360 min (72 versus 46 ng/ml P < 0.01). Elastase was elevated in the non-bonded circuits at 30 (570 versus 145 micrograms/l P < 0.01), 60 (646 versus 278 micrograms/l P < 0.01) and 120 min (613 versus 403 micrograms/l P < 0.05) and interleukin-8 at 120 (705 versus 520 pg/ml P < 0.05) and 360 min (11326 versus 9910 pg/ml P < 0.05). A similar picture was found for the thrombin generation markers. Thrombin-antithrombin complexes were raised in the non-bonded circuits compared with heparin-bonded circuits at 60 (24 versus 13 micrograms/l P < 0.05) and 120 min (46 versus 17 micrograms/l P < 0.05) as was prothrombin fragment F1 + 2 at 30 (1.1 versus 0.7 nmol/l P < 0.01), 60 (1.3 versus 0.7 nmol/l P < 0.01), 120 (1.8 versus 0.9 nmol/l P < 0.01) and 360 min (15.0 versus 13.6 nmol/l P < 0.05). Scanning electron microscopy revealed a greater amount of adherent material on the non-bonded surface relative to the heparin-bonded surface. CONCLUSIONS: In a cardiopulmonary bypass circuit perfused with human blood the activation of platelets and white blood cells has been seen to be significantly reduced in the presence of a heparin-bonded surface. Thrombin generation due to contact activation of the intrinsic coagulation pathway is also reduced.

Adult↗

Nonselective and semiselective catheters for renal artery evaluation: experimental study.

Abdominal aortography is widely used for evaluation of potential renal donors and for patients with renal failure or hypertension in whom a renal artery ostial or polar branch stenosis is suspected. It would be desirable to use a catheter that consistently enables good bilateral renal artery and polar branch visualization without opacification of overlying mesenteric vessels. Existing and newly designed catheters were compared to determine the optimal design necessary for these studies. An in vitro model of the abdominal aorta and its branches was made, and dye dilution densitometry was employed for quantitative evaluation. Semiselective catheters demonstrated significantly increased renal artery opacification with decreased mesenteric opacification in this in vitro model.

Aorta, Abdominal↗