Biomedical subjects

N Stergiopulos

Publications and source records attributed to N Stergiopulos.

At least 19 recordsLinked to original sources

PubMed2005

Nonlinear isochrones in murine left ventricular pressure-volume loops: how well does the time-varying elastance concept hold?

The linear time-varying elastance theory is frequently used to describe the change in ventricular stiffness during the cardiac cycle. The concept assumes that all isochrones (i.e., curves that connect pressure-volume data occurring at the same time) are linear and have a common volume intercept. Of specific interest is the steepest isochrone, the end-systolic pressure-volume relationship (ESPVR), of which the slope serves as an index for cardiac contractile function. Pressure-volume measurements, achieved with a combined pressure-conductance catheter in the left ventricle of 13 open-chest anesthetized mice, showed a marked curvilinearity of the isochrones. We therefore analyzed the shape of the isochrones by using six regression algorithms (two linear, two quadratic, and two logarithmic, each with a fixed or time-varying intercept) and discussed the consequences for the elastance concept. Our main observations were 1) the volume intercept varies considerably with time; 2) isochrones are equally well described by using quadratic or logarithmic regression; 3) linear regression with a fixed intercept shows poor correlation (R(2) < 0.75) during isovolumic relaxation and early filling; and 4) logarithmic regression is superior in estimating the fixed volume intercept of the ESPVR. In conclusion, the linear time-varying elastance fails to provide a sufficiently robust model to account for changes in pressure and volume during the cardiac cycle in the mouse ventricle. A new framework accounting for the nonlinear shape of the isochrones needs to be developed.

Algorithms↗

PubMed2004

Gelsolin superfamily proteins: key regulators of cellular functions.

Cytoskeletal rearrangement occurs in a variety of cellular processes and involves a wide spectrum of proteins. Among these, the gelsolin superfamily proteins control actin organization by severing filaments, capping filament ends and nucleating actin assembly [1]. Gelsolin is the founding member of this family, which now contains at least another six members: villin, adseverin, capG, advillin, supervillin and flightless I. In addition to their respective role in actin filament remodeling, these proteins have some specific and apparently non-overlapping particular roles in several cellular processes, including cell motility, control of apoptosis and regulation of phagocytosis (summarized in table 1). Evidence suggests that proteins belonging to the gelsolin superfamily may be involved in other processes, including gene expression regulation. This review will focus on some of the known functions of the gelsolin superfamily proteins, thus providing a basis for reflection on other possible and as yet incompletely understood roles for these proteins.

Actins↗

PubMed2004

Comparative assessment of intimal hyperplasia development after 14 days in two different experimental settings: tissue culture versus ex vivo continuous perfusion of human saphenous vein.

BACKGROUND: Intimal hyperplasia (IH) is a vascular remodeling process which often leads to failure of arterial bypass or hemodialysis access. Experimental and clinical work have provided insight in IH development; however, further studies under precise controlled conditions are required to improve therapeutic strategies to inhibit IH development. Ex vivo perfusion of human vessel segments under standardized hemodynamic conditions may provide an adequate experimental approach for this purpose. Therefore, chronically perfused venous segments were studied and compared to traditional static culture procedures with regard to functional and histomorphologic characteristics as well as gene expression. MATERIALS AND METHODS: Static vein culture allowing high tissue viability was performed as previously described. Ex vivo vein support system (EVVSS) was performed using a vein support system consisting of an incubator with a perfusion chamber and a pump. EVVSS allows vessel perfusion under continuous flow while maintaining controlled hemodynamic conditions. Each human saphenous vein was divided in two parts, one cultured in a Pyrex dish and the other part perfused in EVVSS for 14days. Testing of vasomotion, histomorphometry, expression of CD 31, Factor VIII, MIB 1, alpha-actin, and PAI-l were determined before and after 14days of either experimental conditions. RESULTS: Human venous segments cultured under traditional or perfused conditions exhibited similar IH after 14 days as shown by histomorphometry. Smooth-muscle cell (SMC) was preserved after chronic perfusion. Although integrity of both endothelial and smooth-muscle cells appears to be maintained in both culture conditions as confirmed by CD31, factor VIII, and alpha-actin expression, a few smooth-muscle cells in the media stained positive for factor VIII. Cell-proliferation marker MIB-1 was also detected in the two settings and PAI-1 mRNA expression and activity increased significantly after 14 days of culture and perfusion. CONCLUSION: This study demonstrates the feasibility to chronically perfuse human vessels under sterile conditions with preservation of cellular integrity and vascular contractility. To gain insights into the mechanisms leading to IH, it will now be possible to study vascular remodeling not only under static conditions but also in hemodynamic environment mimicking as closely as possible the flow conditions encountered in reconstructive vascular surgery.

Culture Techniques↗

PubMed2003

Geometrical, functional, and histomorphometric adaptation of rat carotid artery in induced hypertension.

Acute and long-term (up to 56 days) evolution of geometry, structural properties, vascular smooth muscle (VSM) tone and histomorphometric properties of the rat common carotid arteries under induced hypertension were investigated. Hypertension was induced in 8-week old male Wistar rats by total ligation of the aorta between the two kidneys. Rats were sacrificed 2, 4, 8 and 56 days postsurgery. The arterial wall layers thicken non-uniformly during the adaptation process, the inner layers thicken more in the acute phase of hypertension, whereas the outer layers of the wall are thicker than the inner layers at the end of the adaptation phase. Collagen content in the wall media exhibits a non-linear evolution, with a rapid increase in the acute hypertension phase followed by a slower increase at long-term. The elastin content increase is slight and steady, whereas VSM shows a steady but considerable increase which outdoes the collagen increase in long-term phase. VSM tone increases rapidly in the acute phase of remodelling (0-8 days) and this increase in tone contributes to a considerable increase in arterial compliance in the operating pressure range. At long-term (56 days) VSM tone returns to near control level, but compliance is even further increased, which suggests that at long-term the compliance increase is attributed primarily to structural remodelling.

Adaptation, Physiological↗

PubMed2003

Hemodynamics induced after acute reduction of proximal thoracic aorta compliance.

OBJECTIVE: to investigate the affect of reduced aortic compliance on cardiovascular hemodynamics. MATERIALS AND METHOD: fourteen Yucatan miniature swine were divided into two equal groups, a Sham Operated Group and a Banding Group. A Teflon prosthesis was wrapped around the aortic arc in order to limit proximal aortic compliance (Banding Group). Data were recorded operatively (after implantation of a pressure sensor and a flow probe in the ascending aorta), after banding (only in the Banding Group) and at 2 days postoperatively. RESULTS: after banding, compliance decreased by 52 +/- 13% ((-)X +/- SEM) (p < 0.01) while systolic and pulse pressure increased by 37 +/- 8% (p < 0.05) and 87 +/- 31% (p < 0.01), respectively. Diastolic pressure, mean blood pressure, cardiac output and systemic vascular resistance did not change significantly. Aortic characteristic impedance increased nearly 2.5 times. Amplitudes of forward and reflected pressure waves (derived from the aortic pressure wave) increased by 96 +/- 41% and 174 +/- 46%, respectively (p < 0.05), while the time delay between the two decreased by 36 +/- 7% (p < 0.05). CONCLUSIONS: about half of the total arterial compliance is located in the proximal thoracic aorta. Arterial reconstruction of the proximal aorta with a non-compliant graft results in a significant decrease in systemic arterial compliance, which in turn increases systolic and pulse pressure. The development of more compliant prosthesis, which matches the host artery compliance, is expected to reduce the hemodynamic changes induced after their implantation.

Animals↗

PubMed2001

Predicting systolic and diastolic aortic blood pressure and stroke volume in the intact sheep.

We developed a mathematical model describing the interaction between the heart and the arterial system. The model was constructed and tested on basis of invasive hemodynamic data in six sheep. Data from a first group of three animals (49 cardiac cycles) were used to assess a template time-varying elastance curve for the left ventricle, while the baseline steady-state data of a second group of three animals were used to assess reference cardiac and arterial parameters in sheep. The model is fully characterized by nine parameters, which were converted into 6 dimensionless numbers using the Buckingham pi theorem. The model was then used to generate LV pressure and volume and aortic pressure and flow for 86 conditions obtained by varying parameters 50 to 200% of their reference value. Systolic (SBP) and diastolic (DBP) blood pressure and stroke volume (SV) were determined from these model-generated curves and multiple linear regression analysis yielded the following expressions: SBP = Pisovolumic [0.638 - 0.0773 Emax C + 0.0507 RC/T] (r2 = 0.89); DBP = Pisovolumic [0.438-0.0712 Emax C + 0.0655RC/T] (r2 = 0.88) and SV = LVEDV [1.265-1.040 LVEDV/(LVEDV - Vd) + 0.125 Emax C-0.0777RC/T] (r2 = 0.93) with Pisovolumic = Emax (LVEDV - Vd), Emax and Vd being the slope and intercept of the end-systolic pressure-volume relation, R and C the total peripheral resistance and compliance, LVEDV the left ventricular end-diastolic volume, and T the cardiac cycle length. These expressions were validated using data from the second group of three animals obtained during vena cava occlusion at baseline and during administration of dobutamine (61 cycles). The correlation between measured and predicted values was 0.98, 0.97 and 0.92 for SBP, DBP and SV, respectively. Compared to the measured values, SBP and DBP were, on average, underestimated by 5 and 6mmHg, respectively, and SV overestimated by 1.4 ml. We conclude that the derived expressions for blood pressure and stroke volume remain valid in the intact sheep for various hemodynamic conditions, and, taking into account their dimensionless form, may hold in other species and in humans.

Animals↗

PubMed2001

In vitro diameter response of rat femoral artery to flow in the presence and absence of endothelium.

We have examined the diameter response of rat femoral artery segments in the presence and absence of endothelium to changes in flow rate. The segments were isolated, mounted on microcannulae, maintained at 37 degrees C, and perfused at 90 mmHg with Tyrode's solution. The external arterial diameter was measured using video-microscopy. The mean control diameter was 741+/-22 microm (mean+/-SEM,n=7). The arteries were preconstricted to 75+/-1% of the control diameter with a superfusion of 1 microM norepinephrine (NE). Endothelial function was verified by perfusion of 1 micro;M acetylcholine (ACh). Two different flow protocols were employed: step changes in flow (n=7) and low-frequency sinusoidal flow changes (0.01Hz 0.05). Sinusoidal flow oscillations resulted in sinusoidal diameter oscillations, whose amplitude and phase lag were inversely proportional to the frequency of the flow oscillations. A first-order low-pass filter, with a time constant of 28+/-3 and 30+/-5s for arteries with and without functional endothelium, respectively, was used to describe the relation between oscillatory flow and diameter. The response of the rat femoral arteries to changes in flow was not found to be different whether the endothelium was intact or removed.

Analysis of Variance↗

PubMed2001

Cytosolic-free calcium in smooth-muscle and endothelial cells in an intact arterial wall from rat mesenteric artery in vitro.

The regulation of cytosolic-free calcium concentration of smooth-muscle and endothelial cells was mainly studied on cultured cells where the cross talk between these two coupled cell types is lost. In the present study, the cytosolic-free calcium concentration in the endothelial and the smooth-muscle cells was examined in an intact arterial wall in vitro. Strips of the main branch of rat mesenteric artery were used. Cytosolic-free calcium concentration [Ca2+]i was estimated by determining the fluorescence ratio of the two calcium probes, Fluo-4 and Fura red. The emitted fluorescence of both probes was measured with a confocal microscope. We showed that potassium and phenylephrine, which increase the cytosolic -free calcium concentration of the smooth-muscle cells, also indirectly influence the calcium concentration in the endothelial cells. By simultaneously determining [Ca2+]i in the endothelial and the smooth-muscle cells of an arterial strip, we observed that when calcium increases in the endothelial cells in response to acetylcholine, it slightly decreases in the smooth-muscle cells. We conclude that the regulation of [Ca2+]i in the arterial endothelial cell, depends according to the stimuli either upon the endothelial cells themselves, or upon the coupled smooth-muscle cells.

Acetylcholine↗

PubMed2001

Short-Term biomechanical adaptation of the rat carotid to acute hypertension: contribution of smooth muscle.

The biomechanical adaptation of the arterial wall to hypertension has been studied extensively in recent years; however, the exact biomechanical contribution of vascular smooth muscle cells (VSMCs) during the adaptation process in conduit vessels is not known. We induced hypertension in 8 wk old Wistar rats by total ligation of the aorta between the two kidneys. Mean blood pressure increased from 92 +/- 2 (mean +/- SE) mm Hg to approximately 150 mmHg. Rats were sacrificed 2, 4, and 8 d after surgery and the left common carotid artery was excised for analysis. Wall thickness increased by 18% in 8 d and the opening angle by 32% in 4 d. The elastic properties were measured under normal VSMC tone (i.e., the amount of VSMC tone under normal conditions also called basal VSMC tone or normal resting VSMC tone), under maximally contracted VSMC (NE, 5 x 10(-7) mol/L) and under totally relaxed VSMC conditions (papaverine, 10(-4) mol/L). The most pronounced modifications were the changes in elastic properties related to normal VSMC tone. The functional contraction ratio at 100 mm Hg, defined as the relative contraction under normal conditions (normal VSMC tone), increased by 439% 4 d after the induction of hypertension. The total contraction capacity of the VSMC increased by 38% within 8 d. The changes in normal VSMC tone led to important changes in the mechanical properties of the arterial wall. Under normal VSMC conditions, compliance at mean pressure (148 mm Hg) increased by 159% within 8 d, whereas in the absence of VSMC tone, compliance did not increase significantly. We conclude that in conduit vessels, the VSMC, which is the sensing and effecting element of the adaptation process, is subjected to large-scale changes during the early phase of arterial adaptation to acute hypertension.

Adaptation, Physiological↗

PubMed2001

Simultaneous arterial calcium dynamics and diameter measurements: application to myoendothelial communication.

The goal of the present study was to analyze the intercellular calcium communication between smooth muscle cells (SMCs) and endothelial cells (ECs) by simultaneously monitoring artery diameter and intracellular calcium concentration in a rat mesenteric arterial segment in vitro under physiological pressure (50 mmHg) and flow (50 microl/min) in a specially developed system. Intracellular calcium was expressed as the fura 2 ratio. The diameter was measured using a digital image acquisition system. Stimulation of SMCs with the alpha(1)-agonist phenylephrine (PE) caused not only an increase in the free intracellular calcium concentration of the SMCs as expected but also in the ECs, suggesting a calcium flux from the SMCs to the ECs. The gap junction uncoupler palmitoleic acid greatly reduced this increase in calcium in the ECs on stimulation of the SMCs with PE. This indicates that the signaling pathway passes through the gap junctions. Similarly, although vasomotion originates in the SMCs, calcium oscillates in both SMCs and ECs during vasomotion, suggesting again a calcium flux from the SMCs to the ECs.

Animals↗

PubMed2001

Model of geometrical and smooth muscle tone adaptation of carotid artery subject to step change in pressure.

Recent experimental studies have shown significant alterations of the vascular smooth muscle (VSM) tone when an artery is subjected to an elevation in pressure. Therefore, the VSM participates in the adaptation process not only by means of its synthetic activity (fibronectins and collagen) or proliferative activity (hypertrophy and hyperplasia) but also by adjusting its contractile properties and its tone level. In previous theoretical models describing the time evolution of the arterial wall adaptation in response to induced hypertension, the contribution of VSM tone has been neglected. In this study, we propose a new biomechanical model for the wall adaptation to induced hypertension, including changes in VSM tone. On the basis of Hill's model, total circumferential stress is separated into its passive and active components, the active part being the stress developed by the VSM. Adaptation rate equations describe the geometrical adaptation (wall thickening) and the adaptation of active stress (VSM tone). The evolution curves that are derived from the theoretical model fit well the experimental data describing the adaptation of the rat common carotid subjected to a step increase in pressure. This leads to the identification of the model parameters and time constants by characterizing the rapidity of the adaptation processes. The agreement between the results of this simple theoretical model and the experimental data suggests that the theoretical approach used here may appropriately account for the biomechanics underlying the arterial wall adaptation.

Adaptation, Physiological↗

PubMed2000

A mathematical model of umbilical venous pulsation.

Pulsations in the fetal heart propagate through the precordial vein and the ductus venosus but are normally not transmitted into the umbilical vein. Pulsations in the umbilical vein do occur, however, in early pregnancy and in pathological conditions. Such transmission into the umbilical vein is poorly understood. In this paper we hypothesize that the mechanical properties and the dimensions of the vessels do influence the umbilical venous pulsations, in addition to the magnitude of the pressure and flow waves generated in the fetal atria. To support this hypothesis we established a mathematical model of the umbilical vein/ductus venosus bifurcation. The umbilical vein was modeled as a compliant reservoir and the umbilical vein pressure was assumed to be equal to the stagnation pressure at the ductus venosus inlet. We calculated the index of pulsation of the umbilical vein pressure ((max-min)/mean), the reflection and transmission factors at the ductus venosus inlet, numerically and with estimates. Typical dimensions in the physiological range for the human fetus were used, while stiffness parameters were taken from fetal sheep. We found that wave transmission and reflection in the umbilical vein ductus venosus bifurcation depend on the impedance ratio between the umbilical vein and the ductus venosus, as well as the ratio of the mean velocity and the pulse wave velocity in the ductus venosus. Accordingly, the pulsations initiated by the fetal heart are transmitted upstream and may arrive in the umbilical vein with amplitudes depending on the impedance ratio and the ratio between the mean velocity and the pulse wave velocity in the ductus venosus.

Fetus↗

PubMed2000

Left ventricular wall stress normalization in chronic pressure-overloaded heart: a mathematical model study.

It is generally accepted that the left ventricle (LV) hypertrophies (LVH) to normalize systolic wall stress (sigma(s)) in chronic pressure overload. However, LV filling pressure (P(v)) may be elevated as well, supporting the alternative hypothesis of end-diastolic wall stress (sigma(d)) normalization in LVH. We used an LV time-varying elastance model coupled to an arterial four-element lumped-parameter model to study ventricular-arterial interaction in hypertension-induced LVH. We assessed model parameters for normotensive controls and applied arterial changes as observed in hypertensive patients with LVH (resistance +40%, compliance -25%) and assumed 1) no cardiac adaptation, 2) normalization of sigma(s) by LVH, and 3) normalization of sigma(s) by LVH and increase in P(v), such that sigma(d) is normalized as well. In patients, systolic and diastolic blood pressures increase by approximately 40%, cardiac output (CO) is constant, and wall thickness increases by 30-55%. In scenarios 1 and 2, blood pressure increased by only 10% while CO dropped by 20%. In scenario 2, LV wall thickness increased by only 10%. The predictions of scenario 3 were in qualitative and quantitative agreement with in vivo human data. LVH thus contributes to the elevated blood pressure in hypertension, and cardiac adaptations include an increase in P(v), normalization of sigma(s), and preservation of CO in the presence of an impaired diastolic function.

Adaptation, Physiological↗

PubMed2000

Quantification of the contribution of cardiac and arterial remodeling to hypertension.

The study aim was to quantify the individual and combined contributions of both the arterial system and the heart to systolic blood pressure in hypertension. We assessed the parameters of a heart-arterial model for normotensive control subjects and hypertensive patients with left ventricular adaptation patterns classified as normal, concentric remodeling, concentric hypertrophy, or eccentric hypertrophy. The present simulations show that vascular stiffening alone increases the pulse pressure without increasing systolic blood pressure. It is only in combination with an increased peripheral resistance that arterial stiffening leads to systolic hypertension in concentric remodeling and concentric hypertrophy. The contribution of cardiac pump function to the increase in blood pressure depends on cardiac remodeling, hypertrophy, or both. In hypertensive patients with a normal left ventricle, the heart is responsible for 55% of the increase in systolic blood pressure. In concentric remodeling, concentric hypertrophy, and eccentric hypertrophy, the cardiac contribution to the increase in systolic blood pressure is 21%, 65%, and 108%, respectively. We conclude that along with arterial changes, cardiac remodeling and hypertrophy contribute to hypertension.

Arteries↗

PubMed2000

Models of the arterial tree.

The arterial system can be modelled by means of distributed analogs and by lumped parameter representations, such as the Windkessel. The distributed models, together with biological data, lead to the explanation of arterial function in terms of pressure and flow. The lumped parameter models form the basis of arterial compliance and characteristic impedance estimation. They also make comparison between mammals possible and it could be shown that input impedance, when scaled, is similar in mammals.

Animals↗

PubMed1999

Mechanism of pulmonary venous pressure and flow waves.

The pulmonary venous systolic flow wave has been attributed both to left heart phenomena, such as left atrial relaxation and descent of the mitral annulus, and to propagation of the pulmonary artery pressure pulse through the pulmonary bed from the right ventricle. In this study we hypothesized that all waves in the pulmonary veins originate in the left heart, and that the gross wave features observed in measurements can be explained simply by wave propagation and reflection. A mathematical model of the pulmonary vein was developed; the pulmonary vein was modeled as a lossless transmission line and the pulmonary bed by a three-element lumped parameter model accounting for viscous losses, compliance, and inertia. We assumed that all pulsations originate in the left atrium (LA), the pressure in the pulmonary bed being constant. The model was validated using pulmonary vein pressure and flow recorded 1 cm proximal to the junction of the vein with the left atrium during aortocoronary bypass surgery. For a pressure drop of 6 mmHg across the pulmonary bed, we found a transit time from the left atrium to the pulmonary bed of tau approximately 150ms, a compliance of the pulmonary bed of C approximately 0.4 ml/mmHg, and an inertance of the pulmonary bed of 1.1 mmHgs2/ml. The pulse wave velocity of the pulmonary vein was estimated to be c approximately 1m/s. Waves, however, travel both towards the left atrium and towards the pulmonary bed. Waves traveling towards the left atrium are attributed to the reflections caused by the mismatch of impedance of line (pulmonary vein) and load (pulmonary bed). Wave intensity analysis was used to identify a period in systole of net wave propagation towards the left atrium for both measurements and model. The linear separation technique was used to split the pressure into one component traveling from the left atrium to the pulmonary bed and a reflected component propagating from the pulmonary bed to the left atrium. The peak of the reflected pressure wave corresponded well with the positive peak in wave intensity in systole. We conclude that the gross features of the pressure and flow waves in the pulmonary vein can be explained in the following manner: the waves originate in the LA and travel towards the pulmonary bed, where reflections give rise to waves traveling back to the LA. Although the gross features of the measured pressure were captured well by the model predicted pressure, there was still some discrepancy between the two. Thus, other factors initiating or influencing waves traveling towards the LA cannot be excluded.

Biomechanical Phenomena↗

PubMed1999

Pulse wave attenuation measurement by linear and nonlinear methods in nonlinearly elastic tubes.

Reasons for the continuing difficulty in making definitive measurements of pulse wave attenuation in elastic tubes and arteries in the presence of reflections are sought. The measurement techniques available were re-examined in elastic tubes mimicking the arterial compliance nonlinearity, under conditions of strong reflection. The pulse was of physiological shape, and two different pulse amplitudes in the physiological range were used. Measurements of pressure, flow-rate and diameter pulsation allowed the deployment of four of the classical linear methods of analysis. In addition, a method of separating the forward- and backward-travelling waves that does not require linearising assumptions was used, and the attenuation in the forward and reverse directions was calculated from the resulting waveforms. Overall, the results obtained here suggest that a fully satisfactory way of measuring arterial attenuation has yet to be devised. The classical linear methods all provided comparable attenuation estimates in terms of average value and degree of scatter across frequency. Increased scatter was generally found at the higher pulse amplitude. When the forward waveforms from the separation were similarly compared in terms of frequency components, the average value at energetic harmonics was similar to both the value indicated by the linear methods and the values predicted from linear theory on the basis of estimated viscous and viscoelastic parameter data. The backward waveforms indicated a physically unreasonable result, attributed as the expression for this technique of the same difficulties that normally manifest in scatter. Data in the literature suggesting that one of the classical methods, the three-point, systematically over-estimates attenuation were not supported, but it was confirmed that this method becomes prone to negative attenuation estimates at low harmonics as pulse amplitude increases. Although the goal of definitive attenuation measurement remains elusive, the task provides a sensitive tool for the examination of the effect of nonlinearities in the arterial system.

Arteries↗

PubMed1999

Total arterial inertance as the fourth element of the windkessel model.

In earlier studies we found that the three-element windkessel, although an almost perfect load for isolated heart studies, does not lead to accurate estimates of total arterial compliance. To overcome this problem, we introduce an inertial term in parallel with the characteristic impedance. In seven dogs we found that ascending aortic pressure could be predicted better from aortic flow by using the four-element windkessel than by using the three-element windkessel: the root-mean-square errors and the Akaike information criterion and Schwarz criterion were smaller for the four-element windkessel. The three-element windkessel overestimated total arterial compliance compared with the values derived from the area and the pulse pressure method (P = 0.0047, paired t-test), whereas the four-element windkessel compliance estimates were not different (P = 0.81). The characteristic impedance was underestimated using the three-element windkessel, whereas the four-element windkessel estimation differed marginally from the averaged impedance modulus at high frequencies (P = 0.0017 and 0.031, respectively). When applied to the human, the four-element windkessel also was more accurate in these same aspects. Using a distributed model of the systemic arterial tree, we found that the inertial term results from the proper summation of all local inertial terms, and we call it total arterial inertance. We conclude that the fourelement windkessel, with all its elements having a hemodynamic meaning, is superior to the three-element windkessel as a lumped-parameter model of the entire systemic tree or as a model for parameter estimation of vascular properties.

Animals↗