Non-invasive assessment of ventriculo-arterial coupling using aortic wave intensity analysis combining central blood pressure and phase-contrast cardiovascular magnetic resonance

BACKGROUND

Wave intensity analysis (WIA) in the aorta offers important clinical and mechanistic insight into ventriculo-arterial coupling, but is difficult to measure non-invasively. We performed WIA by combining standard cardiovascular magnetic resonance (CMR) flow-velocity and non-invasive central blood pressure (cBP) waveforms.

METHODS AND RESULTS

Two hundred and six healthy volunteers (age range 21-73 years, 47% male) underwent sequential phase contrast CMR (Siemens Aera 1.5 T, 1.97 × 1.77 mm2, 9.2 ms temporal resolution) and supra-systolic oscillometric cBP measurement (200 Hz). Velocity (U) and central pressure (P) waveforms were aligned using the waveform foot, and local wave speed was calculated both from the PU-loop (c) and the sum of squares method (cSS). These were compared with CMR transit time derived aortic arch pulse wave velocity (PWVtt). Associations were examined using multivariable regression. The peak intensity of the initial compression wave, backward compression wave, and forward decompression wave were 69.5 ± 28, -6.6 ± 4.2, and 6.2 ± 2.5 × 104 W/m2/cycle2, respectively; reflection index was 0.10 ± 0.06. PWVtt correlated with c or cSS (r = 0.60 and 0.68, respectively, P < 0.01 for both). Increasing age decade and female sex were independently associated with decreased forward compression wave (-8.6 and -20.7 W/m2/cycle2, respectively, P < 0.01) and greater wave reflection index (0.02 and 0.03, respectively, P < 0.001).

CONCLUSION

This novel non-invasive technique permits straightforward measurement of wave intensity at scale. Local wave speed showed good agreement with PWVtt, and correlation was stronger using the cSS than the PU-loop. Ageing and female sex were associated with poorer ventriculo-arterial coupling in healthy individuals.

Wave intensity analysis in the internal carotid artery of hypertensive subjects using phase-contrast MR angiography and preliminary assessment of the effect of vessel morphology on wave dynamics

Objective: Hypertension is associated with reduced cerebral blood flow, but it is not known how this impacts on wave dynamics or potentially relates to arterial morphology. Given the location of the internal carotid artery (ICA) and risks associated with invasive measurements, wave dynamics in this artery have not been extensively assessed in vivo. This study explores the feasibility of studying wave dynamics in the internal carotid artery non-invasively. Approach: Normotensive, uncontrolled and controlled hypertensive participants were recruited (daytime ambulatory blood pressure  <135/85 mmHg and  >135/85 mmHg, respectively; n  =  38). Wave intensity, reservoir pressure and statistical shape analyses were performed on the right ICA and ascending aorta high-resolution phase-contrast magnetic resonance angiography data. Main results: Wave speed in the aorta was significantly lower in normotensive compared to hypertensive participants (6.7  ±  1.8 versus 11.2  ±  6.2 m s⁻¹ for uncontrolled and 11.8  ±  4.6 m s⁻¹ for controlled hypertensives, p  =  0.02), whilst there were no differences in wave speed in the ICA. There were no significant differences between the groups for the wave intensity or reservoir pressure. Interestingly, a significant association between the anatomy of the ICA and wave energy (FCW and size, r²  =  0.12, p  =  0.04) was found. Significance: This study shows it is feasible to study wave dynamics in the ICA non-invasively. Whilst changes in aortic wave speed confirmed an expected increase in arterial stiffness, this was not observed in the ICA. This might suggest a protective mechanism in the cerebral circulation, in conjunction with the effect of vessel tortuosity. Furthermore, it was observed that ICA shape correlated with wave energy but not wave speed.

A history of previous gestational diabetes mellitus is associated with adverse changes in insulin secretion and VLDL metabolism independently of increased intrahepatocellular lipid

AIMS/HYPOTHESIS

We have previously reported a high prevalence of non-alcoholic fatty liver disease (NAFLD) among women with previous gestational diabetes mellitus (pGDM). We wanted to confirm that intrahepatocellular lipid (IHCL) is associated with pGDM independently of adiposity and determine: (1) if VLDL metabolism is dysregulated; and (2) the extent to which NAFLD and IHCL account for the dysmetabolic phenotype in pGDM.

METHODS

We analysed data from a cohort of 234 women (114 with pGDM) and identified effects of pGDM on lipid and glucoregulation that were independent of ultrasound-diagnosed NAFLD. We then measured IHCL by MR spectroscopy in a representative subgroup (n = 36) and conducted detailed metabolic studies (IVGTT, VLDL apolipoprotein B [apoB] kinetics and palmitate turnover) and measurement of regional body fat by MRI to demonstrate effects of IHCL that were independent of a history of pGDM.

RESULTS

pGDM was associated with increased IHCL (p = 0.04) after adjustment for adiposity. Independently of IHCL, pGDM was associated with a lower IVGTT disposition index (p = 0.02) and acute insulin response to glucose (pGDM+/NAFLD-, 50% lower; pGDM+/NAFLD+, 36% lower; effect of pGDM, p = 0.03), increased VLDL apoB pool size (pGDM+/NAFLD-, 3.1-fold higher; pGDM+/NAFLD+, 1.2-fold higher; effect of pGDM, p = 0.02) and, at borderline significance (p = 0.05), increased rate of VLDL apoB synthesis.

CONCLUSIONS/INTERPRETATION

pGDM is associated with increased IHCL independently of adiposity. The increased liver fat contributes to the phenotype, but pGDM status is independently associated with diminished insulin secretion and (shown for the first time) augmented VLDL metabolism. IHCL with pGDM may compound a dysmetabolic phenotype.

Evaluation of droplet dispersion during non-invasive ventilation, oxygen therapy, nebuliser treatment and chest physiotherapy in clinical practice: implications for management of pandemic influenza and other airborne infections

BACKGROUND

Influenza viruses are thought to be spread by droplets, but the role of aerosol dissemination is unclear and has not been assessed by previous studies. Oxygen therapy, nebulised medication and ventilatory support are treatments used in clinical practice to treat influenzal infection are thought to generate droplets or aerosols.

OBJECTIVES

Evaluation of the characteristics of droplet/aerosol dispersion around delivery systems during non-invasive ventilation (NIV), oxygen therapy, nebuliser treatment and chest physiotherapy by measuring droplet size, geographical distribution of droplets, decay in droplets over time after the interventions were discontinued.

METHODS

Three groups were studied: (1) normal controls, (2) subjects with coryzal symptoms and (3) adult patients with chronic lung disease who were admitted to hospital with an infective exacerbation. Each group received oxygen therapy, NIV using a vented mask system and a modified circuit with non-vented mask and exhalation filter, and nebulised saline. The patient group had a period of standardised chest physiotherapy treatment. Droplet counts in mean diameter size ranges from 0.3 to > 10 µm were measured with an counter placed adjacent to the face and at a 1-m distance from the subject/patient, at the height of the nose/mouth of an average health-care worker.

RESULTS

NIV using a vented mask produced droplets in the large size range (> 10 µm) in patients (p = 0.042) and coryzal subjects (p = 0.044) compared with baseline values, but not in normal controls (p = 0.379), but this increase in large droplets was not seen using the NIV circuit modification. Chest physiotherapy produced droplets predominantly of > 10 µm (p = 0.003), which, as with NIV droplet count in the patients, had fallen significantly by 1 m. Oxygen therapy did not increase droplet count in any size range. Nebulised saline delivered droplets in the small- and medium-size aerosol/droplet range, but did not increase large-size droplet count.

CONCLUSIONS

NIV and chest physiotherapy are droplet (not aerosol)-generating procedures, producing droplets of > 10 µm in size. Due to their large mass, most fall out on to local surfaces within 1 m. The only device producing an aerosol was the nebuliser and the output profile is consistent with nebuliser characteristics rather than dissemination of large droplets from patients. These findings suggest that health-care workers providing NIV and chest physiotherapy, working within 1 m of an infected patient should have a higher level of respiratory protection, but that infection control measures designed to limit aerosol spread may have less relevance for these procedures. These results may have infection control implications for other airborne infections, such as severe acute respiratory syndrome and tuberculosis, as well as for pandemic influenza infection.

The thermic response to food is related to sensitivity to adrenaline in a group at risk for the development of type II diabetes

OBJECTIVES

To analyze whether a decreased sensitivity to adrenaline in women with earlier gestational diabetes (GDM) explains the impairment in the thermogenic response to food (=post-prandial thermogenesis (PPT)) that is observed in these women at future risk of obesity and type II diabetes.

SUBJECTS/METHODS

Ten normal-weight women with previous GDM and 10 controls matched for body weight, all with normal glucose tolerance, had insulin sensitivity, PPT and the thermogenic response to an adrenaline infusion measured.

RESULTS

Insulin sensitivity was similar in the previous GDM compared with control groups: (mean+/-s.e.m.) 29.1+/-3.2 vs 30.9+/-1.6 mg/l/min. The early (0-30 min) PPT response was diminished and delayed in women with previous GDM compared with controls: (10+/-2 vs 15+/-1 kJ, P=0.04); time constant for PPT (median (interquartile range)) (57 (47-79) vs 29 (25-49) min, P=0.01). The overall PPT response and the thermogenic response to adrenaline were not significantly different between the groups. The 30 min and 2 h PPT response correlated positively and significantly with the increment in energy expenditure as a result of the adrenaline infusion (rho=+0.65; P=0.04 and rho=+0.71; P=0.02, respectively) in women with previous GDM only. There was no correlation between adrenaline and insulin sensitivity.

CONCLUSIONS

There is no evidence of diminished adrenaline sensitivity but a positive relationship exists between PPT and sensitivity to adrenaline in women with previous GDM. The mechanism is not mediated through insulin resistance. This relationship may predispose these normal-weight at-risk women to future weight gain.

Forward and backward waves in the arterial system: impedance or wave intensity analysis?

Both impedance analysis and wave intensity analysis are used to separate measured pressure and flow waveforms into their forward and backward components. The separation is sensitive to the characteristic impedance or wave speed determined from the data. In all other aspects, the results are identical.

Separation of the reservoir and wave pressure and velocity from measurements at an arbitrary location in arteries

Previous studies based on measurements made in the ascending aorta have demonstrated that it can be useful to separate the arterial pressure P into a reservoir pressure P* generated by the windkessel effect and a wave pressure p generated by the arterial waves: P = P*+p. The separation in these studies was relatively straightforward since the flow into the arterial system was measured. In this study the idea is extended to measurements of pressure and velocity at sites distal to the aortic root where flow into the arterial system is not known. P* is calculated from P at an arbitrary location in a large artery by fitting the pressure fall-off in diastole to an exponential function and assuming that p is proportional to the flow into the arterial system. A local reservoir velocity U* that is proportional to P* is also defined. The separation algorithm is applied to in vivo human and canine data and to numerical data generated using a one-dimensional model of pulse wave propagation in the larger conduit arteries. The results show that the proposed algorithm is reasonably robust, allowing for the separation of the measured pressure and velocity into reservoir and wave pressures and velocities. Application to data measured simultaneously in the aorta of the dog shows that the reservoir pressure is fairly uniform along the aorta, a test of self-consistency of the assumptions leading to the algorithm. Application to data generated with a validated numerical model indicates that the parameters derived by fitting the pressure data are close to the known values which were used to generate the numerical data. Finally, application to data measured in the human thoracic aorta indicates the potential usefulness of the separation.

Arterial pulse wave velocity in coronary arteries

Pulse wave velocity is related to arterial stiffness. Pulse wave velocity changes with age and disease and is a useful indicator of cardiovascular disease. Different methods are used for evaluating pulse wave velocity in systemic vessels, but none is applicable to coronary arteries. In this study we first compare values of wave speed (c) calculated from measurements of pressure (P) and velocity (U) using different analytical methods: PU-loop, beta stiffness parameter, characteristic impedance, foot-to-foot method, and the sum of squares (Sigma(2)), a novel way of calculating the wave speed (calculated from the square root of the sum of the ratio of the dP(2) and dU(2) over a complete cardiac cycle). Results from human measurements using Doppler ultrasound on carotid arteries show good correlation between the PU-loop method, beta stiffness parameter and Sigma(2). Characteristic impedance calculations show the greatest variation of all methods. The Sigma(2) method was further assessed in vitro for use in coronary vessels. Pressure and velocity measurements were obtained from human coronary arteries following angiographic studies. The measurements were made invasively by co-locating two wires with pressure and velocity transducers. Pressure and velocity data in the left anterior descending, circumflex, left main stem and right coronary arteries were acquired simultaneously along with the ECG signal. Wave speed was calculated using Sigma(2). Wave intensity analysis was used to determine forward and backward traveling waves at different times in different locations, for which wave speed, approximate distance and timings between waves need to be known.

Simultaneous determination of wave speed and arrival time of reflected waves using the pressure–velocity loop

In a previous paper we demonstrated that the linear portion of the pressure-velocity loop (PU-loop) corresponding to early systole could be used to calculate the local wave speed. In this paper we extend this work to show that determination of the time at which the PU-loop first deviates from linearity provides a convenient way to determine the arrival time of reflected waves (Tr). We also present a new technique using the PU-loop that allows for the determination of wave speed and Tr simultaneously. We measured pressure and flow in elastic tubes of different diameters, where a strong reflection site existed at known distances away form the measurement site. We also measured pressure and flow in the ascending aorta of 11 anaesthetised dogs where a strong reflection site was produced through total arterial occlusion at four different sites. Wave speed was determined from the initial slope of the PU-loop and Tr was determined using a new algorithm that detects the sampling point at which the initial linear part of the PU-loop deviates from linearity. The results of the new technique for detecting Tr were comparable to those determined using the foot-to-foot and wave intensity analysis methods. In elastic tubes Tr detected using the new algorithm was almost identical to that detected using wave intensity analysis and foot-to-foot methods with a maximum difference of 2%. Tr detected using the PU-loop in vivo highly correlated with that detected using wave intensity analysis (r (2) = 0.83, P < 0.001). We conclude that the new technique described in this paper offers a convenient and objective method for detecting Tr, and allows for the dynamic determination of wave speed and Tr, simultaneously.

A dynamical model of lipoprotein metabolism

We present a dynamical model of lipoprotein metabolism derived by combining a cascading process in the blood stream and cellular level regulatory dynamics. We analyse the existence and stability of equilibria and show that this low-dimensional, nonlinear model exhibits bistability between a low and a high cholesterol state. A sensitivity analysis indicates that the intracellular concentration of cholesterol is robust to parametric variations while the plasma cholesterol can vary widely. We show how the dynamical response to time-dependent inputs can be used to diagnose the state of the system. We also establish the connection between parameters in the system and medical and genetic conditions.

Can the modified Allen's test always detect sufficient collateral flow in the hand? A computational study

Blood flow in the largest arteries of the arm up to the digital arteries is numerically modelled using the one-dimensional equations of pressure and flow wave propagation in compliant vessels. The model can be applied to different anatomies of arterial networks and can simulate compression of arteries, these allowing us to simulate the modified Allen's test (MAT) and to assess its suitability for the detection of sufficient collateral flow in the hand if radial blood supply is interrupted. The test measures blood flow in the superficial palmar arch before and during compression of the radial artery. The absence of reversal flow in the palmar arch with the compression indicates insufficient collateral flow and is referred to as a positive MAT. This study shows that small calibres of the superficial palmar arch and insufficient compression of the radial artery can lead to false-positive results. Measurement of the drop in digital systolic pressures with compression of the radial artery has proved to be a more sensitive test to predict the presence of sufficient ulnar collateral flow in networks with small calibres of the superficial palmar arch. However, this study also shows that digital pressure measurements can fail in detecting enough collateral flow if the radial artery is insufficiently compressed.

Modelling the circle of Willis to assess the effects of anatomical variations and occlusions on cerebral flows

Blood flow in the circle of Willis (CoW) is modelled using the 1-D equations of pressure and flow wave propagation in compliant vessels. The model starts at the left ventricle and includes the largest arteries that supply the CoW. Based on published physiological data, it is able to capture the main features of pulse wave propagation along the aorta, at the brachiocephalic bifurcation and throughout the cerebral arteries. The collateral ability of the complete CoW and its most frequent anatomical variations is studied in normal conditions and after occlusion of a carotid or vertebral artery (VA). Our results suggest that the system does not require collateral pathways through the communicating arteries to adequately perfuse the brain of normal subjects. The communicating arteries become important in cases of missing or occluded vessels, the anterior communicating artery (ACoA) being a more critical collateral pathway than the posterior communicating arteries (PCoAs) if an internal carotid artery (ICA) is occluded. Occlusions of the VAs proved to be far less critical than occlusions of the ICAs. The worst scenario in terms of reduction in the mean cerebral outflows is a CoW without the first segment of an anterior cerebral artery combined with an occlusion of the contralateral ICA. Furthermore, in patients without any severe occlusion of a carotid or VA, the direction of flow measured at the communicating arteries corresponds to the side of the CoW with an absent or occluded artery. Finally, we study the effect of partial occlusions of the communicating arteries on the cerebral flows, which again confirms that the ACoA is a more important collateral pathway than the PCoAs if an ICA is occluded.

Developing a tissue perfusion sensor

The development of a electrochemical tissue perfusion sensor is presented. The sensor is a platinum/platinum ring-disc microelectrode that relies on the principle of collector-generator to monitor mass transport within its vicinity. Tissue perfusion is a mass transport mechanism that describes the movement of respiratory gases, nutrients and metabolites in tissue. The sensor's capability of detecting perfusion at the cellular level in a continuous fashion is unique. This sensor will provide insight into the way nutrients and metabolites are transported in tissue especially in cases were perfusion is low such as in wounds or ischemic tissue. We present experimental work for the development and testing of the sensors in vitro. Experimental flow recordings in free steam solutions as well as the flow through tissue-like media are shown. Tests on post operative human tissue are also presented. The sensor's feature such as the continuous recoding capacities, spatial resolution and the measurement range from ml/min to microl/min are highlighted.

Effects of osmotic pressure in the extracellular matrix on tissue deformation

In soft tissues, large molecules such as proteoglycans trapped in the extracellular matrix (ECM) generate high levels of osmotic pressure to counter-balance external pressures. The semi-permeable matrix and fixed negative charges on these molecules serve to promote the swelling of tissues when there is an imbalance of molecular concentrations. Structural molecules, such as collagen fibres, form a network of stretch-resistant matrix, which prevents tissue from over-swelling and keeps tissue integrity. However, collagen makes little contribution to load bearing; the osmotic pressure in the ECM is the main contributor balancing external pressures. Although there have been a number of studies on tissue deformation, there is no rigorous analysis focusing on the contribution of the osmotic pressure in the ECM on the viscoelastic behaviour of soft tissues. Furthermore, most previous works were carried out based on the assumption of infinitesimal deformation, whereas tissue deformation is finite under physiological conditions. In the current study, a simplified mathematical model is proposed. Analytic solutions for solute distribution in the ECM and the free-moving boundary were derived by solving integro-differential equations under constant and dynamic loading conditions. Osmotic pressure in the ECM is found to contribute significantly to the viscoelastic characteristics of soft tissues during their deformation.

Wave-energy patterns in carotid, brachial, and radial arteries: a noninvasive approach using wave-intensity analysis

The study of wave propagation at different points in the arterial circulation may provide useful information regarding ventriculoarterial interactions. We describe a number of hemodynamic parameters in the carotid, brachial, and radial arteries of normal subjects by using noninvasive techniques and wave-intensity analysis (WIA). Twenty-one normal adult subjects (14 men and 7 women, mean age 44 ± 6 yr) underwent applanation tonometry and pulsed-wave Doppler studies of the right common carotid, brachial, and radial arteries. After ensemble averaging of the pressure and flow-velocity data, local hydraulic work was determined and a pressure-flow velocity loop was used to determine local wave speed. WIA was then applied to determine the magnitude, timings, and energies of individual waves. At all sites, forward-traveling (S) and backward-traveling (R) compression waves were observed in early systole. In mid- and late systole, forward-traveling expansion waves (X and D) were also seen. Wave speed was significantly higher in the brachial (6.97 ± 0.58 m/s) and radial (6.78 ± 0.62 m/s) arteries compared with the carotid artery (5.40 ± 0.34 m/s; P < 0.05). S-wave energy was greatest in the brachial artery (993.5 ± 87.8 mJ/m2), but R-wave energy was greatest in the radial artery (176.9 ± 19.9 mJ/m2). X-wave energy was significantly higher in the brachial and radial arteries (176.4 ± 32.7 and 163.2 ± 30.5 mJ/m2, respectively) compared with the carotid artery (41.0 ± 9.4 mJ/m2; P < 0.001). WIA illustrates important differences in wave patterns between peripheral arteries and may provide a method for understanding ventriculo-arterial interactions in the time domain.

Wave intensity in the ascending aorta: effects of arterial occlusion

We examine the effects of arterial occlusion on the pressure, velocity and the reflected waves in the ascending aorta using wave intensity analysis. In 11 anaesthetised, open-chested dogs, snares were used to produce total arterial occlusion at 4 sites: the upper descending aorta at the level of the aortic valve (thoracic); the lower thoracic aorta at the level of the diaphragm (diaphragm); the abdominal aorta between the renal arteries (abdominal) and the left iliac artery, 2 cm downstream from the aorta iliac bifurcation (iliac). Pressure and flow in the ascending aorta were measured, and data were collected before and during the occlusion. During thoracic and diaphragm occlusions a significant increase in mean aortic pressure (46% and 23%) and in wave speed (25% and 10%) was observed, while mean flow rate decreased significantly (23% and 17%). Also, the reflected compression wave arrived significantly earlier (45% and 15%) and its peak intensity was significantly greater (257% and 125%), all compared with control. Aortic occlusion distal to the renal arteries, however, caused an indiscernible change in the pressure and velocity waveforms, and in the intensities and timing of the waves in the forward and backward directions. The measured pressure and velocity waveforms are the result of the interaction between the heart and the arterial system. The separated pressure, velocity and wave intensity are required to provide information about arterial hemodynamic such as the timing and magnitude of the forward and backward waves. The net wave intensity is simpler to calculate but provides information only about the predominant direction of the waves and can be misleading when forward and backward waves of comparable magnitudes are present simultaneously.

Wave propagation in a model of the arterial circulation

The propagation of the arterial pulse wave in the large systemic arteries has been calculated using a linearised method of characteristics analysis to follow the waves generated by the heart. The model includes anatomical and physiological data for the 55 largest arteries adjusted so that the bifurcating tree of arteries is well matched for forward travelling waves. The peripheral arteries in the model are terminated by resistance elements which are adjusted to produce a physiologically reasonable distribution of mean blood flow. In the model, the pressure and velocity wave generated by the contraction of the left ventricle propagates to the periphery where it is reflected. These reflected waves are re-reflected by each of the bifurcations that they encounter and a very complex pattern of waves is generated. The results of the calculations exhibit many of the features of the systemic arteries, including the increase of the pulse pressure with distance away from the heart as well as the initial decrease and then the large increase in the magnitude of back flow during late systole going from the ascending aorta to the abdominal aorta to the arteries of the leg. The model is then used to study the effects of the reflection or absorption of waves by the heart and the mechanisms leading to the incisura are investigated. Calculations are carried out with the total occlusion of different arterial segments in order to model experiments in which the effects of the occlusion of different arteries on pressure and flow in the ascending aorta were measured. Finally, the effects of changes in peripheral resistance on pressure and velocity waveforms are also studied. We conclude from these calculations that the complex pattern of wave propagation in the large arteries may be the most important determinant of arterial haemodynamics.

Semiautomated computer analysis of vessel growth in preterm infants without and with ROP

AIMS

To measure characteristics of the retinal blood vessels close to the optic disc in full term and preterm infants, with and without retinopathy of prematurity (ROP), using digital imaging. To determine whether these measures are indicative of the presence or severity of ROP in the retinal periphery.

METHODS

52 digital fundus images from 42 babies were analysed with a semiautomated analysis program developed at Imperial College London. Analysis was limited to the principal temporal vessels close to the optic disc: recording venular diameter and arteriolar diameter and tortuosity.

RESULTS

Each result was categorised by the gestational age of the infant ("very premature" 24-27 weeks, "moderately premature" 28-31 weeks, and "near term" > or =32 weeks) and by the highest stage of ROP present ("no ROP," "mild ROP" stage 1 or 2, and "severe ROP" stage 3). Arteriolar tortuosity was found to vary significantly (Kruskal-Wallis p=0.002) with ROP severity. Although venular and arteriolar diameters increased monotonically with ROP severity the differences were not significant. Venular diameter, arteriolar diameter, and arterial tortuosity did not vary significantly between gestational age groups.

CONCLUSIONS

This study confirms it is possible to quantify the size and tortuosity of retinal blood vessels in term and preterm babies using digital image analysis software. This method detected significant increases in arteriolar tortuosity with increasing ROP severity.

Local and regional wave speed in the aorta: effects of arterial occlusion

Arterial wave speed is widely used to determine arterial distensibility and has been utilised as a surrogate marker for vascular disease. A comparison between the results of the traditional foot-to-foot method for measuring wave speed to those of the pressure-velocity loop (PU-loop) method is one of the primary objectives of this paper. We also investigate the regional wave speed along the aorta, and the effect of arterial occlusion on the PU-loop measured in the ascending aorta. In 11 anaesthetised dogs, a total occlusion lasting 3 min was produced at four sites: upper thoracic, diaphragm, abdominal and left iliac artery. Pressure and flow in the ascending aorta and pressure proximal to the occlusion site were measured, and data were collected before, during the occlusion and after the occlusion had been removed. In control conditions, the wave speeds determined by the PU-loop in the aortic root were systematically lower than those measured by the foot-to-foot method. During thoracic and diaphragm occlusions, mean aortic pressure and wave speed increased significantly but returned to control values after each occlusion had been removed. The PU-loop is an objective and easy to use method for determining wave speed and can be advantageous for use in short arterial segments when local measurements of pressure and velocity are available.

Quantification of the non-planarity of the human carotid bifurcation

The carotid bifurcation has been a region of particular interest due to its predilection for clinically significant atherosclerosis. It has been shown that the vessel geometry is a major determinant of the local haemodynamic properties which are believed to be associated with the location of atherosclerotic lesions. Current knowledge of the geometry of the carotid bifurcation is insufficient and restricted to basic geometric parameters. To provide some means of quantifying the degree of complexity of the 3D shape of the bifurcation, we made an initial attempt by evaluating the non-planarity of an arterial bifurcation based upon the singular value decomposition theorem. In this paper we present our results obtained on the right carotid bifurcations of six normal subjects, each of whom was scanned twice using the 2D time-of-flight MR sequence. The acquired 2D cross sectional images were processed by using our in-house software which comprises 2D segmentation, 3D reconstruction and smoothing. The centroids of each transverse slices were determined and used as input data for the non-planarity analysis. Our results using the singular value decomposition method have demonstrated discernible differences in non-planarity among individuals. Comparisons with the planarity definition proposed by other investigators suggest that the singular value decomposition method offers more information about the linearity and planarity of the bifurcation. However, it is also realised that a single measure of non-planarity can never fully characterise a bifurcation owing to the great variety of geometries.

Measurements of wave speed and reflected waves in elastic tubes and bifurcations

Wave intensity analysis is a time domain method for studying waves in elastic tubes. Testing the ability of the method to extract information from complex pressure and velocity waveforms such as those generated by a wave passing through a mismatched elastic bifurcation is the primary aim of this research. The analysis provides a means for separating forward and backward waves, but the separation requires knowledge of the wave speed. The PU-loop method is a technique for determining the wave speed from measurements of pressure and velocity, and investigating the relative accuracy of this method is another aim of this research. We generated a single semi-sinusoidal wave in long elastic tubes and measured pressure and velocity at the inlet, and pressure at the exit of the tubes. In our experiments, the results of the PU-loop and the traditional foot-to-foot methods for determining the wave speed are comparable and the difference is on the order of 2.9+/-0.8%. A single semi-sinusoidal wave running through a mismatched elastic bifurcation generated complicated pressure and velocity waveforms. By using wave intensity analysis we have decomposed the complex waveforms into simple information of the times and magnitudes of waves passing by the observation site. We conclude that wave intensity analysis and the PU-loop method combined, provide a convenient, time-based technique for analysing waves in elastic tubes.

Changes in aortic rotational flow during cardiopulmonary bypass studied by transesophageal echocardiography and magnetic resonance velocity imaging: a potential mechanism for atheroembolism during cardiopulmonary bypass

The human aorta is a curved conduit with a complex three-dimensional geometry. The curvature influences axial velocity distribution and introduces transverse velocity components. Rotational flow in the aorta can be demonstrated during normal pulsatile flow using transesophageal echocardiography. Cardiopulmonary bypass may affect the pattern of rotational flow in the aorta and thus influence the generation of atheroemboli. We investigated rotational flow in the descending aorta using color flow mapping and pulse-wave Doppler on transesophageal echocardiography before and during cardiopulmonary bypass. We correlated our findings with magnetic resonance velocity imaging in a model of a human aortic arch connected to a cardiopulmonary bypass circuit. Before cardiopulmonary bypass, rotational flow in the descending aorta was seen in 37 of 40 patients (93%). In the majority of these patients, rotational flow was in the clockwise direction during systole, looking in the direction of flow (30 of 37 patients, 81%, P < 0.01 vs counterclockwise rotation). During cardiopulmonary bypass, there were almost equal numbers of patients with clockwise (18 patients) and counterclockwise rotation (19 patients). Forty-seven percent of patients with clockwise rotation before cardiopulmonary bypass developed reversal in the direction of rotation to counterclockwise during cardiopulmonary bypass. Twenty-nine percent of patients with counterclockwise rotation developed reversal of the direction of rotation during cardiopulmonary bypass. The transverse velocity component increased during cardiopulmonary bypass regardless of the direction of rotation. We also demonstrated clockwise rotation in the descending aorta of a human aortic arch model connected to a cardiopulmonary bypass circuit using magnetic resonance velocity mapping. Before cardiopulmonary bypass, rotation was predominantly clockwise, while during cardiopulmonary bypass, there was no preferred direction of rotation. The geometry of the aorta, which is fairly constant in all patients, imposes handedness to aortic flow before cardiopulmonary bypass. However, during cardiopulmonary bypass, other extrinsic factors such as aortic cannula orientation may influence the direction of rotation. The change in direction of rotational flow and increase in its transverse velocity component during cardiopulmonary bypass may have implications for atheroembolism and arterial branch perfusion during extended periods of non-pulsatile flow.

Arterial waves in humans during peripheral vascular surgery

The purpose of this study was to investigate the effect of aortic clamping on arterial waves during peripheral vascular surgery. We measured pressure and velocity simultaneously in the ascending aorta, in ten patients (70+/-5 years) with aortic-iliac disease intra-operatively. Pressure was measured using a catheter tip manometer, and velocity was measured using Doppler ultrasound. Data were collected before aortic clamping, during aortic clamping and after unclamping. Hydraulic work in the aortic root was calculated from the measured data, the reflected waves were determined by wave-intensity analysis and wave speed was determined by the PU-loop (pressure-velocity-loop) method; a new technique based on the 'water-hammer' equation. The wave speed is approx. 32% (P<0.05) higher during clamping than before clamping. Although the peak intensity of the reflected wave does not alter with clamping, it arrives 30 ms (P<0.05) earlier and its duration is 25% (P<0.05) longer than before clamping. During clamping, left ventricule (LV) hydraulic systolic work and the energy carried by the reflected wave increased by 27% (P<0.05) and 20% (P<0.05) respectively, compared with before clamping. The higher wave speed during clamping explains the earlier arrival of the reflected waves suggesting an increase in the afterload, since the LV has to overcome earlier reflected compression waves. The longer duration of the reflected wave during clamping is associated with an increase in the total energy carried by the wave, which causes an increase in hydraulic work. Increased hydraulic work during clamping may increase LV oxygen consumption, provoke myocardial ischaemia and hence contribute to the intra-operative impairment of LV function known in patients with peripheral vascular disease.

Left ventricular wave speed

Left ventricular (LV) wave speed (LVWS) was studied experimentally and confirmed in theory. Combining the definition of elastance (E) with the equations for the conservation of mass and momentum shows that LVWS is proportional to the square root of ELA, where L is long-axis length and A is the cross-sectional area, and the density of the blood. (We defined ELA = gamma, where gamma is compressibility.) We studied nine open chest, anesthetized dogs, three of which were studied during caval constriction when LV end-diastolic pressure was < or =0 mmHg. The hearts were paced at approximately 90 beats/min, and LV cross-sectional area was measured by using two pairs of ultrasonic crystals; E was calculated from the LV pressure-area loop. A pulse generator was connected to the LV apex, and LVWS was measured by using two pressure transducers: one near the apex and the other near the base. Their distance was measured roentgenographically and compared with the diameter of a reference ball. LVWS ranged from approximately 1 m/s during diastole to approximately 10 m/s during systole. The slope of the log c (where c is wave speed) vs. log gamma was 0.546, which is in agreement with theory (0.5). When gamma < or = 0, LVWS was approximately 1.5 m/s.

Determination of wave speed and wave separation in the arteries

Considering waves in the arteries as infinitesimal wave fronts rather than sinusoidal wavetrains, the change in pressure across the wave front, dP, is related to the change in velocity, dU, that it induces by the "water hammer" equation, dP=+/-rhocdU, where rho is the density of blood and c is the local wave speed. When only unidirectional waves are present, this relationship corresponds to a straight line when P is plotted against U with slope rhoc. When both forward and backward waves are present, the PU-loop is no longer linear. Measurements in latex tubes and systemic and pulmonary arteries exhibit a linear range during early systole and this provides a way of determining the local wave speed from the slope of the linear portion of the loop. Once the wave speed is known, it is also possible to separate the measured P and U into their forward and backward components. In cases where reflected waves are prominent, this separation of waves can help clarify the pattern of waves in the arteries throughout the cardiac cycle.

Negative wave reflections in pulmonary arteries

The pulmonary arterial branching pattern suggests that the early systolic forward-going compression wave (FCW) might be reflected as a backward-going expansion wave (BEW). Accordingly, in 11 open-chest anesthetized dogs we measured proximal pulmonary arterial pressure and flow (velocity) and evaluated wave reflection using wave-intensity analysis under low-volume, high-volume, high-volume + 20 cmH2O positive end-expiratory pressure (PEEP), and hypoxic conditions. We defined the reflection coefficient R as the ratio of the energy of the reflected wave (BEW [-]; backward-going compression wave, BCW [+]) to that of the incident wave (FCW [+]). We found that R = -0.07 +/- 0.02 under low-volume conditions, which increased in absolute magnitude to -0.20 +/- 0.04 (P < 0.01) under high-volume conditions. The addition of PEEP increased R further to -0.26 +/- 0.02 (P < 0.01). All of these BEWs were reflected from a site ~3 cm downstream. During hypoxia, the BEW was maintained and a BCW appeared (R = +0.09 +/- 0.03) from a closed-end site ~9 cm downstream. The normal pulmonary arterial circulation in the open-chest dog is characterized by negative wave reflection tending to facilitate right ventricular ejection; this reflection increases with increasing blood volume and PEEP.

Wave-intensity analysis: a new approach to coronary hemodynamics

In 10 anesthetized dogs, we measured high-fidelity left circumflex coronary (P(LCx)), aortic (P(Ao)), and left ventricular (P(LV)) pressures and left circumflex velocity (U(LCx); Doppler) and used wave-intensity analysis (WIA) to identify the determinants of P(LCx) and U(LCx). Dogs were paced from the right atrium (control 1) or right ventricle by use of single (control 2) and then paired pacing to evaluate the effects of left ventricular contraction on P(LCx) and U(LCx). During left ventricular isovolumic contraction, P(LCx) exceeded P(Ao), paired pacing increasing the difference. Paired pacing increased DeltaP(X) (the P(LCx)-P(Ao) difference at the P(Ao)-P(LV) crossover) and average dP(LCx)/dt (P < 0.0001 for both). During this time, WIA identified a backward-going compression wave (BCW) that increased P(LCx) and decreased U(LCx); the BCW increased during paired pacing (P < 0.0001). After the aortic valve opened, the increase in P(Ao) caused a forward-going compression wave that, when it exceeded the BCW, caused U(LCx) to increase, despite P(LV) and (presumably) elastance continuing to increase. Thus WIA identifies the contributions of upstream (aortic) and downstream (microcirculatory) effects on P(LCx) and U(LCx).

The deformation of spherical vesicles with permeable, constant-area membranes: application to the red blood cell

The deformation of an initially spherical vesicle of radius a with a permeable membrane under extensive forces applied at its poles is calculated as a function of the in-plane shear modulus, H, and the out-of-plane bending modulus, B, using an axisymmetric theory that is valid for large deformations. Suitably nondimensionalized, the results depend upon a single nondimensional parameter, C identical with a(2)H/B. For small deformations, the calculated force-polar strain curves are linear and, under these conditions, the slope of the curve determines only C, not the values of H and B separately. Independent determination of H and B from experimental measurements require deformations that are large enough to produce nonlinear behavior. Simple approximations for large and small C are given, which are applied to experimental measurements on red blood cell ghosts that have been made permeable by treatment with saponin.

Glucose production by the human placenta in vivo

The human placenta transports glucose by facilitated diffusion down a concentration gradient from mother to fetus. It has previously been considered incapable of glucose synthesis. However, recent work has demonstrated the presence in placental tissue of glucose-6-phosphatase, which is required for the final step in the synthesis of glucose. Following continuous intravenous infusion into the maternal circulation of the stable isotope, 6,6-(2)H(2)glucose, during elective caesarean section, we have observed isotope dilution in the umbilical vein, without further dilution in the umbilical artery. Using a mathematical model containing maternal, placental and fetal compartments, the data were compatible with the release of glucose by the placenta. We conclude that the human placenta at term can produce glucose.

Analysis of wave reflections in the arterial system using wave intensity: a novel method for predicting the timing and amplitude of reflected waves

The timing and amplitude of reflected arterial waves in the ascending aorta were studied by analysis of the aortic pressure waveform and were compared with those derived using wave intensity analysis. Wave intensity analysis considers aortic pressure changes to be the result of forward and backward wavelets carrying energy. Wave intensity (dI = dPdU) is calculated from changes in pressure (dP) and flow velocity (dU), and its sign indicates the direction of travel of propagating wavelets (positive for forward-traveling waves and vice versa). We measured aortic pressure and flow velocity in 14 patients, mean age 60+/-9 years, with three-vessel coronary artery disease at the time of surgical revascularization. The travel time of the reflected wave derived from analysis of the aortic pressure waveform (tp) was measured from the foot of the aortic pressure waveform to the inflection point of the aortic pressure (derived objectively from the zero of second derivative of aortic pressure). From wave intensity analysis, the travel time of the reflected wave was measured to the onset of the wave intensity of the backward-traveling wave dI_ (t(i)), and to the onset of the separated backward pressure wave (t(b)). All patients showed an aortic pressure waveform characterized by an inflection point on the rising limb of the aortic pressure, followed by a secondary rise in pressure, representing the return of reflected waves. Wave intensity analysis consistently showed a negative peak in mid systole, the timing of its onset corresponding closely to the inflection point of the aortic pressure. The travel time of the reflected wave derived from the analysis of the aortic pressure waveform (t(p)) was 121+/-21ms and showed close agreement with ti (118+/-28 ms) and t(b) (115+/-29ms), with mean differences of 4 and 6ms, and 95% confidence intervals of difference (-2 to 7 ms) and (1 to 12ms), respectively. The augmentation index, a measure of the secondary increase in aortic pressure due to reflected waves, was significantly correlated with the magnitude of dI_ (r = 0.63, P < 0.001). Wave intensity is a quantity that indicates the rate of energy flux due to wave travel and since its value is positive for forward-traveling waves and negative for backward-traveling waves, its calculation allows the timing of reflected waves to be accurately predicted. Furthermore, the magnitude of wave intensity in backward-traveling waves (dI_) is related to the augmentation index and may provide a measure of the amplitude of the reflected wave. This analysis of the arterial system is done in the time domain and therefore can be easily applied to assess temporal changes in arterial characteristics.

Physicochemical properties of arterial elastin and its associated glycoproteins

Microfibrillar glycoproteins are a significant component of vascular elastic tissue, but little is known about their contribution to vascular physiology and pathology. We have investigated some physicochemical properties of the glycoproteins that may be pertinent to these roles. Because of the difficulty in isolating intact glycoproteins in a form and quantity suitable for physicochemical examination, we based our analysis on a comparison of the properties of porcine thoracic aorta and pulmonary artery extracted with GuHCl and collagenase (preparation GC) and after further treatment with dithioerythritol to remove glycoproteins (preparation GC/DTE). Amino acid analysis showed that GC/DTE had the amino acid composition of pure elastin while GC contained a higher proportion of polar amino acids, particularly in the aortic preparation. GC stained with alcian blue, particularly in the intimal region, but GC/DTE did not. GC had a higher water content and a slower viscoelastic response and the circumferential elastic modulus was approximately 50% lower (whether expressed in terms of sample weight or elastin content). Clearly, therefore, the microfibrils do not stiffen the network and may prevent the alignment of elastin fibers in the circumferential direction. Their effect on hydration may arise either because they impose mechanical constraints on the geometry of the network or because they modify the inter- and intramolecular hydrophobic or electrostatic interactions that influence the tissue organization and hydration. Molecular probe measurements of the intrafibrillar pore structure using radiolabeled and fluorescent probes showed that removal of the microfibrils caused a slight decrease in the extrafibrillar water space and a larger decrease in the intrafibrillar water space. Sucrose, a small probe molecule, was able to penetrate most of the intrafibrillar water space when microfibrils were present but was virtually excluded when they were not. Potentiometric titration and radiotracer assays of ion binding both showed that the microfibrils contribute a considerable negative charge (-9 mumoles/g wet tissue in the aortic preparation and -16 mumoles/g wet weight in the pulmonary artery) and increase calcium binding by approximately 30%.

Effects of the glycocalyx on the electrophoretic mobility of red cells and on streaming potentials in blood vessels: predictions of a structurally-based model

The polyelectrolyte layer coating mammalian cells, known as the glycocalyx, may be important in communicating flow information to the cell. In this paper, the layer is modelled as a semi-infinite, doubly periodic array of parallel charged cylinders. The electric potential and ion distributions surrounding such an array are found using the linearized Poisson-Boltzmann equation and an iterative domain decomposition technique. Similar methods are used to calculate Strokes flows, driven either by a shear at infinity or by an electric field, parallel or transverse to the cylinders. The resulting electric streaming currents due to flow over endothelial cells, and the electrophoretic mobilities of red blood cells are deduced as functions of polymer concentration and electrolyte molarity. It is shown that only the top portion of the layer is important in these effects.

Measurement of the charge properties of articular cartilage by an electrokinetic method

The charge structure of the surface of articular cartilage determines its interactions with the macromolecules and cells of synovial fluid. It may thereby be important to the physiological function and pathological degeneration of the tissue. To determine whether the electrokinetic properties of the surface differ from those of the bulk tissue, we measured the streaming potential generated by the flow of electrolyte over the surface of a cartilage plug mounted in a chamber built for that purpose. We then calculated the effective surface charge density. In nonfibrillated cartilage from the human femoral head, the surface charge density, 0.037+/-0.004 Cm(-2) (mean+/-SD), was approximately half that measured at the surface of slices cut from the middle and deep zones. In addition, the surface charge density fell relatively little at low pH; this is consistent with a higher proportion of strongly acidic groups. The variations in surface charge density were found to be similar to those in total fixed charge density in the slices by the tracer cation method. Therefore, no evidence exists that the actual surface differs in composition from the immediately underlying matrix. The addition of synovial fluid (0.0025 ml/ml) to the superfusing solution reduced the surface charge density by 25+/-9% (n=5), and we attributed this to the binding of synovial-fluid macromolecules.

The osmotic pressure of chondroitin sulphate solutions: experimental measurements and theoretical analysis

We used equilibrium dialysis to measure the osmotic pressure of chondroitin sulphate (CS) solutions as a function of their concentration and fixed charge density (FCD) and the ionic strength and composition of the solution. Osmotic pressure varied nonlinearly with the concentration of chondroitin sulphate and in 0.15 M NaCl at FCDs typical of uncompressed cartilage (approximately 0.4 mmol/g extrafibrillar H2O) was approximately 3 atmospheres. Osmotic pressure fell by 60% as solution ionic strength increased up to about 1 M, but remained relatively constant at higher ionic strengths. The ratio of Ca2+ to Na+ in the medium was a minor determinant of osmotic pressure. The data are compared with a theoretical model of the electrostatic contribution to osmotic pressure calculated from the Poisson-Boltzmann equation using a rod-in-cell model for CS. The effective radius of the polyelectrolyte rod is taken as a free parameter. The model qualitatively reproduces the non-linear concentration dependence, but underestimates the osmotic pressure by an amount that is independent of ionic strength. This difference, presumably arising from oncotic and entropic effects, is approximately 1/3 of the total osmotic pressure at physiological polymer concentrations and ionic strength.

The contributions of glycosaminoglycans, collagen and other interstitial components to the hydraulic resistivity of porcine aortic wall

A pressure-driven flux of water occurs across the arterial wall in vivo. We have investigated the role of several interstitial components in determining the resistance of the wall to this flow. Pieces of porcine thoracic aorta were modified by thermal denaturation, enzymatic digestion or disruptive chemical treatments. The effect of these procedures on the wall content of glycosaminoglycans, collagen and elastin was determined by biochemical assay of uronic acid and hydroxyproline. Effects on hydraulic conductivity were measured by using a flow cell in which tissue was free to deform under applied pressure. Untreated tissue showed considerable variation in uronic acid content but conductivities were substantially less variable and averaged 0.75 x 10(-12) cm4/dyne.s. In tissue autoclaved for < 1 h, resistivity increased, possibly because interstitial components had been denatured but not removed from the wall. After longer periods, resistivity decreased by a factor of one hundred. More specific treatments showed that resistivity decreased by up to a factor of ten when glycosaminoglycans were removed and by a similar factor when collagen was removed. Tissue in which both were removed showed a hundred-fold decrease in resistivity. As with tissue subjected to prolonged autoclaving, the resistivity was still an order of magnitude higher than that of alkali- or acid-extracted elastin despite an apparently similar composition, suggesting the existence of a non-assayed component with important properties. The resistivity of the samples was decreased further by treatment with chymotrypsin, consistent with this component being microfibrillar protein.

The circadian rhythm of leptin is preserved in growth hormone deficient hypopituitary adults

OBJECTIVE

Leptin acts as a satiety factor in regulating food intake and body homeostasis, but its regulation is not well defined. Specific leptin receptors have been found in the brain and it has been hypothesized that leptin production by adipose tissue is under neuroendocrine control. A circadian rhythm has been demonstrated with highest leptin levels between midnight and early morning hours. The possibility that hypopituitarism (or pituitary surgery +/- radiotherapy) abolishes this leptin rhythm was investigated by measuring serum leptin levels during a 24-h period in patients with impaired pituitary function.

PATIENTS AND DESIGN

Circulating leptin levels were measured hourly over 24-h in 14 hypopituitary patients (8 women and 6 men) using a sensitive and specific radioimmunoassay. Hypopituitarism was the consequence of pituitary tumors treated surgically and/or with radiotherapy. All patients were GH deficient and were receiving conventional replacement with cortisol (n = 13), thyroxine (n = 12) and desmopressin (n = 4) but not with GH.

RESULTS

A significant diurnal variation in circulating leptin concentrations was observed in 13 of the 14 patients. The mean (+/- SEM) leptin levels for 8 women were 51.9 (+/- 10.7) ng/ml and for 6 men 11.0 (+/- 2.0) micrograms/l. The overall lowest leptin levels (29.3 +/- 7.9 ng/ml) were observed at 0830 h after overnight fasting, rising gradually to maximum levels (43.0 +/- 9.8 ng/ml) at 0200 h declining thereafter towards fasting values. The mean (+/- SEM) magnitude of circadian variation in absolute leptin levels from the calculated mean level for each patient was 5.6 (+/- 1.2) ng/ml (8.4 +/- 1.4 for women and 1.9 +/- 0.3 for men). The mean (+/- SEM) of the ratio of the amplitude versus mean leptin levels over 24 h for each individual patient was 0.18 (+/- 0.02) (0.19 +/- 0.03 for women and 0.18 +/- 0.02 for men).

CONCLUSIONS

A circadian rhythm for leptin is generally present in hypopituitary patients who had undergone pituitary surgery and/or radiotherapy, with the highest serum leptin levels being obtained between midnight and early morning hours. Although some patients had some residual pituitary activity, intact hypothalamic-pituitary function is not essential for leptin's circadian rhythm.

Movement of spherical particles in capillaries using a boundary singularity method

As a first step to investigate the motion of blood cells in capillaries, we have studied the movement of a spherical particle falling in a vertical cylindrical tube using a boundary singularity method. The tube is filled with a Newtonian viscous fluid which would otherwise be stationary. The Reynolds number of the flow is much less than one. The sphere falls at arbitrary positions in the tube and is free to rotate. Point forces, Stokeslets, with unknown strength and direction, are distributed on the surfaces of the tube and the sphere. By forcing the flow field generated by all of the Stokeslets to satisfy proper boundary conditions, we solve for the strength and direction of each Stokeslet. The velocity, U, and rotation, omega, of the sphere are then calculated from a force and a torque balance. For a sphere falling on the axis of the tube, our results agree with Bohlin's approximate solution. When the sphere takes eccentric positions in the tube, it rotates as it translates down the tube, the direction of rotation being opposite to that it would have if the sphere rolled along the nearest side of the tube. This results from the zero net torque on the sphere and facilitates flow passing around the sphere. As the distance between the centre of the sphere and the axis of the tube increases, omega increases almost linearly, while U changes little. When the radius of the tube increases, U increases and approaches the Stokes velocity, while omega decreases rapidly. The boundary singularity method is relatively simple compared to other numerical methods and can be extended much more easily to the complex geometries typical of blood cells.

Wave-intensity analysis: a new approach to left ventricular filling dynamics

In order to explore a new approach to the analysis of diastolic dysfunction, we adapted wave-intensity analysis (WIA), a time-domain analysis that provides information regarding both upstream and downstream events, to left ventricular (LV) filling. WIA considers the pressure and flow waves as summations of successive wavelets, characterised by the direction they travel and by the sign of the pressure gradient associated with them. Wave intensity is the product, dPdU, calculated from the incremental differences in LV pressure (dP) and mitral velocity (dU) and, during the diastolic filling interval, yields up to five dPdU peaks. Peak 1 is caused by backward-travelling expansion waves that accelerate the blood while LV pressure falls, and may be related to "diastolic suction". Peak 2 is caused by forward-travelling compression waves which occur if acceleration continues after LV pressure begins to increase. Peak 3 is caused by backward compression waves and is associated with rising LV pressure and deceleration. Peak 4 is caused by forward compression waves and is associated with the increasing LV pressure and acceleration caused by atrial contraction. Peak 5 is caused by backward compression waves and is associated with increasing pressure and deceleration. These preliminary observations suggest that WIA can be useful in describing the mechanics of LV filling and, after much further work has been accomplished, it might prove useful in the detection and characterization of diastolic dysfunction.

Measurements of oxygenation and perfusion in skeletal muscle using multiple microelectrodes

This paper describes an apparatus to measure tissue oxygenation and perfusion (as measured by the wash-in rate of gaseous hydrogen) simultaneously at multiple points in muscle using needle microelectrodes. The development of suitable electrodes and apparatus is described, as well as the development of the method and its validation. In particular, the potential for tissue damage secondary to electrode insertion, the need for in vivo voltammetric determination of the operating potential and the extent of any electrode-tissue and of electrode-electrode interactions are explored, and are shown to be insufficient in magnitude to affect the technique. Its subsequent use to characterise oxygenation and perfusion in rabbit skeletal muscle at rest is also described. In resting tibialis anterior muscle of the rabbit the mean pO2 was 18 +/- 13.3 mm Hg and the mean perfusion was 4.4 +/- 1.3 ml s-1 100 g-1. There was a heterogeneity in simultaneously-measured values of pO2 and perfusion at different points within muscle, and also a temporal variation at the same site. The spans between the highest and lowest simultaneously-measured values of pO2 in muscle ranged from 14 to 80 mm Hg, and for perfusion, from 1 to 12 mls-1 100 g-1. No significant correlation was evident from histological examination between either pO2 or perfusion and surrounding fibre type or capillary density.

Abnormal carotid arterial wall dynamics in symptom-free hypopituitary adults

OBJECTIVE

Although vascular mortality is increased in hypopituitary adults on routine replacement, there are limited data on the atherosclerotic process during life in these patients. Measurement of arterial stiffness may provide an index of early vascular changes that predispose to the development of major vascular accidents.

DESIGN

Thirty-four hypopituitary adults on conventional replacement therapy and 39 age- and sex-matched controls were studied. They had no history or clinical evidence of macrovascular disease. The common carotid artery distensibility coefficient (DC), compliance coefficient (CC) and arterial stiffness index (beta index) were calculated from high-resolution ultrasonic imaging of the two common carotid arteries and from the brachial blood pressure.

RESULTS

There was no difference between patients and controls in carotid diastolic diameter (mean +/- S.E.M) (5.55 +/- 0.16 vs 5.45 +/- 0.08 mm) and pulse pressure (6.66 +/- 0.30 vs 6.58 +/- 0.24 kPa). The increase in diameter during systole was significantly lower in the hypopituitary patients (0.39 +/- 0.02 vs 0.50 +/- 0.03 mm, P < 0.001). The DC was significantly lower in patients than in controls (24.2 +/- 2.29 vs 30.1 +/- 2.01 10(-3) kPa-1, P < 0.05). The carotid CC was also significantly lower in patients than in controls (5.7 +/- 0.49 vs 7.0 +/- 0.45 10(-7) m2 kPa-1, P < 0.05). The beta index was higher in the patient group (8.4 +/- 1.3 vs 5.9 +/- 0.37, P < 0.05). When men and women were considered separately, the differences between patients and controls were statistically significant in women but not in men and were more marked in the older women subgroup.

CONCLUSIONS

Asymptomatic hypopituitary adults (especially women) on conventional replacement therapy have increased stiffness of the common carotid arteries. These findings provide additional evidence for a process leading to premature atherosclerosis in this group of patients.

Interactions of elastin and aorta with sugars in vitro and their effects on biochemical and physical properties

Stiffening of blood vessel walls occurs in the early stages of atherosclerosis, and this process is known to occur earlier in diabetic subjects. The effect could be due, in part, to glycation. Although collagen is responsible for ensuring the ultimate tensile strength of the tissue, elastin largely determines the compliance of the vessel wall in the normal physiological range of pressures and this appears to be closely matched to haemodynamic requirements. Changes in elastin are therefore likely to affect optimal function of the tissue. We have investigated the susceptibility of elastin to glycation and effects of glycation on its mechanical and physicochemical properties. We found that purified elastin and a collagen-elastin preparation from the porcine thoracic aorta rapidly incorporated glucose and ribose, the extent increasing linearly with increasing concentration and reaching a maximum after 7 days at 37 degrees C. Biochemical analysis showed that about one of the five lysines available per elastin monomer was glycated after 12 days incubation at a sugar concentration of 250 mmol/l. In long-term incubations glycation was associated with the appearance of the advanced glycation end products, the fluorescent cross-link pentosidine and the non-fluorescent putative cross-link NFC-1. In both purified elastin and the whole elastin-collagen matrix the slope of the force-extension curve increased significantly with glycation. The greatest increase in stiffness was observed in the elastin-collagen preparation after ribose incubation (250 mmol/l for 1 month), where the slope, at large strain, increased by 56 +/- 19% (mean +/- SD, n = 12). The diameter of the tissue at 1 N force also changed: for elastin there was an increase in length of approximately 5%, but for the elastin-collagen there was a decrease of similar magnitude indicating that glycation introduces differential strains within the fibrous protein matrix. Potentiometric titration demonstrated that glycation was associated both with loss of basic groups and shifts in pK of the acidic groups, which indicated changes in the environment of the charge groups due to conformational rearrangements. Changes in ion binding were dependent on pH, and were consistent with a reduction in effective anionic charge. Calcium binding to elastin was increased at acid pH, but decreased at higher pH. We suggest that these effects are not only due to changes in the charge profile, but also in the conformation of the molecule resulting from glycation of the charged lysine and arginine side-chain residues.

Theoretical studies of steady-state transcapillary exchange in countercurrent systems

OBJECTIVE

As a first step in modeling microvascular exchange in the renal medulla, we developed mathematical models to explore the effects of blood flow, permeability, and anatomical arrangement of microvessels on the steady-state distribution of solute in the blood and the interstitial fluid (ISF).

METHODS

Single capillaries and countercurrent capillary loops were used to model microvessels that were surrounded by a secretory epithelium over either the whole or part of the capillary length. Solute concentration in the vessels and the ISF were derived analytically. We also derived approximate solutions that ignored axial diffusion of solute.

RESULTS

The full and approximate solutions were in good agreement with data based on measurements in the renal medulla. Model results revealed that concentration in the ISF falls rapidly with distance beyond the region of solute secretion and equilibrates with the concentration in capillaries, even with countercurrent exchange between the two limbs of the capillary loop. The ratio of the product of the permeability and area to the flow of the afferent limb, gamma 1, is an important parameter. When gamma 1 > 4, countercurrent exchange in a capillary loop facilitates a greater ISF concentration gradient than with a single capillary. Changes in flow also have a greater effect on this gradient.

CONCLUSION

The model of countercurrent exchange presented here not only demonstrates the sensitivity of interstitial concentration gradients of solute to flow through capillary loops but also reveals the importance of the absolute value of gamma 1 in determining the magnitude and direction of these gradients.

Blood velocity profiles in the human renal artery by Doppler ultrasound and their relationship to atherosclerosis

Blood velocity profiles were measured in the renal branch (diameter 5.9 +/- 1.3 mm) of the aortorenal bifurcation using a 20-MHz 80-channel pulsed Doppler velocimeter during retroperitoneal surgery in 10 patients. The peak Reynolds number was 1145 +/- 140 and the frequency parameter (Wormersley parameter) was 3.0 +/- 0.8. Immediately distal to the ostium of the renal artery, reverse flow, indicating flow separation, was observed near the cranial wall mainly during the first part of the cardiac cycle. There were flows from the cranial to the caudal side of the artery at this location, indicating the presence of strong secondary flows. Two diameters downstream of the ostium, the velocity profiles were skewed to the caudal side in all patients. Four diameters downstream, the flow profile was symmetrical (3 patients) or only slightly skewed (7 patients) and virtually parabolic throughout the cardiac cycle. These observations mean that the flow on the cranial side of the renal branch of the human aortorenal bifurcation is characterized by (1) a bidirectional oscillation of the flow, (2) separation of the flow during systole, and (3) low time-averaged shear rate. These blood velocity patterns may be related to the localization and development of atheromatous plaque that occurs preferentially in this region of the renal artery. Conversely, the unidirectional, axisymmetrical flow found in more distal parts of the renal artery are associated with a very low incidence of lesions.

Early diastolic left ventricular inflow pressures in normal subjects and patients with dilated cardiomyopathy. Reconstruction from pulsed Doppler echocardiography

OBJECTIVE

To estimate early diastolic left ventricular inflow pressures in normal subjects and patients with dilated cardiomyopathy, and thus to assess the potential effect of restoring forces.

METHODS

Early diastolic left ventricular inflow pressures were reconstructed using the ventricular blood as an accelerometer, by measuring velocity at 1 cm intervals within the left ventricle from mitral ring to apex by pulsed Doppler echocardiography, and differentiating the records to obtain the acceleration. Aortic component of second heart sound (A2) was used to fix relative timings. The local pressure gradient was determined from the acceleration at each level, and the total pressure drop during the acceleration (+ peak PD) and deceleration (- peak PD) phases of the filling interval were determined by summing the local increments. The total stroke volume (SV) at the left ventricular outflow tract and the mitral stroke distances (MSD) were also determined, using the time-velocity integral at mitral ring level. Effective flow orifice area was thus SV/MSD. Inflow jet width across the mitral valve was estimated by cross sectional colour Doppler flow mapping.

PATIENTS

32 patients with dilated cardiomyopathy with a dominant mitral E or summation wave, and 24 normal subjects of similar ages.

RESULTS

Normal + peak PD was 3.9 (SD 0.7) v 7.4 (2.2) mm Hg in dilated cardiomyopathy (P < 0.01). Normal - peak PD was 2.5 (0.9) v 5.6 (2.8) mm Hg in cardiomyopathy (P < 0.01). Normal effective flow orifice area was 5.9 (1.3) v 1.9 (0.8) [range 0.9 approximately 3.7] cm2 in cardiomyopathy (P < 0.01). This corresponded to 71 (18)% of the end systolic cavity cross section in normals v 11 (6)% in dilated cardiomyopathy (P < 0.01). Normal cross sectional colour inflow jet width was 2.7 (0.3) v 1.5 (0.4) cm in cardiomyopathy (P < 0.01). The jet width correlated with flow width calculated from effective flow orifice area (r = 0.82, P < 0.01).

CONCLUSIONS

(1) Total early diastolic positive and negative peak pressure drop are normally low, so that significant negative left ventricular pressures are not needed to explain normal resting early diastolic mitral flow velocities. (2) These low pressure drops are only possible with a large effective orifice area approaching end systolic left ventricular cavity area. (3) Atrioventricular pressure drops are much greater in dilated cardiomyopathy, where increased inflow accelerations are due to reduced effective flow orifice area. These disturbances will impair filling independently of any abnormality of relaxation or compliance.

Magnetic resonance velocity mapping of normal human transmitral velocity profiles

We used magnetic resonance imaging (MRI) velocity mapping to assess the velocity profile of early diastolic mitral inflow in 11 normal subjects. Velocity maps of left ventricular inflow were obtained in the horizontal long axis of the left ventricle at the time of peak early diastolic filling. Velocity profile curves across the mitral inflow were obtained at 1-cm intervals from the mitral ring to 4 cm into the cavity. The jet width was 3.06 +/- 0.64 cm at the mitral ring level, increasing to 3.6 +/- 0.61 cm at 4 cm. The peak/mean velocity was 1.2 +/- 0.07 at the mitral ring and increased to around 1.4 at 3-4 cm from the mitral ring. The point at which the peak velocity was recorded at each level was skewed towards the septal side by 10%-13% of jet width from the center at the mitral ring and 2-4 cm from the ring. However, at a depth of 1 cm, corresponding to the mitral tip level, the peak velocity was at the center of the jet. The ratio of vertical and horizontal dimensions of the jet cross section was 1.11 +/- 0.05. Thus, the mitral inflow velocity profile is relatively flat at the mitral ring and tip level; the inflow jet cross section is effectively circular.