Intracranial pressure. II. Experimental verification of a mathematical model]

The authors report the results of experiments (performed on the dog in vitro and in vivo) which were designed to verify hypotheses made concerning vascular elasticity and characteristics of CSF resorption, as well as to test the validity of a mathematical model that was described in a previous paper. The authors concluded that the equations of the model account for most of the phenomena satisfactorily, but fail to predict a rebound phenomena which occurs after sudden injections in the cisterna magna. The elasticity coefficient S appears to be constant over a range of 200 mm Hg. On the other hand, the filtration coefficient K depends upon pressure, probably due to morphological changes in the size and shape of the CSF valves. These discrepancies are taken into account in a more general model that is presented in the following paper.     

Pulsatile pressure and flow in the skeletal muscle microcirculation

Although blood flow in the microcirculation of the rat skeletal muscle has negligible inertia forces with very low Reynolds number and Womersley parameter, time-dependent pressure and flow variations can be observed. Such phenomena include, for example, arterial flow overshoot following a step arterial pressure, a gradual arterial pressure reduction for a step flow, or hysteresis between pressure and flow when a pulsatile pressure is applied. Arterial and venous flows do not follow the same time course during such transients. A theoretical analysis is presented for these phenomena using a microvessel with distensible viscoelastic walls and purely viscous flow subject to time variant arterial pressures. The results indicate that the vessel distensibility plays an important role in such time-dependent microvascular flow and the effects are of central physiological importance during normal muscle perfusion. In-vivo whole organ pressure-flow data in the dilated rat gracilis muscle agree in the time course with the theoretical predictions. Hemodynamic impedances of the skeletal muscle microcirculation are investigated for small arterial and venous pressure amplitudes superimposed on an initial steady flow and pressure drop along the vessel.     

Wavelet and Fourier analysis of ventricular and main arteries pulsations in anesthetized dogs

The purpose of this study was to characterize time-frequency behavior using the Continuous Wavelet Transform (CWT) and Fast Fourier Transform (FFT) to analyze ventricular and arterial pressure signals from anesthetized mongrel dogs. Both ventricular and arterial pressure pulsations were recorded using catheter-tip manometers and the CWT was applied to these signals to obtain module coefficients, associated contours, and the 3-D representation of these modules. FFT was applied to obtain the Fourier spectrum. The mathematical analysis of the cardiovascular pressure pulsations permitted the identification of the evolution of the frequency components for the aortic and pulmonary valve functions as well as the intra-ventricular and respiratory influences on the cardiovascular dynamics. The CWT is a very sensitive and reliable procedure for determining the three-dimensional (time-frequency-amplitude) of the oscillatory phenomena during each cardiac cycle, providing more, although complementary, information than the spectral analysis obtained with the FFT. Thanks to the FFT, exact values in Hz could be found for the different events produced in each cycle, and thus the information provided by CWT could be related to the information provided by FFT. The combination of both mathematical methodologies permitted identification of each component of the analyzed signals. The 3D representation allowed an easy comparison of the relative importance of the complex magnitudes in frequency for the different components of the pulsatile waves.     

Short-term variability of blood pressure: effects of lower-body negative pressure and long-duration bed rest

Mild lower-body negative pressure (LBNP) has been utilized to selectively unload cardiopulmonary baroreceptors, but there is evidence that arterial baroreceptors can be transiently unloaded after the onset of mild LBNP. In this paper, a black box mathematical model for the prediction of diastolic blood pressure (DBP) variability from multiple inputs (systolic blood pressure, R-R interval duration, and central venous pressure) was applied to interpret the dynamics of blood pressure maintenance under the challenge of LBNP and in long-duration, head-down bed rest (HDBR). Hemodynamic recordings from seven participants in the WISE (Women's International Space Simulation for Exploration) Study collected during an experiment of incremental LBNP (-10 mmHg, -20 mmHg, -30 mmHg) were analyzed before and on day 50 of a 60-day-long HDBR campaign. Autoregressive spectral analysis focused on low-frequency (LF, ~0.1 Hz) oscillations of DBP, which are related to fluctuations in vascular resistance due to sympathetic and baroreflex regulation of vasomotor tone. The arterial baroreflex-related component explained 49 ± 13% of LF variability of DBP in spontaneous conditions, and 89 ± 9% (P < 0.05) on day 50 of HDBR, while the cardiopulmonary baroreflex component explained 17 ± 9% and 12 ± 4%, respectively. The arterial baroreflex-related variability was significantly increased in bed rest also for LBNP equal to -20 and -30 mmHg. The proposed technique provided a model interpretation of the proportional effect of arterial baroreflex vs. cardiopulmonary baroreflex-mediated components of blood pressure control and showed that arterial baroreflex was the main player in the mediation of DBP variability. Data during bed rest suggested that cardiopulmonary baroreflex-related effects are blunted and that blood pressure maintenance in the presence of an orthostatic stimulus relies mostly on arterial control.     

Aminopeptidase A, which generates one of the main effector peptides of the brain renin-angiotensin system, angiotensin III, has a key role in central control of arterial blood pressure

Overactivity of the brain renin-angiotensin system (RAS) has been implicated in the development and maintenance of hypertension in several experimental animal models. We have recently reported that, in the murine brain RAS, angiotensin II (AngII) is converted by aminopeptidase A (APA) into angiotensin III (AngIII),which is itself degraded by aminopeptidase N (APN), both peptides being equipotent to increase vasopressin release and arterial blood pressure when injected by the intracerebroventricular (i.c.v.) route. Because AngII is converted in vivo into AngIII, the exact nature of the active peptide is not precisely known. To delineate their respective roles in the central control of cardiovascular functions, specific and selective APA and APN inhibitors are needed to block the metabolic pathways of AngII and AngIII respectively. In the absence of such compounds for APA, we first explored the organization of the APA active site by site-directed mutagenesis. This led us to propose a molecular mechanism of action for APA similar to that proposed for the bacterial enzyme thermolysin deduced from X-ray diffraction studies. Secondly, we developed a specific and selective APA inhibitor, compound EC33 [(S)-3-amino-4-mercaptobutylsulphonic acid], as well as a potent and selective APN inhibitor, PC18 (2-amino-4-methylsulphonylbutane thiol). With these new tools we examined the respective roles of AngII and AngIII in the central control of arterial blood pressure. A central blockade of APA with the APA inhibitor EC33 suppressed the pressor effect of exogenous AngII, suggesting that brain AngII must be converted into AngIII to increase arterial blood pressure. Furthermore, EC33, injected alone i.c.v. but not intravenously, caused a dose-dependent decrease in arterial blood pressure by blocking the formation of brain AngIII but not systemic AngIII. This is corroborated by the fact that the selective APN inhibitor PC18 administered alone via the i.c.v. route increased arterial blood pressure. This pressor response was blocked by prior treatment with the angiotensin type 1 receptor antagonist losartan, showing that blocking the action of APN on AngIII metabolism leads to an increase in endogenous AngIII levels, resulting in arterial blood pressure increase through an interaction with angiotensin type 1 receptors. These results demonstrate that AngIII is a major effector peptide of the brain RAS, exerting a tonic stimulatory control over arterial blood pressure. Thus APA, the enzyme responsible for the formation of brain AngIII, represents a potential central therapeutic target that justifies the development of APA inhibitors, crossing the blood-brain barrier, as central anti-hypertensive agents.     

Direct identification of gamma-carboxyglutamic acid in the sequencing of vitamin K-dependent proteins.

We report the first direct method for the identification of the vitamin K-dependent Ca2+ binding amino acid, gamma-carboxyglutamic acid (Gla), in the sequencing of proteins. The carboxyl groups on the protein are first converted to methyl esters with methanolic HCl, a procedure that reduces the polarity of the resulting ATZ derivative of dimethyl-Gla and so greatly improves its extraction from the polybrene-treated glass fiber filter. After conversion to the PTH derivative in methanolic HCl, the resulting dimethyl ester of PTH Gla can be identified directly by a simple modification of the standard HPLC program for the separation of PTH derivatives. This methylation procedure can be used to identify Gla residues in proteins bound to PVDF membranes, as we demonstrate for matrix Gla protein and prothrombin, and to evaluate directly the degree of partial gamma-carboxylation at given glutamic acid residues, as we demonstrate for the 50% gamma-carboxylation of residue 17 in human bone Gla protein.     

Enzymatic synthesis of 3'-hydroxyacetaminophen catalyzed by tyrosinase

3'-Hydroxyacetaminophen, a catechol metabolite of N-acetyl-p-aminophenol (acetaminophen) and N-acetyl-m-aminophenol (a structural analogue of acetaminophen and considered as a possible alternative because it is not hepatotoxic), is enzymatically synthesized for the first time using mushroom tyrosinase. Although reported to be weakly hepatotoxic in vivo, this catechol derivative of acetaminophen is not commercially available. This compound was obtained from its monophenolic precursor, acetaminophen, using the enzyme tyrosinase in the presence of an excess of ascorbic acid, thus reducing back the o-quinone product of catalytic activity to the catechol acetaminophen derivative. A mathematical model of the system is proposed, which is also applicable to the tyrosinase-mediated synthesis of any o-diphenolic compound from its corresponding monophenol. This synthesis procedure is continuous, easy to perform and control, and adaptable to a bioreactor with the immobilized enzyme for industrial purposes in a nonpolluting way.     

Quality by Design: Scale-Up of Freeze-Drying Cycles in Pharmaceutical Industry

This paper shows the application of mathematical modeling to scale-up a cycle developed with lab-scale equipment on two different production units. The above method is based on a simplified model of the process parameterized with experimentally determined heat and mass transfer coefficients. In this study, the overall heat transfer coefficient between product and shelf was determined by using the gravimetric procedure, while the dried product resistance to vapor flow was determined through the pressure rise test technique. Once model parameters were determined, the freeze-drying cycle of a parenteral product was developed via dynamic design space for a lab-scale unit. Then, mathematical modeling was used to scale-up the above cycle in the production equipment. In this way, appropriate values were determined for processing conditions, which allow the replication, in the industrial unit, of the product dynamics observed in the small scale freeze-dryer. This study also showed how inter-vial variability, as well as model parameter uncertainty, can be taken into account during scale-up calculations.     

A finite-element model of blood flow in arteries including taper, branches, and obstructions

A nonlinear mathematical model of arterial blood flow, which can account for tapering, branching, and the presence of stenosed segments, is presented. With the finite-element method, the model equations are transformed into a system of algebraic equations that can be solved on a high-speed digital computer to yield values of pressure and volume rate of flow as functions of time and arterial position. A model of the human femoral artery is used to compare the effects of linear and nonlinear modeling. During periods of rapid alternations in pressure or flow, the nonlinear model shows significantly different results than the linear model. The effect of a stenosis on pressure and flow waveforms is also simulated, and the results indicate that these waveforms are significantly altered by moderate and severe stenoses.     

Hemodynamic-kinetic controlled extracorporeal circulation in heart surgery]

Mimicking the physiological characteristics of the circulatory system, pulsatile bloodflow has also been introduced into extracorporeal perfusion to avoid known postoperative complications. In a mathematical consideration of the situation bloodflow is seen as a function of time F(t) for approximately constant vessel diameter over a given time. The kinetic energy of a column of blood produced by the heart-lung machine is transmitted directly to the arterial circulation via the aorta. The nature of the energy release can give rise to both positive (organ perfusion) and negative (damage to endothelium) effects. This study investigates how this energy release can be optimised, using the following experimental approach. A Doppler flow-measuring probe is placed on the ascending aorta to monitor the extracorporeal circulation. At the same time, the blood pressure is measured and converted to a pressure-flow curve via an A/D converter. On the basis of the parameters thus obtained, the energy released by the heart-lung machine is calculated. By regulating the functional parameters of a new generation of heart-lung machines, the bloodflow can then be adapted to the physiological requirements. Within the pulse period (cycle) a 20% rise phase ending in a slightly increasing plateau is established. The energy increase within a cycle should not exceed 150 joules. To optimize the mode of functioning of the heart-lung machine, we introduced the "energy-equivalent pressure" (EEP). Adaptation of the EEP to the physiological conditions required a basic flow of 60% at a pulse rate of 60/min and a pulse duration of 35% within the pulsatile flow interval.     

Dynamic time course of hemodynamic responses after passive head-up tilt and tilt back to supine position.

Mechanisms involved in the control of arterial pressure during postural changes were studied by analysis of the dynamic time course of cardiovascular changes during head-up tilt (HUT) and tilt back to supine position (TB). Beat-to-beat values of cardiovascular variables were recorded continuously before, during, and after passive HUT to 30 degrees in seven healthy humans. Left cardiac stroke volume (SV, Doppler ultrasound), mean arterial blood pressure (MAP), heart rate (HR), cardiac output (CO), and total peripheral conductance (TPC) were recorded. During HUT, MAP at the level of the carotid baroreceptors decreased by approximately 5 mmHg. There was a striking asymmetry between the time courses of cardiovascular changes on HUT and on TB. Adjustments generally took up to 30 s after HUT, whereas most changes were completed during the first 10 s after TB. Cardiovascular reflex adjustments of HR and TPC were more symmetrical. After HUT, SV was maintained during the first 4-6 s and then decreased steadily during the next 30 s to a stable level approximately 25% below its pretilt value. However, after TB, SV increased rapidly to its pretilt value in <10 s. This asymmetry in SV dynamics may be explained in part by a more rapid change in left cardiac filling after TB than after HUT. On TB, there must be a rapid inflow of stagnant blood from the legs, whereas venous valves will impede backward filling of veins in the lower body on HUT. In conclusion, we have revealed a characteristic asymmetry in cardiovascular responses to inverse variations in gravity forces in humans. This asymmetry can be explained in part by nonlinear, hydrodynamic factors, such as the one-way effect of venous valves in the lower part of the body.     

A data-driven model to study utero-ovarian blood flow physiology during pregnancy

In this paper, we describe a mathematical model of the cardiovascular system in human pregnancy. An automated, closed-loop 1D–0D modelling framework was developed, and we demonstrate its efficacy in (1) reproducing measured multi-variate cardiovascular variables (pulse pressure, total peripheral resistance and cardiac output) and (2) providing automated estimates of variables that have not been measured (uterine arterial and venous blood flow, pulse wave velocity, pulsatility index). This is the first model capable of estimating volumetric blood flow to the uterus via the utero-ovarian communicating arteries. It is also the first model capable of capturing wave propagation phenomena in the utero-ovarian circulation, which are important for the accurate estimation of arterial stiffness in contemporary obstetric practice. The model will provide a basis for future studies aiming to elucidate the physiological mechanisms underlying the dynamic properties (changing shapes) of vascular flow waveforms that are observed with advancing gestation. This in turn will facilitate the development of methods for the earlier detection of pathologies that have an influence on vascular structure and behaviour.

     

A new method for accurate assessment of DNA quality after bisulfite treatment

The covalent addition of methylgroups to cytosine has become the most intensively researched epigenetic DNA marker. The vast majority of technologies used for DNA methylation analysis rely on a chemical reaction, the so-called ‘bisulfite treatment’, which introduces methylation-dependent sequence changes through selective chemical conversion of non-methylated cytosine to uracil. After treatment, all non-methylated cytosine bases are converted to uracil but all methylated cytosine bases remain cytosine. These methylation dependent C-to-T changes can subsequently be studied using conventional DNA analysis technologies.

The bisulfite conversion protocol is susceptible to processing errors, and small deviation from the protocol can result in failure of the treatment. Several attempts have been made to simplify the procedure and increase its robustness. Although significant achievements in this area have been made, bisulfite treatment remains the main source of process variability in the analysis of DNA methylation. This variability in particular impairs assays, which strive for the quantitative assessment of DNA methylation. Here we present basic mathematical considerations, which should be taken into account when analyzing DNA methylation. We also introduce a PCR-based assay, which allows ab initio assessment of the DNA quality after bisulfite treatment and can help to prevent inaccurate quantitative measurement resulting from poor bisulfite treatment.

     

Circadian Time Structure of Cardiovascular Characteristics in Human Pregnancy

Conventional time-unspecified single measurements of blood pressure and heart rate may be misleading because they may be influenced, among other factors, by the patient's emotional state, position, diet, and external stimuli. All of these effects depend on the stages of a (mathematical) spectrum of rhythms and trends with age. The evaluation of predictable variability in blood pressure and heart rate by (a) the use of fully ambulatory devices, and (b) chronobiologic data processing, assesses early cardiovascular disease risk, e.g., in pregnancy. We have used this approach to quantify changes in 24-h synchronized (circadian) characteristics of cardiovascular variables in two consecutive pregnancies of a clinically healthy woman. Blood pressure and heart rate were automatically monitored, with few interruptions, at I-h intervals, each time for at least 48 consecutive h, and for a total of 76 days of monitoring in each pregnancy. Circadian parameters of those circulatory variables were computed for each single day of measurement by the least-squares fit of a 24-h cosine curve. Regression analysis of parameters thus obtained revealed patterns of variation of circadian-rhythm-adjusted means and amplitudes with gestational age. In both pregnancies, the predictable variability of the circadian-rhythm-adjusted mean of blood pressure can be approximated by a second-order polynomial model on gestational age: a steady linear decrease in systolic, diastolic, and mean arterial blood pressure up to the 22nd week of pregnancy is followed by an increase in blood pressure up to the day of delivery. This longitudinal study confirms and extends to ambulatory everyday life conditions the predictable pregnancy-associated variability in blood pressure and heart rate and also allows the establishment of prediction and confidence limits for cardiovascular parameters in a healthy pregnancy.     

The allyl group for protection in carbohydrate chemistry. 17. Synthesis of propyl O-(3,6-di-O-methyl-beta-D-glucopyranosyl)-(1----4)-O-(2,3- di-O-methyl-alpha-L-rhamnopyranosyl)-(1----2)-3-O-methyl-alpha- L-rhamnopyranoside: the oligosaccharide portion of the major serologically active glycolipid from Mycobacterium leprae

Allyl 4-O-benzyl-alpha-L-rhamnopyranoside was converted into allyl 4-O-benzyl-3-O-methyl-alpha-L-rhamnopyranoside and this was condensed with 2,3,4-tri-O-acetyl-alpha-L-rhamnopyranosyl chloride to give a disaccharide derivative which was converted into allyl 4-O-benzyl-2-O-(2,3-O-isopropylidene-alpha-L-rhamnopyranosyl)-3-O-methyl -alpha- L-rhamnopyranoside. This disaccharide derivative was condensed with 2,4-di-O-acetyl-3,6-di-O-methyl-alpha-D-glucopyranosyl chloride to give a trisaccharide derivative which was converted into the title compound. This compound represents the oligosaccharide portion of the major serologically active glycolipid from Mycobacterium leprae which is required to prepare a synthetic diagnostic agent for leprosy infection at an early stage and to investigate the specificities of monoclonal antibodies directed towards the glycolipid.     

Mutual information detects a decreased interdependence between RR and SAP in orthostatic intolerance after microgravity condition

Orthostatic intolerance is the most serious symptom of cardiovascular deconditioning induced by microgravity. However, the exact mechanisms underlying these alterations have not been completely clarified. Several methods for studying the time series of systolic arterial pressure and RR interval have been proposed both in the time and in the frequency domain. However, these methods did not produce definitive results. In fact heart rate and arterial pressure show a complex pattern of global variability which is likely due to non linear feedback which involves the autonomic nervous system and to "stochastic" influences. Aim of this study was to evaluate the degree of interdependence between the mechanisms responsible for the variability of SAP and RR signals in subjects exposed to head down (HD). This quantification was achieved by using Mutual Information (MI).     

On the propagation of a wave front in viscoelastic arteries

In formulating a mathematical model of the arterial system, the one-dimensional flow approximation yields realistic pressure and flow pulses in the proximal as well as in the distal regions of a simulated arterial conduit, provided that the viscoelastic damping induced by the vessel wall is properly taken into account. Models which are based on a purely elastic formulation of the arterial wall properties are known to produce shocklike transitions in the propagating pulses which are not observed in man under physiological conditions. The viscoelastic damping characteristics are such that they are expected to reduce the tendency of shock formation in the model. In order to analyze this phenomenon, the propagation of first and second-order pressure waves is calculated with the aid of a wave front expansion, and criteria for the formation of shocks are derived. The application of the results to the human arterial system show that shock waves are not to be expected under normal conditions, while in case of a pathologically increased pressure rise at the root of the aorta, shocklike transitions may develop in the periphery. In particular, it is shown that second-order waves never lead to shock formation in finite time for the class of initial conditions and mechanical wave guides which are of interest in the mammalian circulation.     

Synthesis and reactions of a nucleoside derivative of phosphoric sulfonic anhydride. Studies related to the mechanisms of coupling reactions in the chemical synthesis of oligodeoxyribonucleotides by phosphotriester procedures

The synthesis of a model compound, diphenylphosphoric toluene-p-sulfonic anhydride, an arylsubstituted phosphoric sulfonic mixed anhydride, is described. Using the same procedure a thymidyl substituted derivative was prepared. The phosphoric sulfonic anhydride is the presumed intermediate in oligonucleotide coupling reactions involving phosphodiester activation by arenesulfonyl derivatives. This mixed anhydride reacts with a variety of nucleophiles. It can be converted to phophotriester derivatives in the presence of simple alcohols. Phosphotriester formation using the 5'-hydroxyl of a thymidine derivative requires additionally a catalyst such as N-methylimidazole. The reactive intermediate produced upon the addition of N-methylimidazole to the phosphoric sulfonic anhydride has been observed spectroscopically using 31P-NMR.     

A Mathematical Model of Valveless Pumping: A Lumped Model with Time-Dependent Compliance,Resistance, and Inertia

A new lumped model of flow driven by pumping without valves is presented, motivated by biomedical applications: the circulation of the human fetus before the development of the heart valves and mechanism of blood flow during the external cardiopulmonary resuscitation (CPR). The phenomenon of existence of a unidirectional net flow around a loop of tubing that consists of two different compliances is called valveless pumping. The lumped parameter model of valveless pumping in this paper is governed by the ordinary differential equations for pressure and flow, with time-dependent compliance, resistance, and inertia. This simple model can represent the essential features of valveless pumping we observed in earlier mathematical models and physical experiments of valveless pumping. We demonstrate that not only parameters of the driving function, such as frequency or amplitude, but also physical parameters, such as wall thickness and tube stiffness, are important in determining the direction and magnitude of a net flow. In this system, we report two new and interesting phenomena of valveless pumping: One is that the shifted peak frequency can be predicted by the pulsewave speed and the other is that time-dependent resistance is a crucial factor in generating valveless pumping. We also demonstrate that this lumped model can be extended to a one-dimensional flow model of valveless pumping and explain why a linear case, the case of the constant compliance, resistance, and inertia, generates almost zero net flow. This emphasizes that the nonlinearity of valveless pumping is also an important factor to generate a net flow in a closed loop model of valveless pumping.     

Is postexercise hypotension related to excess postexercise oxygen consumption through changes in leg blood flow?

After a single bout of aerobic exercise, oxygen consumption remains elevated above preexercise levels [excess postexercise oxygen consumption (EPOC)]. Similarly, skeletal muscle blood flow remains elevated for an extended period of time. This results in a postexercise hypotension. The purpose of this study was to explore the possibility of a causal link between EPOC, postexercise hypotension, and postexercise elevations in skeletal muscle blood flow by comparing the magnitude and duration of these postexercise phenomena. Sixteen healthy, normotensive, moderately active subjects (7 men and 9 woman, age 20-31 yr) were studied before and through 135 min after a 60-min bout of upright cycling at 60% of peak oxygen consumption. Resting and recovery VO2 were measured with a custom-built dilution hood and mass spectrometer-based metabolic system. Mean arterial pressure was measured via an automated blood pressure cuff, and femoral blood flow was measured using ultrasound. During the first hour postexercise, VO2 was increased by 11 +/- 2%, leg blood flow was increased by 51 +/- 18%, leg vascular conductance was increased by 56 +/- 19%, and mean arterial pressure was decreased by 2.2 +/- 1.0 mmHg (all P <0.05 vs. preexercise). At the end of the protocol, VO2 remained elevated by 4 +/- 2% (P <0.05), whereas leg blood flow, leg vascular conductance, and mean arterial pressure returned to preexercise levels (all P >0.7 vs. preexercise). Taken together, these data demonstrate that EPOC and the elevations in skeletal muscle blood flow underlying postexercise hypotension do not share a common time course. This suggests that there is no causal link between these two postexercise phenomena.