Detection of growth-restricted fetuses using a patient-specific model

Fetal growth restriction (FGR) is one of the major contributors to adverse perinatal outcome. The purpose of this work was to extend the use of Ultrasound Doppler measurements and allow early and accurate detection of FGR. To this end, a mathematical model was developed to represent the major fetal hemodynamic mechanisms involved. Based on model parameters' values, the forward model predicted flow waveforms at the locations where Doppler measurements are routinely performed. Blood velocity waveforms measured in 20 FGR and 20 normal fetuses were used as inputs to an inverse model solution to obtain the parameters' values of the specific fetus. Model predictions indicated significant changes in the circulation of FGR fetuses compared to normal fetuses. Estimated cardiac output was significantly lower in the FGR group compared to the control group (330 ± 52 ml min(-1) Kg(-1) compared to 396 ± 52 ml min(-1) Kg(-1), P<0.001). Also, estimated cardiac output distribution towards the placenta was lower for the FGR group (145 ± 49 ml min(-1) Kg(-1) compared to 181 ± 31 ml min(-1) Kg(-1), P<0.01). In the FGR group the model indicated also significant increase in estimated cardiac output distribution towards the brain (9.6 ± 0.7%, compared to 8.0 ± 1.6 %, P<0.01) and in the degree of blood shunted by the ductus venosus (60.6 ± 17.7 %, compared to 39.7 ± 14.8 %, P<0.01), indicating severe brain-sparing state in these fetuses. We conclude that patient-specific mathematical modeling is a promising direction for personalizing and optimizing the treatment options in pregnancies complicated by fetal growth-restriction.

A three dimensional heart model based on anatomically aligned trusses

A new approach for modeling and simulating the contraction of the heart is presented. The model is based on anatomical images and accounts for cardiac muscle fibers and their orientation. The heart is modeled as a structure built of trusses, each representing a group of myofibers with calculated deformations using matrix structural analysis. Three elements are represented; these are the contractile cardiac muscle, the elastic passive collagen, and intracardiac blood interacting with the heart's preload and afterload. Incompressibility of each element is preserved. The conduction system is simulated in the model by transferring the activating signal from one element to another or by Purkinje fibers activation. The method was demonstrated using a three-dimensional one-layer geometrical ventricle with orthogonal fibers and with anatomically oriented fibers.

Cavernosometry: a theoretical analysis

Erectile dysfunction may be caused by hormonal, neural, arterial, or venous factors. Cavernosometry is used to test for venous leaks. The outcome of surgical procedures attempting to block off veins that allow blood to leak from the penile tissues is still poor. This procedure commonly follows a diagnostic procedure based on cavernosometry after good arterial inflow has been established. To study the cavernosometry test, a mathematical model of penile hemodynamics was used to analyze the significance of its indications and its sensitivity to both arterial and venous factors. The model elucidates the mechanism of cavernosometry and shows that indeed this test is sensitive to venous factors and insensitive to arterial factors. The model also supports the use of supra-arterial pressure during cavernosometry, and the use of the slope of the flow-to-maintain vs maintained-pressure curve as an indicator of venous leak severity.

Mathematical analysis of atelectasis formation in middle ears with sealed ventilation tubes

AIM

A mathematical model was developed to identify time periods of atelectasis induction in middle ear (ME) ventilated via ventilating tubes (VT). Atelectatic ears are characterized by a total gas pressure lower than 760 mmHg.

METHODS

Ventilating tubes were deliberately sealed and ME gas content changed in the presence of a preset blood gas pressure. Once sealed, CO2 rapidly diffuses out of the blood via lining tissues into the ME cleft. This results in initially a total ME pressure rise followed by a decrease in subatmospheric pressures. Time periods for atelectasis reformation was determined once ME pressure crossed the 760 mmHg value and continued to decline as the atelectasis reached higher grades.

RESULTS

Time periods calculated by the model varied from 18 to 125 min in ME cavities ranging in volume from 0.5 to 3.5 mL, respectively. These results were calculated for conditions of venous blood in the lining mucosa blood and are consistent with prior clinical tests that measured an induced return to previous atelectasis state following the closure of the VT in 33 tested ears within 25-120 min (43 min on average).

CONCLUSIONS

The model demonstrates that under the above conditions, diffusive gas transfer in relation to blood gas content is the leading mechanism to alterations in ME pressure and volume. It may be used as a tool to determine ME physiological cavity volume of ears with VT.

Evaluation of center-line extraction algorithms in quantitative coronary angiography

Objective testing of centerline extraction accuracy in quantitative coronary angiography (QCA) algorithms is a very difficult task. Standard tools for this task are not yet available. We present a simulation tool that generates synthetic angiographic images of a single coronary artery with predetermined centerline and diameter function. This simulation tool was used creating a library of images for the objective comparison and evaluation of QCA algorithms. This technique also provides the means for understanding the relationship between the algorithms' performance and limitations and the vessel's geometrical parameters. In this paper, two algorithms are evaluated and the results are presented.

Model-based estimation of male urethral resistance and elasticity using pressure-flow data

To assess urethral resistance and changes in the urethral elasticity during voiding, a lumped parameter model of the urethra was developed. The model uses pressure and flow measurements to estimate time-dependent resistance and elasticity factor. The model includes a resistance that has a function of the cross-section and urethral elasticity. Two resistivity types are compared in the constricted flow-controlling zone of the urethra: Poiseouille resistance and the Bernoulli effect. Using real pressure-flow data sets, the model was used to estimate urethral resistance and changes in urethral elasticity during voiding. Estimation of the elasticity show that in a normal patient relaxation of the urethra is a process that continues until the end of voiding. This has important implications with regard to the present methods that are used in the clinic to assess urethral obstruction or constriction. The resistance as calculated by this model, may be a useful indicator of urethral constriction and obstruction, since it is especially independent of the bladder function. Changes in the urethral elasticity during voiding which are estimated by the model add a new diagnostic parameter to pressure-flow studies.

Hemodynamic mechanisms of penile erection

A model of penile hemodynamics was developed to explain the process of erection that is not yet fully understood. Contradicting observations regarding blood flow and vessels occlusion during erection were examined. The model that was based on the physical structure and physiological function of the system was validated by comparing its predictions to clinical and experimental observations. Simulation of the process for both normal and pathological conditions indicates that pressure buildup in the corpus cavernosum during erection depends mainly on the interaction between the arterial inflow system and the venous draining system and that the venous draining vessels do not fully collapse and flow through the penis continues throughout the erection period. In pathological conditions, the model predicts that tumescence can be obtained without functional rigidity and demonstrates that small increases in vessel stiffness can result in such behavior.

Computer simulation of hypothermia during "damage control" laparotomy

"Damage control" is a surgical strategy for the staged repair of severe trauma that aims to avoid an irreversible physiologic insult marked by a self-propagating combination of hypothermia, coagulopathy, and acidosis. The point beyond which the physiologic insult becomes irreversible, however, remains ill-defined. The aim of this study was to address this problem by means of a dynamic computer model of heat loss during laparotomy for exsanguinating hemorrhage. A single compartment model was developed using a graphic modeling tool and was implemented to calculate the time interval from the beginning of laparotomy to a core temperature of 32 degrees C, which is a marker of irreversible physiologic derangement in injured patients. A series of simulation runs showed that the exposed peritoneum is the dominant factor contributing to heat loss; the bleeding rate has a less marked effect. Elevation of the ambient temperature and rapid abdominal closure are effective interventions available to the surgeon to modify the heat loss curve. This study shows that during a "damage control" laparotomy for exanguinating hemorrhage the window of opportunity for salvage before the onset of an irreversible physiologic insult is no longer than 60 to 90 minutes.

Effect of estradiol on rat ileum

1. Sex hormones may influence gastrointestinal motility and thus may be responsible for symptoms that are common during pregnancy or hormone replacement therapy. The purpose of this study was to evaluate the effect of estradiol on the gut. 2. Segments of rat ileum (n=9) were suspended in an organ bath and exposed to increasing concentrations of carbachol, in the presence or absence of 17beta-estradiol. 17beta-estradiol markedly reduced the force developed by the ileum in response to carbachol. 3. These results suggest that estradiol reduces gastrointestinal motility.

Estimation of oxygen delivery in newborns with a univentricular circulation

BACKGROUND

The management of neonates with complex congenital anomalies depends on careful interpretation of arterial blood gas values. Improved interpretation of these oxygen parameters may allow clinicians to avoid unexpected cardiovascular events. This study examined whether systemic oxygen delivery (DO2) can be maximized by the use of indices derived from oxygen saturation measurements in neonates with hypoplastic left heart syndrome.

METHODS AND RESULTS

For the single-ventricle heart with both circulations in parallel, we used a previously developed computer simulation to obtain DO2 as a function of systemic arterial (SaO2) and venous (SvO2) oxygen saturation, arteriovenous oxygen difference (Sa-vO2), or pulmonary-to-systemic flow ratio (Qp/Qs). We also examined the oxygen excess factor, SaO2/Sa-vO2 (Omega). We found that (1) slight increases in SaO2 may be associated with large decreases in DO2. (2) Low values for SvO2 indicate low values for DO2. (3) Curves for Sa-vO2 and Qp/Qs are redundant in the data provided. (Qp/Qs, however, provides these data in more physiologically relevant terms.) (4) High values for Qp/Qs (>4) are associated with low DO2. (5) Estimating Qp/Qs from oxygen saturation measurements may result in errors when pulmonary venous oxygen saturation is not available. (6) Maximizing DO2 is extremely difficult using SaO2, SvO2, and Qp/Qs. (7) A linear relationship exists between Omega and DO2, and this linear relationship is not altered by changes in cardiac output.

CONCLUSIONS

Patients with low SvO2 values require attention. Ideally, after reducing Qp/Qs to <1.5, Omega might be a better index to guide further therapy and maximize DO2. Interventions that increased Omega would be considered beneficial, whereas interventions that decreased Omega would be considered detrimental.

Theoretical optimization of pulmonary-to-systemic flow ratio after a bidirectional cavopulmonary anastomosis

A univentricle with parallel pulmonary and systemic circulations is inherently inefficient because mixing of pulmonary and systemic venous return occurs. Thus a cavopulmonary anastomosis is used as a staged palliative procedure to reduce volume overload in patients with cyanotic congenital heart disease. On the basis of oxygen uptake and consumption, an equation was derived that related cardiac output, pulmonary venous oxygen saturation, upper body oxygen consumption, and superior-to-inferior vena caval blood flow ratio (QSVC/QIVC) to oxygen delivery. The primary findings were as follows. 1) As QSVC/QIVC increases, total body oxygen delivery and arterial and superior vena caval oxygen saturations increase. 2) As QSVC/QIVC increases, lower body oxygen delivery and inferior vena caval oxygen saturation initially increase, then peak, and then decrease. 3) As the percentage of lower body oxygen consumption increases, oxygen delivery and saturation decrease. 4) A cavopulmonary anastomosis decreases the required cardiac output for a given oxygen delivery. Thus we concluded that a high systemic arterial oxygen saturation after cavopulmonary anastomosis requires a high percentage of upper body oxygen consumption and a high QSVC/QIVC and that the cavopulmonary anastomosis reduces the volume load on the single ventricle.

Spontaneous skin temperature oscillations in normal human subjects

A noninvasive method based on high-resolution measurements and bandpass filtering of spontaneous skin temperature oscillations (approximately 4.0 x 10(-2) degrees C) in the low-frequency range (0.01-0.04 Hz) was investigated in normal human subjects. We hypothesized that the oscillations (temperature variability) originate from vasomotor activity of small arteries and arterioles in subcutaneous tissues. To test this hypothesis, continuous blood pressure waveforms were obtained with the use of an external piezoelectric sensor. The peak-to-peak envelope of the pressure signal (pressure variability) was used as an indicator of vasomotor activity. The variabilities of temperature and pressure were compared using cross-spectral and coherence analysis. The correlation between the peak frequency of the signals was 0.92, and the coherence was greater than 0.9. The signals demonstrated similar changes in spectral energy and peak frequency in response to mental stress. Reproducibility of the temperature variability in individual subjects was verified by repeating measurements 1-12 wk later. The differences in peak frequency were small (0.0155 +/- 0.001 Hz), and in each subject the signals exhibited similar patterns in response to stress. Correlation between spectral characteristics of the signals suggests that temperature variability can be attributed to changes in blood flow resulting from oscillations in vasomotor smooth muscle tone.

Intraoperative monitoring of IMA flow: what does it mean?

BACKGROUND

This study examines whether the measurement of internal thoracic artery (ITA) graft flow can determine the adequacy of the ITA-left anterior descending coronary artery (LAD) anastomosis.

METHODS

To study a wide range of clinical problems, we used a computer simulation of the cardiovascular system. The model included a time-varying elastance model of the heart, a systemic circulation represented by a multielement nonlinear model of the aorta and its major branches, a nonlinear model of the LAD circulation, and a model of the ITA bypass graft.

RESULTS

With a mild LAD stenosis, ITA graft flow was low and flow reversal occurred. As the percent stenosis increased, ITA flow and the percentage of ITA-to-total LAD flow increased. The ITA graft helped to maintain resting LAD blood flow. A partial obstruction (40%) at the ITA-LAD anastomosis reduced ITA graft flow at similar levels of LAD stenosis. However, overlap in flow values comparing a normal with a partially obstructed anastomosis occurred.

CONCLUSIONS

Flow patterns in the ITA are highly dependent on the degree of stenosis of the LAD as well as the integrity of the anastomosis. The predictive power of ITA flow measurement increases with severe stenosis or total occlusion of the proximal LAD and with high coronary blood flow demands.

A theoretical unidirectional valve based on functional collapse of blood vessels in the penis

A model of a vessel exposed to external pressure was developed. Analytical derivation resulted in closed-form expressions describing pressure-flow relation in the vessel. These expressions describe a behavior of a unidirectional leaky valve. The vessel model was used to represent internal arteries and veins in the penis. Together with a compliant chamber representing the corpus cavernosum, the model demonstrates the valve action of the partially collapsed vessels during penile erection. This explains observations regarding arterial backflow during erectile contraction of the ischiocavernous muscles and demonstrates the differences in development of tumescence and rigidity.

Myocardial O2 balance during fluid resuscitation in uncontrolled hemorrhage: computer model

OBJECTIVE

To study myocardial oxygen balance during fluid resuscitation for uncontrolled hemorrhage.

DESIGN

A computer simulation.

MATERIALS AND METHODS

A mathematical model of the cardio-vascular system was used to simulate uncontrolled hemorrhage with and without fluid replacement. The parameters of initial bleeding rates, fluid replacement, and time intervals were selected to approximate typical values encountered in an urban emergency medical services system. The model was used to calculate myocardial oxygen supply and demand, and the time from injury to myocardial oxygen deficit was calculated for each fluid regimen.

MAIN RESULTS

The model predicts an exponential decline in bleeding rate when no fluids are administered. Optimal fluid infusion rate was predicted as a function of initial bleeding rate. The time to a negative myocardial oxygen balance was shorter when a fluid bolus (100 mL/min or more) was given compared with no fluid administration.

CONCLUSIONS

For uncontrolled hemorrhage at initial bleeding rates of 100 mL/min or more, the time interval from injury to cardiac oxygen deficit is inversely related to the infusion rate. A detailed study of the myocardial oxygen balance provides a pathophysiologic rationale for fluid restriction in the initial management of uncontrolled hemorrhage.

New model-based indices for maximum expiratory flow-volume curve in patients with chronic obstructive pulmonary disease

New lung function indices based on a lumped parameter model of the maximal expiratory flow-volume (MEFV) curve are presented. The waveforms obtained by the model were compared to the flow-volume curves recorded from normal subjects and from patients with small airways disease, asthma and emphysema. We were able to reproduce the flow-volume curves using the model and calculate new parameters that indicate the degree of lung function impairment and may be applicable to identify mild chronic obstructive pulmonary diseases. Further studies in larger groups of patients are required to better define the true predictive value of the new indices described for the diagnosis of COPD.

Spectral characteristics of skin temperature indicate peripheral stress-response

High-resolution measurement of skin temperature in 11 normal subjects revealed low-amplitude temperature oscillations (40 x 10(-3) degrees C). The temperature signal measured on two hands during baseline, stress, and recovery periods, was filtered to separate the low-amplitude oscillations from the temperature signal. Spectral analysis of the filtered signal showed that most of the energy of the signal is in a range of 0.01 to 0.03 Hz. Frequency shifts and amplitude changes of the largest component were observed in response to mental stress. In subjects with high baseline values of either of these two variables, a decrease was observed in response to stress. An opposite response was observed in subjects with significantly lower baseline levels. Stress-related changes in peak frequency ranged from -25% to +18.2%; changes in peak amplitude ranged from -74.6% to +280%. Changes in the mean temperature were limited to 2.4%. Thus, the oscillatory component showed higher sensitivity to psychological stress than mean temperature. The spectrum of this component was compared to the spectrum of the blood pressure waves measured noninvasively. Both exhibited similar dynamics of energy, peak amplitude, and peak frequency in response to psychological stress. This similarity suggests that the oscillatory temperature component reflects stress-related changes of peripheral vasomotor activity.

Maximum expiratory flow-volume curve: mathematical model and experimental results

A mathematical simulation of the maximum expiratory flow-volume (MEFV) curve was developed using a lumped parameter model. The model uses a theoretical approximation of an activation function representing the lung's pressure-volume relationship during maximally forced expiration. The waveforms obtained by the model were compared to the flow-volume curves recorded from normal subjects and for patients with small airways disease, asthma, and emphysema. We were able to reproduce the flow-volume curves using the model and calculate new parameters that reflect the dependency of airways resistance on expired volume during FVS manoeuvre. These new parameters are based on the entire information presented in the flow-volume curve and on the reduction in flow at all lung volumes. We also calculated the mean slope of the resistance-expired volume curves obtained from the model by fitting a straight line to the curve. Using representative data for normal and COPD patients different mean slopes of 0.095, 0.13, 0.49 and 1.44 litre-1 were obtained for normal subject, small airways disease, asthma and emphysema patients, respectively. The model-based parameters may be applicable to human studies. However, further studies in large groups of patients are required to better define the true predictive value of the new indices described for the diagnosis of COPD.

Balancing the circulation in hypoplastic left heart syndrome

A mathematical model based on oxygen flow was developed to study the effects of pulmonary to systemic flow ratios (QP/QS) on systemic oxygen availability. The model suggests that QP/QS = 1 is the safest ratio that would provide the largest safety margin in either low cardiac output or low pulmonary oxygenation conditions. The optimal value of QP/QS that will result in maximum oxygen availability is smaller than unity and depends on several circulatory parameters such as cardiac output, maximal oxygen capacity, level of pulmonary oxygenation, and oxygen consumption. The values of these parameters also dictate the permissible range of QP/QS beyond which abrupt oxygen deficiency ensues. Decreased pulmonary resistance resulting in increased pulmonary flow may eventually result in QP/QS that is beyond the vital range.

Balancing the circulation: theoretic optimization of pulmonary/systemic flow ratio in hypoplastic left heart syndrome

OBJECTIVES

This study examined the effects of the pulmonary (QP)/systemic (QS) blood flow ratio (QP/QS) on systemic oxygen availability in neonates with hypoplastic left heart syndrome.

BACKGROUND

The management of neonates with hypoplastic left heart syndrome is complex and controversial. Both before and after surgical palliation and before heart transplantation, a univentricle with parallel pulmonary and systemic circulations exists. It is generally assumed that balancing pulmonary and systemic blood flow is best to stabilize the circulation.

METHODS

We developed a mathematical model that was based on the simple flow of oxygen uptake in the lungs and whole-body oxygen consumption to study the effect of varying the QP/QS ratio. An equation was derived that related the key variables of cardiac output, pulmonary venous oxygen saturation and the QP/QS ratio to systemic oxygen availability.

RESULTS

The key findings are 1) as the QP/QS ratio increases, systemic oxygen availability increases initially, reaches a maximum and then decreases; 2) for maximal systemic oxygen availability, the optimal QP/QS ratio is < or = 1; 3) the optimal QP/QS ratio decreases as cardiac output or percent pulmonary venous oxygen saturation, or both, increase; 4) the critical range of QP/QS, where oxygen supply exceeds basal oxygen consumption, decreases as cardiac output and percent pulmonary venous oxygen saturation decrease; 5) the relation between oxygen availability and QP/QS is very steep when QP/QS approaches this critical value; and 6) the percent oxygen saturation of systemic venous blood is very low outside the critical range of QP/QS and high within the critical range.

CONCLUSIONS

This analysis provides a theoretic basis for balancing both the pulmonary and systemic circulation and suggests that evaluating both systemic arterial and venous oxygen saturation may be a useful way to determine the relative pulmonary and systemic flows. When high systemic arterial and low systemic venous oxygen saturation are present, pulmonary blood flow should be decreased; conversely, when both low systemic arterial and venous oxygen saturation are present, more flow should be directed to the pulmonary circulation.

Acute effects of 17 beta-estradiol on the rat heart

OBJECTIVE

Our purpose was to study the acute effects of 17 beta-estradiol on mechanical and electrical activities of cardiac function and on coronary arteries in the rat heart.

STUDY DESIGN

The effects of 17 beta-estradiol were studied on perfused working heart isolated from Charles River male rats. Heart rates, coronary flow, aortic flow, and left ventricular pressure were measured. To avoid coronary interaction, chronotropic and inotropic effects were also tested on isolated atria. Data were analyzed with the paired Student t test.

RESULTS

17 beta-Estradiol produced a dose-dependent negative chronotropic effect in right atria but did not affect the contractility of left atria. A decrease in heart rate was also observed in perfused hearts treated with 5 x 10(-6) mol/L 17 beta-estradiol. 17 beta-Estradiol (5 x 10(-6) mol/L) significantly increased coronary flow (p < 0.005) but had a negligible effect on cardiodynamic index values. A significant effect of 17 beta-estradiol on cardiac function was observed when coronary arteries were precontracted with acetylcholine.

CONCLUSION

Both the experimental coronary vasodilatory effect and the negative chronotropic effect of 17 beta-estradiol support the clinical observations that suggest that this hormone may have an important role in prevention of cardiovascular diseases.

Mathematical analysis of coronary autoregulation and vascular reserve in closed-loop circulation

The autoregulatory capacity of the coronary circulation has traditionally been studied in open-loop animal models where the coronary circulation was decoupled from the systemic circulation. In the closed-loop circulation, changes in arterial pressure alter coronary flow. Pressure variations can be caused by changes in cardiac contractility, preload, afterload, and heart rate. These changes also affect myocardial oxygen consumption. To maintain equilibrium between oxygen supply and consumption, coronary flow is altered by the autoregulation mechanism. Coronary resistance must change to produce the required change in coronary flow. The direction of change in coronary resistance is not directly predictable. Increased arterial pressure may result in either increased or decreased coronary resistance. To study the changes in coronary resistance in response to changes in arterial pressure that are produced by circulatory parameters, we used mathematical models. Coronary resistance was calculated to obtain equilibrium between ventricular oxygen consumption and supply for different values of contractility, preload, afterload, and heart rate. Maximum coronary resistance, indicating largest coronary vascular reserve and highest efficiency of arterial pressure generation, was defined as an optimal condition. The model predicted that the optimal value of cardiac contractility is its resting value. Minimizing end-diastolic volume and heart rate and maximizing peripheral resistance were shown to improve ventricular coronary vascular reserve. These observations suggest that afterload reduction therapy may not be beneficial for improving myocardial oxygen balance while venous vasodilatation and heart rate reduction result in greater coronary reserve.

Autoregulation in the stenosed coronary circulation

Coronary vessel stenosis increases vascular resistance and limits the dynamic range of autoregulation. In this study, the limitation imposed by stenosed vessels on oxygen delivery to the myocardium was investigated using a theoretical model. For different degrees of stenosis and for different levels of arteriovenous oxygen content difference, the model predicted the limits of the contractility range for which ventricular oxygen balance is positive. The model also predicted the existence of an optimal contractility level which minimizes the cost of arterial pressure generation and provides the largest coronary oxygen reserve. With severe stenosis, myocardial oxygen balance is extremely sensitive to changes in the level of stenosis. The range of contractility in which the coronary circulation can meet the myocardial oxygen needs is dramatically reduced by small increases in stenosis severity or small decreases in arteriovenous oxygen difference. When the optimal contractility level is maintained, the heart can tolerate these detrimental changes to a greater extent.

A computer model for analysis of fluid resuscitation

Injuries involving massive blood loss, such as burns, combat wounds, and injuries resulting from car accidents, require fluid resuscitation. The risk involved in fluid therapy is overloading of the circulation, resulting in pulmonary edema which can lead to death. The risk of pulmonary edema may be eliminated by proper determination of maximal infusion volume and rate. Reabsorption of fluid from the extravascular compartment and infusion of fluid following blood loss results in reduction of the hematocrit. This is accompanied by an increase in the heart's preload and afterload. Coronary driving pressure and flow increase due to increased volume. However, because of the reduced hematocrit this increase in coronary flow may not be sufficient to compensate the myocardium, in terms of oxygen supply, for the increase in oxygen consumption. A model of the cardiovascular system, including an extravascular compartment, was designed to analyze the effects of fluid infusion on hemodynamic variables, cardiac oxygen balance, and the redistribution of fluid between intravascular and extravascular compartments. The results indicate that edema is not the only possible adverse effect of overloading the cardiovascular system with fluid. The simulation demonstrated that in certain cases the heart's oxygen balance can become negative. Limiting the rate of infusion can reduce this risk.

Positive inotropic effect in the heart produced by acetylcholine

The effect of acetylcholine on cardiac muscle contractility and hemodynamics was investigated in human atrial strips and in isolated working rat heart. Activation of the muscarinic receptor in the heart muscle is generally known to result in negative chronotropic and inotropic effects. In our study, positive inotropic effects of acetylcholine (ACh) were observed in both human right atrial strips and in the working rat heart. Exposure of the human right atrial strips to ACh (10(-7)-10(-4) M) produced a dose dependent tri-phasic (positive-negative-positive) inotropic effect in approximately 40% of the strips. In muscle strips that exhibited only a negative inotropic effect, a positive response was observed following washout of ACh. Both positive and negative effects were antagonized by atropine. Exposure of the paced working rat heart to ACh (10(-7) - 10(-5) M) resulted in a dose dependent decrease in mean coronary flow followed by depression in cardiac function. When the heart was initially treated with the vasodilator adenosine (2 x 10(-6) M), exposure to ACh (10(-7) - 10(-5) M) had no effect on coronary flow and produced a dose dependent augmentation of all cardiodynamic indices: left ventricular pressure, isovolumic pressure, cardiac output, maximal aortic flow and stroke work. This positive response was antagonized by atropine. Exposure of the rat ventricular strips increased the formation of [3H]phosphoinositide breakdown products (e.g. inositol phosphates IP, IP2, IP3). These observations demonstrate that cholinergic muscarinic stimulation may produce positive inotropic effects in both human and rat cardiac muscle. Furthermore, our results suggest that IP3 may be a mediator in this process.

A blood vessel model based on velocity profiles

A simple model of pressure-flow relationship in blood vessels was developed. The calculation of the model components was based on velocity profiles in the vessels. The flat velocity profile in the entrance of the vessel was considered. By using mean pressure over the cross-section and assuming a polynomial approximation of the velocity profile, it is shown that the resistance of a vessel segment increases with increased flatness of the velocity profile. Moreover, the analysis provides a means to calculate the resistance of a vessel segment based on the shape of the velocity profiles in that segment. The analysis shows that the inertance element of the segment is not affected by the shape of the velocity profile.

Performance optimization of left ventricular assistance. A computer model study

Performance of temporary parallel left ventricular assistance was investigated and the theoretic conditions leading to optimal behavior of the mechanical system were explored. Computer models of nonpulsatile and pulsatile left ventricular assist devices (LVADs) were incorporated into a previously reported closed-loop simulation of the canine cardiovascular system. Assuming the assisted heart was capable of recovery, LVAD performance was assessed based on both myocardial oxygen balance and cardiac output. With a synchronous LVAD, and operating in a counterpulsation mode, these variables were sensitive to the phasing of pump ejection. Maximum reduction in cardiac oxygen consumption, maximum increase in oxygen availability, and maximum increase in cardiac output with the atrio-aortic device were obtained when pump ejection immediately followed aortic valve closure. These variables were directly proportional to the magnitude of bypass volume. The pulsatile asynchronous and nonpulsatile LVAD models affected oxygen balance in a similar manner, but neither performed so well as the synchronous model when equal bypass volumes were used. Ventricular uptake of blood provided a further 27% decrease in oxygen consumption and further 78% increase in oxygen availability than atrial uptake. In summary, the model predicted that the pulsatile synchronous LVAD, filling from the ventricle during heart systole and ejecting into either the ascending or descending aorta just after ventricular systole, would be most beneficial to both myocardial oxygen balance and cardiac output.

Optimal controller for intraaortic balloon pumping

An optimal control algorithm was adapted to identify and track the optimal deflation time of the intraaortic balloon pump (IABP). Routines for handling physiologically imposed constraints were added to the algorithm which was implemented in a computer-controlled system. The system was designed to provide real time optimization for the clinical setting. The controller continuously maximizes a performance index while observing the constraints. The index is composed of clinically available hemodynamic variables which indicate changes in myocardial energy balance. Proper values for the algorithm parameters were determined and the system was tested in animal experiments. The results indicate that controlling deflation time relative to the R wave, which precedes the next ejection phase, reduces the time required for optimization when the heart rate varies.

Coronary autoregulation and optimal myocardial oxygen utilization

The complex relationship among myocardial contractility, preload, afterload, and coronary autoregulation was studied using both analytical and numerical methods. To study autoregulation and coronary reserve changes in response to changes in cardiac oxygen consumption and in arterial pressure generation, a new variable was introduced: myocardial resistance to oxygen flow (RO2). This variable was defined as the ratio of the coronary driving pressure to left-ventricular oxygen uptake. High values for this variable indicate small consumption relative to the generated aortic pressure. Conditions which produce the highest obtainable value for RO2 are considered as optimal. An expression relating RO2 to ventricular hemodynamic variables was developed and studied using a mathematical model of the cardiovascular system. The model included a mechanism of local autoregulation based on the assumption that, in steady state, the amount of oxygen consumed equals the amount extracted from coronary blood. Heart rate, peripheral resistance, end-diastolic volume, and myocardial contractility were varied while the coronary circulation was adjusted to meet ventricular oxygen consumption at each state. The model predicts that, for each state of the circulation, there is an optimal level of cardiac contractility for which the coronary reserve is maximized.

Optimal control system for the intra-aortic balloon pump

An optimal control system for the intra-aortic balloon pump (IABP) is presented. Control of the IABP is based on a performance index formulated to reflect a tradeoff between maximising cardiac oxygen supply and minimising cardiac oxygen consumption. In the performance index, mean diastolic pressure (MDP) was used to represent oxygen availability and peak systolic pressure (PSP) was used to represent oxygen consumption. An algorithm, implemented using an 8-bit microcomputer, changes the deflation time of the IABP to maximise this performance index by using an optimisation technique that employs both a search and an approximation. The search produces three equally spaced points which define a region that includes the maximum of the performance index. From these points, the optimum deflation time is estimated by a quadratic approximation. The algorithm has been successfully tested using performance index curves generated by computer simulations.

Computer simulation of the mechanically-assisted failing canine circulation

A model of the cardiovascular system is presented. The model includes representations of the left and right ventricles, a nonlinear multielement model of the aorta and its main branches, and lumped models of the systemic veins and the pulmonary circulation. A simulation of the intra-aortic balloon pump and representations of physiological compensatory mechanisms are also incorporated in the model. Parameters of the left ventricular model were set to simulate either the normal or failing canine circulation. Pressure and flow waveforms throughout the circulation as well as ventricular pressure and volume were calculated for the normal, failing, and assisted failing circulation. Cardiac oxygen supply and consumption were calculated from the model. They were used as direct indices of cardiac energy supply and utilization to assess the effects of cardiac assistance.

Cardiac energy considerations during intraaortic balloon pumping

Cardiac oxygen availability and oxygen consumption were used in a theoretical study as indexes of myocardial energy supply and utilization, respectively. A detailed computer simulation of the closed-loop canine cardiovascular system was utilized to study the dependence of these indexes on timing of the intraaortic balloon pump. Oxygen availability exhibited higher sensitivity to balloon timing than oxygen utilization. While maximum augmentation of oxygen availability was 58 percent, oxygen consumption could be reduced by only 13 percent. Animal experiments were initiated to validate the theoretical results. The results of both the animal experiments and the computer simulation suggested that neither balloon timing which maximizes oxygen availability nor timing which minimizes oxygen consumption correlates with timing which minimizes aortic end diastolic pressure. Thus, end diastolic pressure, presently used as a determinant of proper timing in patients undergoing cardiac assistance, was found to be a poor index of ventricular energy consumption. A performance index comprised of clinically available variables, was formulated to reflect myocardial energy balance. In this performance index, mean diastolic pressure was used to represent energy availability and peak systolic pressure was used as an index of oxygen consumption. Their relationship to oxygen balance and their dependence on timing were studied using the computer simulation of the canine cardiovascular system and animal experiments. Theoretical and experimental results suggest that such an index is capable of representing O2 balance and can be used to control phasing of the device.

A new method for the estimation of the left ventricular pressure-volume area

We present a new method for obtaining the pressure-volume area (PVA) as defined by Suga. The method allows calculation of the PVA from pressure and flow waveforms of ejecting beats and requires only one isovolumic ventricular contraction performed at any end diastolic volume.