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.