Cerebrospinal fluid micro-volume changes inside the spinal space affect intracranial pressure in different body positions of animals and phantom.

Interpersonal differences can be observed in the human cerebrospinal fluid pressure (CSFP) in the cranium in an upright body position, varying from positive to subatmospheric values. So far, these changes have been explained by the Monroe-Kellie doctrine according to which CSFP should increase or decrease if a change in at least one of the three intracranial volumes (brain, blood, and CSF) occurs. According to our hypothesis, changes in intracranial CSFP can occur without a change in the volume of intracranial fluids. To test this hypothesis, we alternately added and removed 100 or 200 µl of fluid from the spinal CSF space of four anesthetized cats and from a phantom which, by its dimensions and biophysical characteristics, imitates the cat cerebrospinal system, subsequently comparing CSFP changes in the cranium and spinal space in both horizontal and vertical positions. The phantom was made from a rigid "cranial" part with unchangeable volume, while the "spinal" part was made of elastic material whose modulus of elasticity was in the same order of magnitude as those of spinal dura. When a fluid volume (CSF or artificial CSF) was removed from the spinal space, both lumbar and cranial CSFP pressures decreased by 2.0-2.5 cm H2O for every extracted 100 µL. On the other hand, adding fluid volume to spinal space causes an increase in both lumbar and cranial CSFP pressures of 2.6-3.0 cm H2O for every added 100 µL. Results observed in cats and phantoms did not differ significantly. The presented results on cats and a phantom suggest that changes in the spinal CSF volume significantly affect the intracranial CSFP, but regardless of whether we added or removed the CSF volume, the hydrostatic pressure difference between the measuring sites (lateral ventricle and lumbar subarachnoid space) was always constant. These results suggest that intracranial CSFP can be increased or decreased without significant changes in the volume of intracranial fluids and that intracranial CSFP changes in accordance with the law of fluid mechanics.

Doppler mitral inflow variables time course after treadmill stress echo with and without ischemic response.

This study evaluated Doppler mitral inflow variables changes from rest to post-exercise among 104 subjects with and without echocardiographic evidence of ischemic response (IR) to exercise (63.9 ± 11 years, 54% male, 32% with IR) who underwent a clinically indicated treadmill stress echo (TSE) test. The time from exercise cessation to imaging (TIME) was recorded. The changes (after TSE minus baseline values) in the peak E-wave velocity (∆E) [34.2 vs. 24.2, p = 0.024] and E-wave deceleration rate (∆DR) [348.0 vs. 225.7, p = 0.010] were bigger in ischemic than in nonischemic subjects, while the changes in the peak A-wave velocity (∆A) did not differ [7.9 vs. 15.0, p = 0.082]. The correlations between Doppler variables and IR, TIME, and TIME × IR interaction were analyzed. We observed a significant interaction between TIME and IR regarding ∆E and ∆DR. The differences in the regression line slopes of time courses for ∆E and ∆DR based on IR were significant: ∆E (- 0.09 vs. - 8.17, p = 0.037) and ∆DR (11.23 vs. - 82.60, p = 0.022). Main findings: (1) Time courses after exercise of ∆E and ∆DR in subjects with and without IR were different. (2) ∆E and ∆DR did not differ between subjects with and without IR at exercise cessation (TIME = 0). (3) The simple main effect of ischemia on ∆E and ∆DR was significant at TIME of ≥ 3 min. Divergent time courses of ∆E and ∆DR after exercise might be promising for detecting diastolic dysfunction caused by ischemia. After the cessation of exercise, ΔE and ΔDR in nonischemic but not in ischemic subjects quickly tend to zero. The differences in ΔE and ΔDR between the two groups only became significant for TIME of ≥ 3 min. At the time of exercise cessation, the values of ΔE and ΔDR (taken from the regression lines) were not significantly different between the patients with and without IR. This divergent response is promising for detecting diastolic dysfunction caused by ischemia.

A hybrid Windkessel-Womersley model for blood flow in arteries.

A hybrid Windkessel-Womersley (WK-W) coupled mathematical model for the study of pulsatile blood flow in the arterial system is proposed in this article. The model consists of the Windkessel-type proximal and distal compartments connected by a tube to represent the aorta. The blood flow in the aorta is described by the Womersley solution of the simplified Navier-Stokes equations. In addition, we defined a 6-elements Windkessel model (WK6) in which the blood flow in the connecting tube is modeled by the one-dimensional unsteady Bernoulli equation. Both models have been applied and validated using several aortic pressure and flow rate data acquired from different species such as, humans, dogs and pigs. The results have shown that, both models were able to accurately reconstruct arterial input impedance, however, only the WK-W model was able to calculate the radial distribution of the axial velocity in the aorta and consequently the model predicts the time-varying wall shear stress, and frictional pressure drop during the cardiac cycle more accurately. Additionally, the hybrid WK-W model has the capability to predict the pulsed wave velocity, which is also not possible to obtain when using the classical Windkessel models. Moreover, the values of WK-W model parameters have found to fall in the physiologically realistic range of values, therefore it seems that this hybrid model shows a great potential to be used in clinical practice, as well as in the basic cardiovascular mechanics research.

Noninvasive determination of the pulmonary artery input impedance.

A reliable noninvasive method for the estimation of pulmonary function in healthy and diseased subjects should be of great importance in the prognosis, diagnosis, and treatment of pulmonary hypertension. Here we propose such a method, which is based on the parameter identification of the five-element Windkessel model of pulmonary circulation. The method requires the following input variables: the heart rate, the stroke volume, the Doppler echocardiographic measurements of the tricuspid regurgitation and the pulmonary valve velocity profiles, and estimations of the right atrium and the pulmonary vein pressure. The stroke volume is calculated as a product of the left ventricle outflow tract area and the velocity-time integral measured at the same place. The model parameter identification procedure is based on minimization of the root mean square error between the pulmonary artery root pressure calculated from the aforementioned Doppler velocity profiles (from the Bernoulli equation applied during the ejection phase) and the pressure from the Windkessel model during the same period. The output from the model contains the calculated pulmonary artery input impedance (i.e. the model parameters: pulmonary vascular resistance, pulmonary artery proximal and distal compliances, inertance, and characteristic impedance) and the pulmonary artery pressure profile during the whole heart period. Our method is applied to a subject with pulmonary hypertension. The right heart Swan-Ganz catheterization has been performed in this subject. The results obtained by using this method show that the five-element Windkessel model reconstructs the main features of the pulmonary artery input impedance very well: its modulus shows the minimum where the phase angle changes its sign. The pulmonary vascular resistance, the systolic, diastolic and mean pulmonary artery pressures obtained from the method are in good agreement with the values obtained invasively from the catheterization. Sensitivity analysis shows that the mean pulmonary pressure is fairly insensitive to slight overestimation/ underestimation of all input parameters, except for the right atrium pressure. The absolute error in the mean pulmonary artery pressure is nearly the same as the error in the right atrium pressure. Since the proposed method offers a deeper insight into the pulmonary circulation than the catheterization itself because it provides the proximal and distal compliance, the inertance and the characteristic impedance, it seems that it can serve in clinical practice as a good substitute for catheterization.

A fast method for solving a linear model of one-dimensional blood flow in a viscoelastic arterial tree.

For the purpose of optimization of the whole arterial tree, a fast method for solving of one-dimensional model of blood flow is required. A semi-analytic transmission line method for solving a linearized one-dimensional model of blood flow in an arterial tree with viscoelastic walls is proposed. The transmission line method that solves the linearized model in the frequency domain and the method of characteristics that solves either linearized or non-linear one-dimensional models in the time domain are compared regarding accuracy and computational time. For this purpose, the benchmark problem of a 37-artery network with available experimental data is used. In the case of the linearized model, the results from the transmission line method and the method of characteristics are practically the same. The difference between the transmission line method solution of the linearized model and the method of characteristics solution of the non-linear model is much smaller than the error of either method of characteristics or transmission line method numerical solutions with respect to the experimental data. For typical applications, the transmission line method is at least two orders of magnitude faster than the method of characteristics.