The decomposition of apparent stresses in disturbed pulsatile flow in the presence of large scale organized structures

Flow disturbance phenomena that occur in unsteady-in-the-mean flows (i.e. pulsatile or oscillating) at moderate Reynolds numbers are analyzed in both the time domain and the frequency domain. The analysis utilizes variable decomposition into a time-varying underlying waveform and flow disturbances which are composed of large scale organized structures and random fluctuations. A practical technique which incorporates time domain phase conditioning, trend removal, and frequency domain matched filtering, is presented and examined using simulated data of known statistical behavior. The applicability of the method is shown by the decomposition of the simulated data and the technique is then applied to experimental data obtained in pulsatile flow through a constricted tube by means of a laser Doppler anemometer. The cross-sectional area reduction at the constriction throat was 90%. The Womersley parameter in the experiments was 5.3 and the Reynolds number based on the average flow rate per cycle was 300 with a minimum/maximum value of 55/600 based on the instantaneous flow rate. Measurements were taken in the flow region downstream of the constriction throat which included several interesting flow disturbance phenomena. The results of the decomposed flow phenomena demonstrate the significant role of large scale organized structures in such flows. This is particularly important when analyzing blood flow in the large arteries in the presence of severe stenosis or behind prosthetic devices in an attempt to estimate the 'turbulent' stress which act on cellular elements. Estimation of the apparent stress tensor is of importance in an effort to elucidate the mechanical factors which influence the durability of red blood cells under abnormal conditions.     

Estimation of organ transport function: model-free deconvolution by recursive quadratic programming optimization.

A model-free deconvolution method is proposed for evaluating the frequency distribution function of organ transit times. The deconvolution is treated as a nonlinear constrained optimization problem and it is solved by using a modified constrained variable metric approach. The only constraint implemented in the solution is that all the discrete transport function values are not allowed to become negative. The method is tested on model mathematical systems of known analytical transport functions. The tests are performed on systems that included noise in both the input and output functions. The criteria of successful deconvolution are the reconvolution error and, most importantly, the deviation of the computed transport function from the known analytical one. The proposed method is then applied, as a pilot experiment, to biological data obtained from an isolated, perfused rabbit lung preparation contained within a plethysmograph. The results indicate that this type of deconvolution produces stable estimates which faithfully follow the analytical function while negating the need to assume either any functional form for the behavior of the transport function or any educated initial guess of its values.