Transfer function analysis of ultrasonic time-intensity measurements.

Time-intensity measurements of ultrasonic-contrast microbubbles based on the dilution theory have been used to assist blood flow estimation. The compartment model has been employed to describe the dilution process. Under the linear and time-invariant assumption, the time-intensity curve measured at the output of a compartment (i.e., blood mixing chamber) is the convolution of the input time-intensity curve with the compartment's transfer function. Thus, transfer function analysis is possible using deconvolution when the temporal variations in both the input and the output intensities are available. Note that the linear and time-invariant assumption requires a constant flow rate because, with flow pulsation, the flow rate changes with time and the mixing process becomes time varying. Thus, the purpose of this paper was to study the effects of flow pulsation on time-intensity measurements. In addition, a deconvolution technique based on a recursive least squares approach is used for transfer function analysis. Both simulations and experiments were performed; the results from which indicate that the pulsation generally does not affect the validity of time-intensity-based flow estimation. The proposed deconvolution technique is also effective for both constant and pulsatile flows; thus, permitting transfer function analysis in various flow conditions. One potential application of this transfer function analysis is to remove the effects of a noninstantaneous input function. The results from this paper lead to future work in brain-perfusion estimation based on extracranial time-intensity measurements.