Catheter Correction ( UNFINSHED )
When evaluating indicator dilution experiments, one has to take into account the influence of the experimental setup on the measurements. Ideally, a tracer would be instantaneously introduced at a predetermined location within the circulation, and its concentration measured at another predetermined location. In practice, however, application of the tracer and collection of samples is achieved through catheters introduced into the circulation that distort to a certain degree the time course of the measured tracer concentration. Tracer kinetics obeys the principles of linear time-invariant system theory (put in reference). The injection catheter, the investigated organ, and the collection catheter can therefore be regarded as linear systems connected in series, such that the overall impulse response is the convolution of the individual impulse responses. Because convolution is commutative, the injection and collection catheter can be lumped together by considering the convolution of their impulse responses. The impulse response of the organ can then be obtained by deconvolution of the catheter responses from the overall impulse response. Monoexponential catheter distortion Experiments by Goresky and Silverman (1964) have shown that the impulse-response of a single catheter equipped with a peristaltic pump can be approximated by a delay followed by a single exponential decay. In these pilot experiments (without any biological material), the inflow to the catheter was switched between unlabeled and labeled blood, thus providing a step input. The data, normalized to the inflow tracer concentration, are shown in the following applet. These data are described by the following expressions:
c0(t) = 1 − e−α(t − τ), t > τ
c0(t) = 0, t ≤ τ
The impulse response of the catheter, h(t), is obtained as the first derivative of the response to a step input. It is described by the equation
h(t) = α e −α(t − τ), t > τ
h(t) = 0, t ≤ τ
where τ is the time delay and α is the exponential rate (decay) constant. The impulse response of the organ can then obtained from that of the total system by deconvolution according to the following equation: (unfinished)
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