Coulam C M, Warner H R, Marshall H W, Bassingthwaighte J B
Comput Biomed Res. 1967 Jul;1(2):124-38. doi: 10.1016/0010-4809(67)90011-0.
A digital computer program has been developed whereby the distribution of dye-particle transit times across circulatory pathways can be found from recordings of upstream and downstream indicator-dilution curves. This distribution or transfer function is computed from Fourier-series representations of the upstream and downstream indicator curves and makes possible, for the first time, the calculation of transit-time distributions independent of the effects of recirculating dye. Since a discontinuity is introduced into the tails of the upstream and downstream curves at the end of sampling, the method requires an iterative approach in the termination of the upstream and downstream curves. The accuracy of the calculated distribution pattern is determined by comparison of the recorded downstream curve with the results of the convolution of the recorded upstream curve and computed transfer function. Effects of noise, bandwidth and sampling rate have been investigated through the use of analog computer models of the circulatory pathways. These studies show that the transfer-function description is limited by the bandwidth of the upstream (input) curve. Noise, or variations in magnitude and phase angle of input- and output-curve frequencies, tends to introduce oscillations into the time-domain representation of the transfer function as does the use of too few frequencies. This means that in biological systems the upstream sampling site must be relatively close to the dye injection site if the input and output sampling sites are close together. Circulatory transfer functions have been obtained from dogs across their lower extremity, renal and systemic circulations before, during and following moderate exercise (walking on treadmill at two miles per hour for four minutes).
已开发出一种数字计算机程序，通过该程序可以从上游和下游指示剂稀释曲线的记录中找出染料颗粒在循环路径中的传输时间分布。这种分布或传递函数是根据上游和下游指示剂曲线的傅里叶级数表示计算得出的，首次使得能够独立于再循环染料的影响来计算传输时间分布。由于在采样结束时上游和下游曲线的尾部会出现不连续性，该方法在上游和下游曲线的终止处理上需要采用迭代方法。通过将记录的下游曲线与记录的上游曲线和计算出的传递函数的卷积结果进行比较，来确定计算出的分布模式的准确性。已通过使用循环路径的模拟计算机模型研究了噪声、带宽和采样率的影响。这些研究表明，传递函数描述受到上游（输入）曲线带宽的限制。噪声，即输入和输出曲线频率的幅度和相位角变化，往往会像使用过少频率一样，在传递函数的时域表示中引入振荡。这意味着在生物系统中，如果输入和输出采样点靠得很近，那么上游采样点必须相对靠近染料注射点。已在狗身上获取了在适度运动（以每小时两英里的速度在跑步机上行走四分钟）之前、期间和之后，其下肢、肾脏和全身循环的循环传递函数。
