A steady-state transfer function analysis of portions of the circulatory system using indicator dilution techniques

Coulam, Craig M.; Warner, Homer R.; Marshall, Hiram W.; Bassingthwaighte, James B.

doi:10.1016/0010-4809(67)90011-0

Cited by 16 publications

(6 citation statements)

References 6 publications

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“…When the vascular system between A and C is linear and stationary and the sampling system transport functions are identical, then the transport functions h′ AB (t), h′ BC (t), and h′AC(t) must be identical to h AB (t), h BC (t), and h AC (t), respectively, in accordance with the mathematical argument given previously (1,2). This general approach is applicable whether the transport functions are determined in terms of a model or in terms of nonparametric functions (6).…”

Section: General Approachmentioning

confidence: 93%

Effect of flow on transpulmonary circulatory transport functions.

Knopp¹,

Bassingthwaighte²

1969

Journal of Applied Physiology

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Lung transport functions (distributions of circulatory transit times across the lung) were characterized in four anesthetized dogs at various levels of mean pulmonary blood flow. The central circulation was found to approximate a mathematically linear, time-invariant system when respiratory frequencies were maintained at 40/min or more. Lung transport functions were obtained from 144 pairs of lung-input and lung-output dilution curves using a lumped-parameter model and an iterative convolution technique. Average relative dispersion (standard deviation of the transport function divided by mean transit time) was 0.46, about twice that found previously for segments of arteries. The relative dispersion tended to increase as the mean transit time increased, suggesting that the dispersing mechanism of the lung is dependent on the mean transit time (volume/blood flow). Differences between these results and those of single-vessel transport function studies can be resolved by considering the lung as a parallel-pathway system. It is hypothesized that, as total pulmonary blood flow increases, the pathways become more equally perfused and the relative dispersion of the lung decreases. Keywordsindicator-dilution method; central blood volume; circulatory mixing; indocyanine green; cardiac output THE TRANSPORT FUNCTION, h(t), of a segment of the circulation is the probability density function of transit times from the entrance to the exit of that segment (11,19). Because the bolus of indicator becomes dispersed in its traversal of a segment of the circulation, any rapid fluctuations in concentration at the entrance are diminished in amplitude or slurred out during passage through the system; therefore, the system acts as a low-pass filter. It is possible to characterize this filter in mathematical terms-in terms of a model (3,16,20), in terms of nonparametric description as given by the transport function itself (9), or in terms of Fourier components (6).When there is only one pathway between the upstream end of the segment and the downstream end, as in an artery, the dispersion of h(t) is due to the velocity profile and to turbulence or eddies in the stream. Such transport functions have been defined for a segment of artery of the human leg (1) and also for the aorta of the dog (2). It was found that the dispersion occurring in these segments was unaffected by variations in flow rate over a wide range.In the pulmonary vascular bed there are multiple parallel pathways and different regional perfusion rates, and it is possible that the regional pulmonary vascular volume is dependent on flow rate. The purposed of this study were to characterize the transport function of the dog's lung at various mean blood flow rates and to test the effect of changes in flow and in

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Section: General Approachmentioning

confidence: 93%

Effect of flow on transpulmonary circulatory transport functions.

Knopp¹,

Bassingthwaighte²

1969

Journal of Applied Physiology

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“…The applicability of the convolution integral for combining individual responses of segments of the circulation to determine the overall response has been widely recognized [1~13]. The inverse convolution or deconvolution process which will also be used in manipulating the shunt quantification models has been used to derive the responses of specific segments of the circulation using upstream and downstream curves [14,15].…”

Section: General Modeling Considerationsmentioning

confidence: 99%

Shunt Quantification by Mathematical Analysis of Indicator Dilution Curves

Clark

et al. 1978

Catheterization and Cardiovascular Diagnosis

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Mathematical models are presented for describing and analyzing indicator dilution curves recorded in patients with intracardiac and great vessel shunts. The models treat individual segments of the circulation as linear system blocks, each having, at its output, a characteristic time response to a rapid injection of indicator at its input. These blocks are combined in feedback and feed-forward configurations to simulate left-to-right, right-to-left, and bidirectional shunts. A shunt analysis algorithm, using discrete analogs of the linear system models, was implemented in a computer program and used to analyze thermodilution curves recorded in patients with congenital heart defects. Results are presented comparing shunt fractions obtained from thermodilution curve analyses with oximetrically determined values in 20 patients. Comparing left-to-right shunts measured by the two methods, the mean systematic difference was 0.7% of pulmonary flow and the standard deviation was 7.6% of pulmonary flow. Statistical validation of the bidirectional shunt method will require acquisition and analysis of more data; however, reasonable shunt fractions were computed in five cases studied and good agreement with oximetric determinations was obtained in two cases where complete oximetric data were available.

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“…The oldest method for determining the weighting function is based on the resolution of the algebraic System (5) related to the convolution product (7). Although this method offers the advantage of being independent of any mathematical model, the lack of précision of the expérimental data often gives rise to the appearance of increasing oscillations which prevent any valid détermination of the weighting function (5).…”

Section: Si T )=J Eit)-t(t -T)dtmentioning

confidence: 99%

“…A method of resolution proposed by Coulam (7) consists of calculating the expansion of the input and output functions in Fourier séries. Used iteratively for solving the problem of extrapolation, this method gives fairly good results, but the minimum number of measuring points is not easy to fix in advance.…”

Section: Si T )=J Eit)-t(t -T)dtmentioning

confidence: 99%

“…It is also possible to try and characterize the System studied by its weighting function. To describe this function, one can expand it in séries of orthogonal functions and calculate the coefficients of the expansion (7). The problem then lies in determining the number of coefficients (degrees of freedom), and in choosing the suitable system of basic functions.…”

Section: Model and Associated Weighting Functionmentioning

confidence: 99%

See 1 more Smart Citation

Study of renal transport: Calculation of the venous responses for an arterial impulsional injection of dyes and hippuran 131I with the aid of the Pearson functions

Cantraine¹,

Bergmann²

1972

Computers and Biomedical Research

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The authors demonstrate the advantage of the Pearson functions for describing the rénal weighting function. The Pearson f unctions allow easy introduction of a timelag, and their shape is close to that of the dilution curves. The relations between the average characteristics of the input and output f unctions are examined and the weighting f unction is calculated by the moments method. The proposed représentation is used to describe the rénal weighting function of the data of Gomez (dye in man). A theoretical example enables the limits of validity of the moments method to be determined. The authors conclude with a spécimen calculation of the rénal impulsional response to hippuran '^'I. * Work carried out through contract of the Ministère de la Politique Scientif ique within the f ramework of the association Euratom,

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A steady-state transfer function analysis of portions of the circulatory system using indicator dilution techniques

Cited by 16 publications

References 6 publications

Effect of flow on transpulmonary circulatory transport functions.

Effect of flow on transpulmonary circulatory transport functions.

Shunt Quantification by Mathematical Analysis of Indicator Dilution Curves

Study of renal transport: Calculation of the venous responses for an arterial impulsional injection of dyes and hippuran 131I with the aid of the Pearson functions

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