Abstract
Radiotracers are widely used for the investigation of organ perfusion and function. One of the quantitative approaches to analyze radiotracer data is the calculation of the impulse response function, which is obtained by deconvolution analysis of the time-activity curves measured over the organ. Since exactness of the calculated impulse response function depends both on the counting statistics and on the deconvolution algorithm applied, computer simulated time-activity curves were used to test the least squares deconvolution program based on the matrix regularization algorithm. Criteria of clinical importance (error in the calculated organ function parameters) and criteria of mathematical importance (deconvolution and reconvolution error) were investigated. For three typical impulse response functions f(t), it was found that: 1. In cases of noncompartmental vascular-capillary f(t)'s, a high degree of smoothing is preferable during deconvolution, in this way the error becomes systematic but controllable. 2. Noncompartmental vascular-tubular f(t)'s are noise sensitive, but fortunately, noise in the data can be held to a minimum. 3. Compartmental f(t)'s need only a minimal degree of smoothing; their components can be identified in a second step using a multiexponential least squares fit.
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Alderson PO, Douglass KH, Mendenhall KG, Guadiani VA, Watson DC, Links JM, Wagner HN Jr (1979) Deconvolution analysis in radionuclide quantitation of left-to-right cardiac shunts. J Nucl Med 20:502–506
Bacharach SL, Green MV, Vitale D, White G Douglas MA, Bonow RO, Larson SM (1983) Optimum Fourier filtering of cardiac data: A minimum error method: Concise communication. J Nucl Med 24:1176–1184
Brendel AJ, Commenges D, Salamon R, Ducassou D, Blanque P (1983) Deconvolution analysis of radionuclide angiocardiography curves: Problems arising from fragmented bolus injections. Eur J Nucl Med 8:93–98
Britton KE, Nimmon CC, Lee TY, Jerritt PH, Granowska M, Greening A, McAlister JM (1977) Carotid and cerebral blood flow. In: Brill AB, Price RR (eds) Information processing in medical imaging. Oak Ridge National Laboratory, Oak Ridge, pp 499–525
Bronikowski TA, Dawson CA, Linehan JH (1983) Model-free deconvolution techniques for estimating vascular transport functions. Int J Biomed Comput 14:411–429
Cohn JD, Del Guercio LRM (1967) Clinical application of indicator dilution curves as gamma functions J Lab Clin Med 69:675–682
Commenges D, Brendel AJ (1982) A deconvolution program for processing radiotracer dilution curves. Comput Programs Biomed 14:271–276
Coulam CM, Warner HR, Wood EH, Bassingthwaighte JB (1966) A transfer function analysis of coronary and renal circulation calculated from upstream and downstream indicator-dilution curves. Circ Res 19:879–890
Davenport R (1983) The derivation of the gamma-variate relationship for tracer dilution curves. J Nucl Med 24:945–948
Diffey BL, Corfield JR (1976) Data-bounding technique in discrete deconvolution. Med Biol Eng 14:478
Gamel J, Rousseau WF, Katholi CR, Mesel E (1973) Pitfalls in digital computation of the impulse response of vascular beds from indicator-dilution curves. Circ Res 32:516–523
Hunt BR (1970) The inverse problem of radiography. Math Biosci 8:161–179
Kim BM, Harris TR (1970) The identification of transport parameters from truncated physiological tracer curves. Bull Math Biophys 32:355–375
Kuruc A, Caldicott WJH, Treves S (1982) An improved deconvolution technique for the calculation of renal retention functions. Comput Biomed Res 15:46–56
Kuruc A, Treves S, Parker JA (1983a) Accuracy of deconvolution algorithms assessed by simulation studies: Consise communication. J Nucl Med 24:258–263
Kuruc A, Treves S, Parker JA, Cheng C, Sawan A (1983b) Radionuclide angiocardiography: An improved deconvolution technique for improvement after suboptimal bolus injection. Radiology 148:233–238
Marquardt DW (1963) An algorithm for least-squares estimation of nonlinear parameters. J Soc Ind Appl Math 11:431–441
Meier P, Zierler KL (1954) On the theory of the indicator-dilution method for measurement of blood flow and volume. J Appl Physiol 6:731–744
Nakai M (1981) Computation of transport function using multiple regression analysis. Am J Physiol 240:H133-H144
Neufeld GR (1971) Computation of transit time distributions using sampled data Laplace transforms. J Appl Physiol 31:148–153
Nyitrai L (1983) Transzfer függvény értelmezése és kiszámítása perfúziós vizsgálatokban (The interpretation and computation of transfer functions in perfusion studies). Izotóptechnika 26:197–214
Nyitrai L (1984) Simulation experiments to verify the interpretations of transfer function (TF). In: Schmidt HAE, Vauramo E (eds) Nuclearmedizin. Proceedings of the European Nuclear Medicine Congress, Helsinki 1984, Schattauer, Stuttgart New York, pp 371–376
Nyitrai L, Szabó Z (1984) Calculation of regional cerebral blood flow (rCBF) using non-diffusible tracers. A model-free approach. In: Schmidt HAE, Vauramo E (eds) Nuklearmedizin. Proceedings of the European Nuclear Medicine Congress, Helsinki 1984, Schattauer, Stuttgart New York, pp 506–509
Phillips DL (1962) A technique for the numerical solution of certain integral equations of the first kind. J ACM 9:84–97
Skopp J (1984) Estimation of true moments from truncated data. AIChE J 30:151–155
Slinker BK, Glantz SA (1985) Multiple regression for physiological data analysis—the problem of multicollinearity. Am J Physiol 249:R1-R12
Strand ON, Westwater ER (1968) Statistical estimation of the numerical solution of a Fredholm integral equation of the first kind. J ACM 15:100–114
Szabó Z, Nyitrai L, Vosberg H, Wilcke C, Feinendegen LE (1984) Quantitative measurement of renal transplant perfusion using transfer function and a random walk model. In: Schmidt HAE, Vauramo E (eds) Nuklearmedizin. Proceedings of the European Nuclear Medicine Congress, Helsinki 1984, Schattauer, Stuttgart New York, pp 416–419
Szabó Z, Vosberg H, Torsello G, Sandmann W, Feinendegen LE (1985a) Parameters of 99mTc-DTPA-transfer function in renal artery stenosis. Cardiology (Suppl) 72:46–48
Szabó Z, Vosberg H, Sondhaus CA, Feinendegen LE (1985b) Model identification and estimation of organ function parameters using radioactive tracers and the impulse response function. Eur J Nucl Med 11:265–274
Szabó Z, Sondhaus CA, Frick-Gipp C, Vosberg H, Feinendegen LE (1986) Calculation of parameters describing free fatty acid utilization by deconvolution analysis of scintigraphic data. In: Britton KE, Schmidt HAE (eds) Nuklearmedizin, Proceedings of the European Nuclear Medicine Congress, London 1985, Sohattauer, Stuttgart, New York, pp 643–645
Thompson HK, Starmer CF, Whalen RE, McIntosh HD (1964) Indicator transit time considered as a gamma variate. Circ Res 14:502–515
Twomey S (1963) On the numerical solution of Fredholm integral equations of the first kind by the inversion of the linear system procedure by quadrature. J ACM 10:97–101
Twomey S (1965) The application of numerical filtering to the solution of integral equations encountered in indirect sensing measurements. J Franklin Inst 279:95–109
Valentinuzzi ME, Volachec EMM (1975) Discrete deconvolution. Med Biol Eng 13:123–125
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Szabó, Z., Nyitrai, L. & Sondhaus, C. Effects of statistical noise and digital filtering on the parameters calculated from the impulse response function. Eur J Nucl Med 13, 148–154 (1987). https://doi.org/10.1007/BF00289028
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DOI: https://doi.org/10.1007/BF00289028