Selection of a numerical technique for analyzing experimental data of the decay type with special reference to the use of tracers in biological systems

Worsley, Beatrice H.; Lax, Louis C.

doi:10.1016/0006-3002(62)90694-7

Cited by 34 publications

(13 citation statements)

References 13 publications

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“…The cm've indicates the solution obtained by Program I which fitted the points by a sum of two exponentials plus the constant 0.0929. Table VII shows the effect of omitting initial and terminal points on the fitted parameters, a~, as, as, a~ and on the derived functions g and M. Here g is again proportional to the transfer rate and M is the mass of the central compartment [4]. Both fitted parameters and derived functions ate seen to be fairly insensitive to omission of terminal points.…”

Section: Fig 3 Amentioning

confidence: 94%

“…Program I gave convergence to the solution already given by (4), namely, f = 10.4e -°'°56°t + 1.57e -°'°°~47t + 0.084 with E = 0.415, and Program II gave convergence to f = 25.3e -°'nDt + 2.85e -°'°16~t + 0.7172 with E = 0.0748. From the conditions of the experiment, K was known to be 0.084 [12].…”

Section: Treating K As a Fitted Parametermentioning

confidence: 96%

“…It has been applied to artificially-generated data with some success, but the difficulties inherent in applying it to experimental data, especially when there is considerable scatter and irregularly-spaced time intervals, still have to be resolved. The method of fitting by least squares outlined by Reid and developed by Worsley and Lax [3] has been used effectively on physiological data arising from both clinical and animal experiments [4] as well as in other fields [7]. Computer programs employing the leastsquares method were originally developed for the IBM 650 computer and are now also available for the IBM 7090.…”

Section: Woodbtjr¥ Editormentioning

confidence: 99%

“…This problem has been reviewed by Robertson [2]. Preliminary results were published by Worsley, Reid and Lax [3] and the methods more thoroughly analyzed by Worsley and Lax [4].…”

Section: Introductionmentioning

confidence: 98%

“…It is well established that polynomial forms do not give a satisfactory fitting to decay4ype data [4]. Forms involving the sums of exponentials are becoming widely accepted, and these alone will be considered here.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of decay-type data

Worsley

1964

Commun. ACM

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A comparative study has been made of a variety of numerical techniques for fitting experimental data of the decay type by forms involving the sums of exponentials. Statistical errors of the fitted parameters are also calculated. These methods have been applied to artificially-generated sets of data as well as to the results of experiments with radioactive tracers on both human and animal subjects. Results show that the values of the fitted parameters are very sensitive to variations in the fitting procedure. Therefore great care must be exercised in identifying such values with physical constants. Although the values of functions derived from these fitted parameters which can definitely be associated with physical entities are generally more stable under variations in the fitting techniques, error bounds can be so large that no great confidence can be placed even in them. It would therefore appear best to select a uniform technique both for running the experiments and for analyzing the data, and then to consider as significant only relative results between one subject and the next.

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Section: Fig 3 Amentioning

confidence: 94%

Section: Treating K As a Fitted Parametermentioning

confidence: 96%

Section: Woodbtjr¥ Editormentioning

confidence: 99%

“…This problem has been reviewed by Robertson [2]. Preliminary results were published by Worsley, Reid and Lax [3] and the methods more thoroughly analyzed by Worsley and Lax [4].…”

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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Analysis of decay-type data

Worsley

1964

Commun. ACM

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Spinal Fluid Appearance of

Janeway¹,

Maynard²,

Witcofski³

et al. 1968

Archives of Neurology

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THE radiopharmaceutical, 99m Technetium (99mTc), pertechnetate is widely used as an agent for brain scanning. Due to its nearly ideal \g=g\-emission energy (140 kev), short half-life (six hours), and absence of primary particle radiation, relatively large doses can be used so that definition and resolution are quite good with this isotope. At the same time, the radiation dose is reduced when compared to other brain scanning agents. There is relatively little information available explain why certain lesions are associated with abnormal accumulations of radio-$ activity while others do not show this uptake.To determine whether alterations in permeability might possibly account for some of this variation, we observed the fractional rate at which an intravenously injected dose of 99mTc pertechnetate appeared in the cerebrospinal fluid (CSF) of neurologically normal patients. This report describes our observations. Materials and MethodsSterile 99mTc pertechnetate obtained from a molybdenum-Technetium generator was used for injection and for preparation of a suitable counting standard. Sixty-five /¿c/lb were inject¬ ed intravenously which resulted in a total dose between 10 and 12 mc in most patients. Brain scans were obtained in four or five views using a rapid rectilinear scanner and techniques pre¬ viously described.1 Samples of blood with added anticoagulant were obtained before injection of the isotope to establish the background count. A blood sample was taken from each patient either five or ten minutes after intravenous in¬ jection from an arm vein on the side opposite the injection site. Subsequent blood samples were drawn simultaneously with the lumbar puncture and CSF extraction. Eighty-five blood and 68 CSF samples were obtained from 32 pa¬ tients. CSF samples with more than five red blood cells per cubic millimeter were rejected from the study. Duplicate samples of plasma, CSF, and the prepared standard were counted at the same time in an automatic V-counter.The results were corrected for physical decay and recorded as fraction of injected dose per gram of blood plasma or CSF. Samples were obtained over a time period ranging from five minutes to 25 hours after injection of the isotope. Samples were more closely spaced and involved more patients in the early intervals because initial changes with time in the concen¬ tration of the isotope are greater and further¬ more, are critical to the estimation of kinetic parameters. The period of observation spanned four half-lives of the isotope. After this time, count rates were so low in the CSF that they could not be estimated with statistical reliability.Multiexponential least-squares time functions were fitted to the specific activity data for each compartment by means of a numerical iterative technique. Analysis was carried out with the aid of an IBM 7094 digital computer equipped

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Ein Rechenprogramm zur Schätzung der Parameter von Kompartimentmodellen auf der Grundlage von Daten aus Isotopenmarkierungsexperimenten

Winkler¹

1974

Biom. J.

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EinleitungDaten aus Tracerexperimenten dienen haufig ah Grundlage zur Aufstellung von Kompartimentmodellen. Im Rahmen von Untersuchungen des pflanzlichen Proteinstoffwechsels mit Hilfe von i5N-Markierungsexperimenten, deren Ergebnisse a n anderer Stelle veroffentlicht werden (WINKLER, 1972 ; WINKLER, in Vorber. ; DAHLHELM, WINKLER, H~B N E R , in Vorber.) wurde ein Rechenprogramm erarbeitet , welch-die Schatzung der Parameter von Kompartimentmodellen gestattet. Es wurde in FORTRAN fur den Rechner BESM 6 geschrieben. In seinen Grundlagen beruht das Programm auf Arbeiten von BERMAN (1962; 1965) ; entsprechend den speziellen Erfordernissen bei der Bearbeitung des eingangs erwahnten Problems ergaben sich hderungen und Vereinfachungen. Wie das Programm von BERMAN besteht daa nachfolgend beschriebene aus einem problem-(modell-)unabhangigen Hauptteil und einem auswechselbaren problemspezifischen Unterprogramm (LOESG), welchw die theoretiwhen Funktionswerte liefert. Dadurch kann das Programm nicht nur, wie hier beschrieben, fur Kompartimentmodelle, sondern auch bei Vorliegen anderer Modelltypen verwendet werden, wobei das Unterprogramm LOESG entsprechend ausgewechselt werden muB. Problemstellung Gegeben seien Funktionen (ein mathematisches Modell), welche M Parameter p , enthalten, und Funktionen einer Variablen t (z. R. der Zeit) sind:(1) f; 3 f ; ( p , , . . . , p d i , t ) , i = 1, 2, . . .) 71.Weiterhinseienfur bestimmteWertet,derunabhangigenVilriablenf= ( k l , 2 , . .. , K ) MeBwerte x , k vorhanden, die mit den Funktionen (1) durch(2)x t k = f i ( p m 9 t, + &iC verknupft sein sollen. Die GroBen t i , sind ,,MeBfehler" mit dem Erwartungswert Null. Das gestellte Problem besteht darin. auf dcr Grundlage der MeBwerte 2 , '

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Selection of a numerical technique for analyzing experimental data of the decay type with special reference to the use of tracers in biological systems

Cited by 34 publications

References 13 publications

Analysis of decay-type data

Analysis of decay-type data

Spinal Fluid Appearance of

Ein Rechenprogramm zur Schätzung der Parameter von Kompartimentmodellen auf der Grundlage von Daten aus Isotopenmarkierungsexperimenten

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