The application of the method of maximum likelihood to the analysis of tracer kinetic data

Sándor, Tamás; Conroy, M. F.; Hollenberg, Norman K.

doi:10.1016/0025-5564(70)90100-8

Cited by 24 publications

(12 citation statements)

References 3 publications

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“…The flow parameters of a two-compartment cerebral clearance curve were estimated by a maximum- likelihood procedure. 8 Estimates produced by this procedure are within a few percent of the more commonly used unweighted least-squares procedure. 7 Flow values obtained in young normal subjects with this model have been found to correspond to values obtained with the l33 Xe intracarotid injection technique.…”

Section: Methodsmentioning

confidence: 79%

Cerebral blood flow asymmetry in the detection of extracranial cerebrovascular disease.

Robertson

Welch

Tilley

et al. 1988

Stroke

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Regional cerebral blood flow was measured by the l33Xe inhalation technique in patients with unilateral carotid occlusion, unilateral carotid occlusion and contralateral carotid stenosis, bilateral carotid occlusion, or normal arteriograms. After adjusting for age, sex, and history of stroke, hemispheric blood flow asymmetry was shown to be a predictor of unilateral carotid occlusion with a sensitivity of 80.6% and a specificity of 80.5%. Asymmetry of regional cerebral blood flow is useful in the assessment of patients with extracranial cerebrovascular disease. identify asymptomatic and transiently symptomatic patients with impending cerebral infarction. Accordingly, an inexpensive, atraumatic, reliable, and readily available technique for patients at risk for cerebrovascular disease would be of great value. One such technique is the measurement of regional cerebral blood flow (rCBF) by l33 Xe inhalation. Measurement of rCBF has proved of little utility in the evaluation of stroke patients, 1 -3 but assessment of rCBF asymmetries may be of greater value, 3 -6 as in our study of patients with carotid occlusion. Our study was undertaken to determine the efficacy of the l33 Xe inhalation rCBF technique in the detection and evaluation of extracranial carotid occlusive disease. Subjects and MethodsWe studied 104 patients (74 men, 30 women) who had cerebral arteriography and rCBF measurement for the evaluation of suspected cerebrovascular disease (Table 1). In most patients arteriography was performed with four-vessel selective injections via femoral catheterization. A few patients had aortic arch studies or bilateral carotid artery injections. Patients were grouped into those with unilateral carotid occlusion (UCO), unilateral carotid Supported by National Institutes of Health Grant NS 23393 and the Fund for Henry Ford Hospital.Received July 28, 1987; accepted March 8, 1988. occlusion and contralateral carotid stenosis of >50%

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Section: Methodsmentioning

confidence: 79%

Cerebral blood flow asymmetry in the detection of extracranial cerebrovascular disease.

Robertson

Welch

Tilley

et al. 1988

Stroke

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“…There have been a number of proposals advanced and computer programs written (17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30)(31)(32)(33) which attempt to estimate the parameters of nonlinear equations. However, among those using weighted least-squares parameter estimation none appear to combine the rapid and reliable Marquardt convergence technique with both residual error testing to select among models and tests on the validity of the fit to the data.…”

Section: Discussionmentioning

confidence: 99%

“…The method of maximum likelihood has beec applied (29) to multiexponential tracer data, using the Poisson distribution as the probability distribution. If the errors about the final curve are normally distributed (and they very nearly are in the present application), then the maximum-likelihood and the least-squares solution yield the same equations for parameter estimation.…”

Section: Discussionmentioning

confidence: 99%

A Weighted Least-Squares Technique for the Analysis of Kinetic Data and Its Application to the Study of Renal ¹³³ Xenon Washout in Dogs and Man

Dell

Sciacca

Lieberman

et al. 1973

Circulation Research

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A computer program was written in PL/ 1 to successively fit the sum of two, three, and four exponential terms to data by an iterative least-squares technique, using a combination of the steepest-descent and the Newton-Baphson methods for convergence. Each data point was weighted by the reciprocal of its variance, assuming that the errors followed a Poisson distribution. A compartment, i.e., an exponential term, was declared nonsignificant if it did not significantly reduce the least-squares error about the fitted line as judged by an F test. Validity of the data was assessed by a "runs" test and by the frequency with which data points fell outside the 95% confidence range. Results of the analysis showed that (1) 9 of 12 normal human kidney l33 Xe washout curves were best described by a four-compartment model, (2) 18 of 38 studies in patients with essential hypertension yielded a four-compartment curve with significant reduction in compartment-1 flow, (3) nine patients with congestive heart failure all had three-compartment washout curves, (4) t w o patients with oliguric renal failure had washout curves described best by a two-exponential equation (one of these patients responded to an injection of furosemide with the appearance of a third, more rapid compartment). Obvio u sly, this form of analysis can be easily applied to other sets of data which are described by nonlinear equations.KEY WOBDS inert gas washout curves essential hypertension model fitting nonlinear regression analysis intr»renal distribution of blood flow • Mathematical expressions describing quantitative physiological data have a demonstrated value in modern physiological research. Such expressions are usually based on either an empirically derived equation (s) which summarizes the phenomenon under study or a theoretically derived mathematical model. In either case, the mathematical expression contains parameters with unknown values, and the problem is to estimate values for these parameteis from experimental data. Frequently, well-known techniques of linear regression or multiple regression can be used for parameter estimation providing the equation is linear or can be linearized. In many cases, however, nonlinear equations cannot be linearized, e.g., an equation containing the sum of exponentials. In these instances nonlinear regression techniques for parameter estimation are necessary (1). Graphic techniques have been extensively used in the past for nonlinear parameter estimation (2), but this technique has several limitations: (a) it is subjective, (b) it is unable to separate parameters of similar magnitude with a high degree of c o nfidence, (c) it cannot provide confidence limits for the parameter estimates, and (d) it assumes that all of the data points have an equal variance.Because of these limitations we developed a digital computer technique for nonlinear regression analysis by which parameters were estimated by a east-squares procedure with each data point being weighted if the variance was given. Confidence limits for the paramete...

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“…The flow values of a two-compartment cerebral clearance curve (start-fit time when air function reached 20% of peak value) were estimated by a maximum likelihood procedure. 12 Estimates produced by this procedure are within a few percent of the more commonly used unweighted least-squares procedures. 13 A partition coefficient of approximately .83 was used and adjusted for hematocrit.…”

Section: Regional Cerebral Blood Flow Measurementsmentioning

confidence: 92%

Cerebral blood flow in migraine accompaniments and vertebrobasilar ischemia.

Ramadan

Levine

Welch

1994

Stroke

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Transient neurological symptoms of brain stem or occipital lobe origin may be caused by transient ischemic attack in the vertebrobasilar territory (VB-TIA) or late-onset (or late-life) migraine accompaniment (LOMA). It is often clinically difficult to distinguish between VB-TIA and LOMA. Cerebral blood flow of 23 patients with VB-TIA, 24 with LOMA, and 28 age-matched control subjects was measured using the 133Xe inhalation regional cerebral blood flow (rCBF) technique. After adjusting for differences in baseline variables such as blood pressure, hematocrit, and PCO2, patients with VB-TIA had (1) lower mean rCBF than control subjects (P < .003) as measured by the initial slope index method; (2) more frequent anterior rCBF asymmetries than control subjects and patients with LOMA (P < .03 for both comparisons); and (3) higher mean interhemispheric rCBF differences compared with patients with LOMA (P = .08) and control subjects (P < .02). Regional CBF patterns in patients with VB-TIA and LOMA differ, with lower rCBF and more asymmetry of the anterior blood flows in patients with VB-TIA, probably reflecting the effects of stroke risk factors on the cerebral circulation. Patients with LOMA have rCBF patterns more closely resembling those of age-matched healthy subjects. rCBF measurements may assist in the clinical diagnosis of VB-TIA and late-onset migrainous events.

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The application of the method of maximum likelihood to the analysis of tracer kinetic data

Cited by 24 publications

References 3 publications

Cerebral blood flow asymmetry in the detection of extracranial cerebrovascular disease.

Cerebral blood flow asymmetry in the detection of extracranial cerebrovascular disease.

A Weighted Least-Squares Technique for the Analysis of Kinetic Data and Its Application to the Study of Renal ¹³³ Xenon Washout in Dogs and Man

Cerebral blood flow in migraine accompaniments and vertebrobasilar ischemia.

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The application of the method of maximum likelihood to the analysis of tracer kinetic data

Cited by 24 publications

References 3 publications

Cerebral blood flow asymmetry in the detection of extracranial cerebrovascular disease.

Cerebral blood flow asymmetry in the detection of extracranial cerebrovascular disease.

A Weighted Least-Squares Technique for the Analysis of Kinetic Data and Its Application to the Study of Renal 133 Xenon Washout in Dogs and Man

Cerebral blood flow in migraine accompaniments and vertebrobasilar ischemia.

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A Weighted Least-Squares Technique for the Analysis of Kinetic Data and Its Application to the Study of Renal ¹³³ Xenon Washout in Dogs and Man