gms | German Medical Science

65th Annual Meeting of the German Association for Medical Informatics, Biometry and Epidemiology (GMDS), Meeting of the Central European Network (CEN: German Region, Austro-Swiss Region and Polish Region) of the International Biometric Society (IBS)

06.09. - 09.09.2020, Berlin (online conference)

Article

Send article

Modified maximum entropy method

Meeting Abstract

Search Medline for

  • Zahra AminiFarsani - Statistics Department, Lorestan University, Iran, Khorramabad, Iran

Deutsche Gesellschaft für Medizinische Informatik, Biometrie und Epidemiologie. 65th Annual Meeting of the German Association for Medical Informatics, Biometry and Epidemiology (GMDS), Meeting of the Central European Network (CEN: German Region, Austro-Swiss Region and Polish Region) of the International Biometric Society (IBS). Berlin, 06.-09.09.2020. Düsseldorf: German Medical Science GMS Publishing House; 2021. DocAbstr. 124

doi: 10.3205/20gmds342, urn:nbn:de:0183-20gmds3427

Published: February 26, 2021

© 2021 AminiFarsani.
This is an Open Access article distributed under the terms of the Creative Commons Attribution 4.0 License. See license information at http://creativecommons.org/licenses/by/4.0/.

Outline

Text

Background: For kinetic models used in contrast based medical imaging, the determination of the arterial input function (AIF) is essential for the estimation of physiological parameters of the tissue via solving a nonlinear inverse problem named.

Objective: In this paper, we propose to estimate the AIF based on the modified maximum entropy method. The effectiveness of several numerical methods to determine kinetic parameters and the AIF is evaluated – in situations where not enough information about the AIF is on hand. The purpose of this study is to identify the most appropriate method for estimating this function.

Materials and methods: The modified algorithm is a combination of Maximum Entropy principles and optimization method which we named modified maximum entropy method (MMEM). We apply this algorithm in a Bayesian framework to estimate the kinetic parameters via the unique form of the arterial input function. We evaluate the efficiency of our algorithm to estimate the kinetic parameters of Dynamic Contrast-Enhanced Magnetic Resonance Imaging (DCE-MRI) and AIF with some other parameter-estimation methods and a standard fixed AIF-method. A previously analyzed dataset consisting of contrast agent concentration in tissue and plasma is used.

Results and conclusion: We compare the accuracy of the results arrived from the MMEM with the Bayesian method, Empirical Method, Maximum Likelihood, the Modified Maximum Likelihood Method, moment matching (“method of moments”), quantile matching and the least square method. The numerical results proposed the Weibull distribution as an appropriate and robust AIF and they illustrated the power and effectiveness of the proposed methods to estimate its parameters.

The authors declare that they have no competing interests.

The authors declare that an ethics committee vote is not required.

Outline

References

1.
Berg B, Stucht D, Janiga G, Beuing O, Speck O, Thovenin D. Cerebral Blood Flow in a Healthy Circle of Willis and Two Intracranial Aneurysms: Computational Fluid Dynamics Versus Four-Dimensional Phase-Contrast Magnetic Resonance Imaging. ASME J Biomech Eng. 2014;15:041003. DOI: 10.1115/1.4026108 External link
2.
Brix G, Kiessling F, Lucht R, Darai S, Wasser K, Delorme S, Griebe J. Microcirculation and microvasculature in breast tumors: pharmacokinetic analysis of dynamic MR image series. Magnetic Resonance in Medicine. 2004;52(2):420–429.
3.
Casella G, Berger R. Statistical inference 2. Duxbury, CA, USA; 2002.
4.
Cheng HLM. T1 measurement of flowing blood and arterial input function determination for quantitative 3D T1-weighted DCE-MRI. Journal of magnetic resonance imaging JMRI. 2007;25(5):1073–8.
5.
Cheng HLM. Investigation and optimization of parameter accuracy in dynamic contrast-enhanced MRI. Journal of Magnetic Resonance Imaging. 2008;28(3):736–743.
6.
Dikaios N, Arridge S, Hamy V, Punwani S, Atkinson D. Direct parametric reconstruction from undersampled (k, t)-space data in dynamic contrast enhanced MRI. Medical Image Analysis. 2014;18(7):989–1001.
7.
Ebrahimi N, Soofi ES, Soyer R. Multivariate maximum entropy identification, transformation, dependence. Multi Analys. 2008;99:1217–1231.
8.
Elfving T. An Algorithm for Maximum Entropy Image Reconstruction form Noisy Data. Math Comput Modeling. 1989;12:729–745.
9.
Farsani ZA, Schmid VJ. Maximum entropy approach in dynamic contrast-enhanced magnetic resonance imaging. Methods of information in medicine. 2017;56(06):461–468.
10.
Fritz-Hansen T, Rostrup E, Larsson HBW, S\u248 ?ndergaard L, Ring P, Henriksen O. Measurement of the Arterial Concentration of Gd-DTPA Using MRI: A step toward Quantitative Perfusion Imaging. Magnetic Resonance in Medicine. 1996;36(2):225–231.
11.
Gauthier M . Impact of the arterial input function on microvascularization parameter measurements using dynamic contrast-enhanced ultrasonography. World Journal of Radiology. 2012;4(7):291.
12.
Jackson A, Constable C, Gillet N. Maximum entropy regularization of the geomagnetic core field inverse problem. Geophysical Journal International. 2007;171(3):995–1004.
13.
Jaynes ET. Information Theory and Statistical Mechanics. Physics Review. 1957;106(4):620–630.
14.
Justus C, Hargraves W, Mikhail A, Graber D. Methods for estimating wind speed frequency distributions. Journal of applied meteorology. 1978;17(3):350–353.
15.
Larsson HBW, Tofts PS. Measurement of blood-brain barrier permeability using dynamic Gd-DTPA scanning –a comparison of methods. Magnetic Resonance in Medicine. 1992;24(1):174–176.
16.
Murase K. Efficient method for calculating kinetic parameters using T1-weighted dynamic contrast-enhanced magnetic resonance imaging. Magnetic resonance in Medicine. 2004;51(4):858–862.
17.
Orton MR, Collins DJ, Walker-Samuel S, d'Arcy JA, Hawkes DJ, Atkinson D, Leach MO. Bayesian estimation of pharmacokinetic parameters for DCE-MRI with a robust treatment of enhancement onset time. Phys Med Biol. 2007;52:2393–2408.
18.
Parker GJ, Roberts C, Macdonald A, Buonaccorsi GA, Cheung S, Buckley DL, Jackson A, Watson Y, Davies K, Jayson GC. Experimentally-derived functional form for a population-averaged high-temporal-resolution arterial input function for dynamic contrast-enhanced MRI. Magnetic Resonance in Medicine. 2006;56(5):993–1000.
19.
Pougaza DB, Djafari AM. Maximum Entropy Copulas. In: AIP Conference Proceeding. 2011. p. 2069–2072.
20.
Rao RV, Savsani VJ, Vakharia D. Teaching–learning-based optimization: a novel method for constrained mechanical design optimization problems. Computer-Aided Design. 2011;43(3):303–315.
21.
Rao RV, Savsani VJ, Vakharia D. Teaching–learning-based optimization: an optimization method for continuous non-linear large scale problems. Information sciences. 2012;183(1):1–15.
22.
Schmid VJ, Whitcher B, Padhani AR, Taylor NJ, Yang GZ. Bayesian methods for pharmacokinetic models in dynamic contrast-enhanced magnetic resonance imaging. IEEE Transactions on Medical Imaging. 2006;25(12):1627–36.
23.
Thomas A, Cover TM. Elements of Information Theory. John Wiley, New Jersey; 2006.
24.
Tofts PS, Kermode AG. Measurement of the blood-brain barrier permeability and leakage space using dynamic MR imaging – 1. Fundamental concepts. Magnetic Resonance in Medicine. 1991;17(2):357–367.
25.
Weinmann HJ, Laniado M, Mützel W. Pharmokinetics of Gd-DTPA/Dimeglumine after intravenous injection into healthy volunteers. Physiological Chemistry & Physics & Medical NMR. 1984;16:167–172.