Abstract
This study developed an adaptive weighted nonlinear least squares (AWNLS) method for solving the problem of high variability in the estimates of the microrate constants of fluorodeoxyglucose (FDG) kinetics caused by measurement noise. In the AWNLS method for adaptive quantitative analysis, the cost function is adjusted according to the characteristics of the tissue time-activity curve (TTAC). Specifically, the average of the early part of the TTAC was used to modify the cost function when fitting the FDG model to the TTAC. A computer simulation study applying different sets of parameter values and noise conditions was conducted. The accuracy and reliability of the parameter estimates obtained using AWNLS were compared with those of nonlinear least squares (NLS), weighted nonlinear least squares (WNLS), linear least squares (LLS), and generalized linear least squares (GLLS). The errors in k1–k3 obtained using NLS indicate this method’s poor precision in the presence of high noise levels. NLS and WNLS were sensitive to the initial values. Moreover, the results of k4 estimated using LLS and GLLS were inaccurate because of large bias. By contrast, the microrate constants (k1–k4), the FDG metabolic rate (K), and the volume of distribution (k1/k2) obtained using AWNLS were stable and accurate regardless of the noise level and initial values. The AWNLS method could estimate the FDG metabolic rate (K) and the microrate constants (k 1–k 4) of the FDG model accurately at various noise levels, irrespective of the initial values.
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Sokoloff, L., Reivich, M., Kennedy, C., Des Rosiers, M., Patlak, C. S., Pettigrew, K., et al. (1977). The [14C] deoxyglucose method for the measurement of local cerebral glucose utilization: theory, procedure, and normal values in the conscious and anesthetized albino rat. Journal of Neurochemistry, 28(5), 897–916.
Phelps, M., Hoffman, E., Huang, S. C., & Kuhl, D. (1977). Positron tomography:” in vivo” autoradiographic approach to measurement of cerebral hemodynamics and metabolism. Acta Neurologica Scandinavica. Supplementum, 64, 446–477.
Su, K. H., Lee, J. S., Li, J. H., Yang, Y. W., Liu, R. S., & Chen, J. C. (2009). Partial volume correction of the microPET blood input function using ensemble learning independent component analysis. Physics in Medicine & Biology, 54(6), 1823–1846.
Chen, I., Hsu, Y. Y., Chen, C. C., & Lin, K. P. (2002). Multi-parameter evaluation of brain tumor with a www based multimedia database system. Journal of Medical and Biological Engineering, 22(1), 41–48.
Fang, Y. H., Kao, T., Wu, L. C., & Liu, R. S. (2003). Quantitative analysis of 11C-acetate in nasopharyngeal carcinoma with positron emission tomography. Journal of Medical and Biological Engineering, 23(3), 97–102.
Huang, S. C., Phelps, M. E., Hoffman, E. J., Sideris, K., Selin, C. J., & Kuhl, D. E. (1980). Noninvasive determination of local cerebral metabolic rate of glucose in man. American Journal of Physiology-Endocrinology And Metabolism, 238(1), E69–E82.
Phelps, M., Huang, S., Hoffman, E., Selin, C., Sokoloff, L., & Kuhl, D. (1979). Tomographic measurement of local cerebral glucose metabolic rate in humans with (F-18) 2-fluoro-2-deoxy-d-glucose: validation of method. Annals of Neurology, 6(5), 371–388.
Patlak, C. S., Blasberg, R. G., & Fenstermacher, J. D. (1983). Graphical evaluation of blood-to-brain transfer constants from multiple-time uptake data. Journal of Cerebral Blood Flow and Metabolism, 3(1), 1–7.
Patlak, C. S., & Blasberg, R. G. (1985). Graphical evaluation of blood-to-brain transfer constants from multiple-time uptake data. Generalizations. Journal of Cerebral Blood Flow and Metabolism, 5(4), 584–590.
Zheng, X., Wen, L., Yu, S. J., Huang, S. C., & Feng, D. D. (2012). A study of non-invasive Patlak quantification for whole-body dynamic FDG-PET studies of mice. Biomedical Signal Processing and Control, 7(5), 438–446.
Ikoma, Y., Watabe, H., Shidahara, M., Naganawa, M., & Kimura, Y. (2008). PET kinetic analysis: error consideration of quantitative analysis in dynamic studies. Annals of Nuclear Medicine, 22(1), 1–11.
Feng, D., Ho, D., Chen, K., Wu, L. C., Wang, J. K., Liu, R. S., et al. (1995). An evaluation of the algorithms for determining local cerebral metabolic rates of glucose using positron emission tomography dynamic data. IEEE Transactions on Medical Imaging, 14(4), 697–710.
Wu, L. C., Feng, D., Wang, J. K., Lin, H. M., Chou, K. L., Liu, R. S., et al. (1998). Quantitative analysis of FDG PET images. Annals of Nuclear Medicine, 11(2), 29–33.
Feng, D., Huang, S. C., Wang, Z., & Ho, D. (1996). An unbiased parametric imaging algorithm for nonuniformly sampled biomedical system parameter estimation. IEEE Transactions on Medical Imaging, 15(4), 512–518.
Dai, X., Chen, Z., & Tian, J. (2011). Performance evaluation of kinetic parameter estimation methods in dynamic FDG-PET studies. Nuclear Medicine Communications, 32(1), 4–16.
Muzic, R. F., & Christian, B. T. (2006). Evaluation of objective functions for estimation of kinetic parameters. Medical Physics, 33(2), 342–353.
Lammertsma, A. A., Brooks, D. J., Frackowiak, R. S., Beaney, R. P., Herold, S., Heather, J. D., et al. (1987). Measurement of glucose utilisation with [18F] 2-fluoro-2-deoxy-d-glucose: a comparison of different analytical methods. Journal of Cerebral Blood Flow and Metabolism, 7(2), 161–172.
Logan, J., Fowler, J. S., Volkow, N. D., Wang, G. J., Ding, Y. S., & Alexoff, D. L. (1996). Distribution volume ratios without blood sampling from graphical analysis of PET data. Journal of Cerebral Blood Flow and Metabolism, 16(5), 834–840.
Watabe, H., Ikoma, Y., Kimura, Y., Naganawa, M., & Shidahara, M. (2006). PET kinetic analysis—compartmental model. Annals of Nuclear Medicine, 20(9), 583–588.
Epelbaum, R., Frenkel, A., Haddad, R., Sikorski, N., Strauss, L. G., Israel, O., et al. (2013). Tumor aggressiveness and patient outcome in cancer of the pancreas assessed by dynamic 18F-FDG PET/CT. Journal of Nuclear Medicine, 54(1), 12–18.
Zhou, S., Chen, K., Reiman, E. M., Li, D.-M., & Shan, B. (2012). A method of generating image derived input function in quantitative 18F-FDG PET study based on the monotonicity of the input and output function curve. Nuclear Medicine Communications, 33(4), 362–370.
Li, X., Feng, D., & Chen, K. (2000). Optimal image sampling schedule for both image-derived input and output functions in PET cardiac studies. IEEE Transactions on Medical Imaging, 19(3), 233–242.
Fang, Y. H. D., & Muzic, R. F. (2008). Spillover and partial-volume correction for image-derived input functions for small-animal 18F-FDG PET studies. Journal of Nuclear Medicine, 49(4), 606–614.
Chen, K., Huang, S. C., & Feng, D. (1994). New estimation methods that directly use the time accumulated counts in the input function in quantitative dynamic PET studies. Physics in Medicine & Biology, 39(11), 2073–2090.
Carson, R. E., Huang, S. C., & Green, M. V. (1986). Weighted integration method for local cerebral blood flow measurements with positron emission tomography. Journal of Cerebral Blood Flow and Metabolism, 6(2), 245–258.
Wu, H. M., Huang, S. C., Choi, Y., Hoh, C. K., & Hawkins, R. A. (1995). A Modeling Method to Improve Quantitation of Flurodeoxyglucose Uptake in Heterogeneous Tumor Tissue. Journal of Nuclear Medicine, 36(2), 297–306.
Murase, K., Mochizuki, T., Kikuchi, T., & Ikezoe, J. (1999). Kinetic parameter estimation from compartment models using a genetic algorithm. Nuclear Medicine Communications, 20(10), 925–932.
Fang, Y. H., Kao, T., Liu, R. S., & Wu, L. C. (2004). Estimating the input function non-invasively for FDG-PET quantification with multiple linear regression analysis: simulation and verification with in vivo data. European Journal of Nuclear Medicine and Molecular Imaging, 31(5), 692–702.
Hawkins, R. A., Phelps, M. E., & Huang, S. C. (1986). Effects of temporal sampling, glucose metabolic rates, and disruptions of the blood—brain barrier on the FDG model with and without a vascular compartment: studies in human brain tumors with PET. Journal of Cerebral Blood Flow and Metabolism, 6(2), 170–183.
Feng, D., Wong, K. P., Wu, C. M., & Siu, W. C. (1997). A technique for extracting physiological parameters and the required input function simultaneously from PET image measurements: Theory and simulation study. IEEE Transactions on Information Technology in Biomedicine, 1(4), 243–254.
Hawkins, R. A., Choi, Y., Huang, S. C., Messa, C., Hoh, C. K., & Phelps, M. E. (1992). Quantitating tumor glucose metabolism with FDG and PET. Journal of Nuclear Medicine, 33(3), 339–344.
Huang S. C., Wu L. C., Liu R. S., & Lin, K. P. (2009). Optimal initializations of three compartment model for positron emission tomographic image analysis. 2009 International symposium on biomedical engineering combined with the Annual Scientific of Biomedical Engineering Society of ROC, Taipei, 2009, 168-170
Schmidt, K., Mies, G., & Sokoloff, L. (1991). Model of kinetic behavior of deoxyglucose in heterogeneous tissues in brain: a reinterpretation of the significance of parameters fitted to homogeneous tissue models. Journal of Cerebral Blood Flow and Metabolism, 11(1), 10–24.
Lucignani, G., Schmidt, K. C., Moresco, R. M., Striano, G., Colombo, F., Sokoloff, L., et al. (1993). Measurement of regional cerebral glucose utilization with fluorine-18-FDG and PET in heterogeneous tissues: Theoretical considerations and practical procedure. Journal of Nuclear Medicine: Official Publication, Society of Nuclear Medicine, 34(3), 360–369.
Acknowledgement
This study was financially supported in part by the Ministry of Science and Technology (MOST 103-2623-E-033-001, MOST 102-2221-E-033-003-MY3, and MOST 103-2622-E-033-012-CC3) and the Research Program for Taipei Veterans General Hospital (V102C-190 and V102C-082).
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Huang, SC., Wu, LC., Lin, WC. et al. Adaptive Weighted Nonlinear Least Squares Method for Fluorodeoxyglucose Positron Emission Tomography Quantification. J. Med. Biol. Eng. 38, 63–75 (2018). https://doi.org/10.1007/s40846-017-0313-6
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DOI: https://doi.org/10.1007/s40846-017-0313-6