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Online Estimation of Capillary Permeability and Contrast Agent Concentration in Rat Tumors

Year 2010, Volume: 39 Issue: 2, 283 - 293, 01.02.2010

Abstract

This paper presents a two-compartment model for the transfer of optical contrast agent, namely indocyanine green (ICG), in the presence of tumors between the plasma and extracellular extravascular space (EES) compartments. An adaptive extended Kalman filter (EKF) has been derived to estimate the quantities that are transferred between the compartments, Moreover, in order to validate the proposed EKF, real data have been utilized and the experimentally obtained ICG concentration data quantitatively analyzed through the estimation of physiological
parameters related to capillary permeability and the optical contrast agent concentration in the compartments concurrently. The proposed method produces the estimate of tissue permeability, independent of the initial permeability values, without resorting to computationally expensive nonlinear fitting algorithms. Considering the fact that the change in the tissue permeability occurs usually due to a disease such as cancer, an estimated value of the permeability could be used to extract valuable information about tumor cell behavior patterns. 

References

  • Anderson, B. D. O. and Moore, J. B. Optimal Filtering (Prentice Hall, 1979).
  • Botsman, K., Tickle, K. and Smith, J. D. A Bayesian formulation of the Kalman filter applied to the estimation of individual pharmacokinetic parameters, Comput. Biomed. Res. 30, 83–93, 1997.
  • Boutayeb, M. and Aubry, D. A strong tracking extended Kalman observer for nonlinear discrete time systems, IEEE Trans. Automatic Control. 44, 1550–1556, 1999.
  • Bryson, A. E. and Ho, Y. C. Optimization, Estimation and Control (Ginn and Company, 1969).
  • Cuccia, D. J., Bevilacqua F., Durkin, A. J., Merritt S., Tromberg, B. J., Gulsen, G., Yu, H., Wang, J. and Nalcioglu O. In vivo quantification of optical contrast agent dynamics in rat tumors by use of diffuse optical spectroscopy with magnetic resonance imaging coregistra- tion, Appl. Opt. 42, 2940–2950, 2003.
  • Greval, M. S. and Andrews, A. P. Kalman Filtering Teory and Practice (Prentice Hall, 1984). [7] Gurfinkel, M., Thompson, A. B., Ralston, W., Troy, T. L., Moore, A. L., Moore, T. A., Gust, J. D., Tatman, D., Reynolds, J. S., Muggenburg, B., Nikula, K., Pandey, R., Mayer, R. H., Hawrysz, D. J. and Sevick-Muraca, E. M. Pharmacokinetics of ICG and HPPH-car for the detection of normal and tumor tissue using flourescence, near-infrared reflectance imaging: A case study, Photochem. and Photobiol. 72, 94–102, 2000.
  • McClamroch, N. H. State Models of Dynamic Systems (Springer-Verlag, 1980).
  • Ntziachristos, V., Yodh, A. G., Schnall, M. and Chance, B. Concurrent MRI and diffuse optical tomography of breast after indocyanine green enhancement, Proc. Natl. Acad. Sci. USA 97, 2767–2772, 2000.
  • Ozbek, L. and Aliev, F. Comments on adaptive fading Kalman filter with an application, Automatica 34, 1663–1664, 1998.
  • Ozbek, L. and Efe, M. An adaptive extended Kalman filter with application to compartment models, Commun. Stat. Simul. Comput. 33, 145–158, 2004.
  • Reif K. and Unbehauen, R. The extended Kalman filter as an exponential observer for nonlinear systems, IEEE Trans. Signal Processing. 47, 2324–2328, 1999.
  • Springett, R., Sakata, Y. and Delpy, D. T. Precise measurement of cerebral blood flow in newborn piglets from the bolus passage of indocyanine green, Phys. Med. Biol. 46, 2209– 2225, 2001.
  • Su, M.Y., Jao, J. C. and Nalcioglu, O. Measurement of vascular volume fraction and blood- tissue permeability constants with a pharacokinetic model: studies in rat muscle tumors with dynamic Gd-DTPA enhanced MRI, Magn. Reson. Med. 32, 714–724, 1994.
  • Su, M. Y., Wang, Z., Carpenter, P. M., Lao, X., Muhler, A. and Nalcioglu, O. Characteriza- tion of N-ethyl-N-nitrosourea induced malignant and benign breast tumors in rats by using three MR contrast agentsJ. Magn. Reson. Imag. 9, 177–186, 1999.
  • Tofts, P. S. Modeling tracer kinetics in dynamic Gd-DTPA MR imaging, J. Magn. Reson. Imag. 7, 91–101, 1997.
  • Yates, M. S., Bowmer, C. J. and Emmerson, J. The plasma clearance of indocyanine green in rats with acute renal failure: effect of dose and route of administration, Biochem. Phar- macol. 32, 3109–3114, 1983.

Online Estimation of Capillary Permeability and Contrast Agent Concentration in Rat Tumors

Year 2010, Volume: 39 Issue: 2, 283 - 293, 01.02.2010

Abstract

References

  • Anderson, B. D. O. and Moore, J. B. Optimal Filtering (Prentice Hall, 1979).
  • Botsman, K., Tickle, K. and Smith, J. D. A Bayesian formulation of the Kalman filter applied to the estimation of individual pharmacokinetic parameters, Comput. Biomed. Res. 30, 83–93, 1997.
  • Boutayeb, M. and Aubry, D. A strong tracking extended Kalman observer for nonlinear discrete time systems, IEEE Trans. Automatic Control. 44, 1550–1556, 1999.
  • Bryson, A. E. and Ho, Y. C. Optimization, Estimation and Control (Ginn and Company, 1969).
  • Cuccia, D. J., Bevilacqua F., Durkin, A. J., Merritt S., Tromberg, B. J., Gulsen, G., Yu, H., Wang, J. and Nalcioglu O. In vivo quantification of optical contrast agent dynamics in rat tumors by use of diffuse optical spectroscopy with magnetic resonance imaging coregistra- tion, Appl. Opt. 42, 2940–2950, 2003.
  • Greval, M. S. and Andrews, A. P. Kalman Filtering Teory and Practice (Prentice Hall, 1984). [7] Gurfinkel, M., Thompson, A. B., Ralston, W., Troy, T. L., Moore, A. L., Moore, T. A., Gust, J. D., Tatman, D., Reynolds, J. S., Muggenburg, B., Nikula, K., Pandey, R., Mayer, R. H., Hawrysz, D. J. and Sevick-Muraca, E. M. Pharmacokinetics of ICG and HPPH-car for the detection of normal and tumor tissue using flourescence, near-infrared reflectance imaging: A case study, Photochem. and Photobiol. 72, 94–102, 2000.
  • McClamroch, N. H. State Models of Dynamic Systems (Springer-Verlag, 1980).
  • Ntziachristos, V., Yodh, A. G., Schnall, M. and Chance, B. Concurrent MRI and diffuse optical tomography of breast after indocyanine green enhancement, Proc. Natl. Acad. Sci. USA 97, 2767–2772, 2000.
  • Ozbek, L. and Aliev, F. Comments on adaptive fading Kalman filter with an application, Automatica 34, 1663–1664, 1998.
  • Ozbek, L. and Efe, M. An adaptive extended Kalman filter with application to compartment models, Commun. Stat. Simul. Comput. 33, 145–158, 2004.
  • Reif K. and Unbehauen, R. The extended Kalman filter as an exponential observer for nonlinear systems, IEEE Trans. Signal Processing. 47, 2324–2328, 1999.
  • Springett, R., Sakata, Y. and Delpy, D. T. Precise measurement of cerebral blood flow in newborn piglets from the bolus passage of indocyanine green, Phys. Med. Biol. 46, 2209– 2225, 2001.
  • Su, M.Y., Jao, J. C. and Nalcioglu, O. Measurement of vascular volume fraction and blood- tissue permeability constants with a pharacokinetic model: studies in rat muscle tumors with dynamic Gd-DTPA enhanced MRI, Magn. Reson. Med. 32, 714–724, 1994.
  • Su, M. Y., Wang, Z., Carpenter, P. M., Lao, X., Muhler, A. and Nalcioglu, O. Characteriza- tion of N-ethyl-N-nitrosourea induced malignant and benign breast tumors in rats by using three MR contrast agentsJ. Magn. Reson. Imag. 9, 177–186, 1999.
  • Tofts, P. S. Modeling tracer kinetics in dynamic Gd-DTPA MR imaging, J. Magn. Reson. Imag. 7, 91–101, 1997.
  • Yates, M. S., Bowmer, C. J. and Emmerson, J. The plasma clearance of indocyanine green in rats with acute renal failure: effect of dose and route of administration, Biochem. Phar- macol. 32, 3109–3114, 1983.
There are 16 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Mathematics
Authors

Levent Ozbek This is me

Murat Efe This is me

Esin K. Babacan This is me

Nuray Yazihan This is me

Publication Date February 1, 2010
Published in Issue Year 2010 Volume: 39 Issue: 2

Cite

APA Ozbek, L., Efe, M., Babacan, E. K., Yazihan, N. (2010). Online Estimation of Capillary Permeability and Contrast Agent Concentration in Rat Tumors. Hacettepe Journal of Mathematics and Statistics, 39(2), 283-293.
AMA Ozbek L, Efe M, Babacan EK, Yazihan N. Online Estimation of Capillary Permeability and Contrast Agent Concentration in Rat Tumors. Hacettepe Journal of Mathematics and Statistics. February 2010;39(2):283-293.
Chicago Ozbek, Levent, Murat Efe, Esin K. Babacan, and Nuray Yazihan. “Online Estimation of Capillary Permeability and Contrast Agent Concentration in Rat Tumors”. Hacettepe Journal of Mathematics and Statistics 39, no. 2 (February 2010): 283-93.
EndNote Ozbek L, Efe M, Babacan EK, Yazihan N (February 1, 2010) Online Estimation of Capillary Permeability and Contrast Agent Concentration in Rat Tumors. Hacettepe Journal of Mathematics and Statistics 39 2 283–293.
IEEE L. Ozbek, M. Efe, E. K. Babacan, and N. Yazihan, “Online Estimation of Capillary Permeability and Contrast Agent Concentration in Rat Tumors”, Hacettepe Journal of Mathematics and Statistics, vol. 39, no. 2, pp. 283–293, 2010.
ISNAD Ozbek, Levent et al. “Online Estimation of Capillary Permeability and Contrast Agent Concentration in Rat Tumors”. Hacettepe Journal of Mathematics and Statistics 39/2 (February 2010), 283-293.
JAMA Ozbek L, Efe M, Babacan EK, Yazihan N. Online Estimation of Capillary Permeability and Contrast Agent Concentration in Rat Tumors. Hacettepe Journal of Mathematics and Statistics. 2010;39:283–293.
MLA Ozbek, Levent et al. “Online Estimation of Capillary Permeability and Contrast Agent Concentration in Rat Tumors”. Hacettepe Journal of Mathematics and Statistics, vol. 39, no. 2, 2010, pp. 283-9.
Vancouver Ozbek L, Efe M, Babacan EK, Yazihan N. Online Estimation of Capillary Permeability and Contrast Agent Concentration in Rat Tumors. Hacettepe Journal of Mathematics and Statistics. 2010;39(2):283-9.