A Physiologically Based Approach for the Estimation of Recirculatory Parameters

Indicator dilution studies are used to provide estimates for several physiological parameters such as cardiac output as well as intra- and extravascular volumes. This study introduces a novel technique for the estimation of recirculatory parameters. A mathematical model based on a dispersion-convection partial differential equation (PDE), derived from the fractal geometry of the vascular tree and the hydrodynamics of the blood flow, is used to describe the spatiotemporal profile of tracers in the circulatory system. Initially, the equation is fitted to concentration-time (C,t) data of a tracer to derive the parameter estimates of the model equation; in a subsequent step, these estimates along with appropriate changes of the parameters of the PDE are used to generate the early concentration-time profile of a hypothetical appropriate tracer without recirculation. Thus, the area under the concentration-time curve of the first passage of the tracer is calculated and used for the estimation of various physiological parameters, including cardiac output, miscellaneous partial blood volumes, and the corresponding mean transit times. The procedure was applied successfully to literature data of various tracers from humans and dogs.

[1]  J. L. Stephenson,et al.  Theory of the measurement of blood flow by the dilution of an indicator. , 1948, The Bulletin of mathematical biophysics.

[2]  Panos Macheras,et al.  A Model for Transport and Dispersion in the Circulatory System Based on the Vascular Fractal Tree , 2003, Annals of Biomedical Engineering.

[3]  M. Wise,et al.  Tracer dilution curves in cardiology and random walk and lognormal distributions. , 1966, Acta physiologica et pharmacologica Neerlandica.

[4]  C. Niemann,et al.  A Recirculatory Model of the Pulmonary Uptake and Pharmacokinetics of Lidocaine Based on Analysis of Arterial and Mixed Venous Data from Dogs , 1997, Journal of Pharmacokinetics and Biopharmaceutics.

[5]  A. Guyton,et al.  Textbook of Medical Physiology , 1961 .

[6]  J. Boehmer,et al.  A noninvasive method for estimating cardiac output using lung to finger circulation time of oxygen. , 1998, The American journal of cardiology.

[7]  P Lund-Johansen,et al.  Thermodilution method for measuring cardiac output. , 1990, European heart journal.

[8]  K. Zierler.  Equations for Measuring Blood Flow by External Monitoring of Radioisotopes , 1965, Circulation research.

[9]  C A Shanks,et al.  Indocyanine green kinetics characterize blood volume and flow distribution and their alteration by propranolol , 2000, Clinical pharmacology and therapeutics.

[10]  M. Lefcoe,et al.  Clinical studies of measuring extravascular lung water by the thermal dye technique in critically ill patients. , 1983, Chest.

[11]  J. Shaver.  Hemodynamic monitoring in the critically ill patient. , 1983, The New England journal of medicine.

[12]  C. Goresky,et al.  A linear method for determining liver sinusoidal and extravascular volumes. , 1963, The American journal of physiology.

[13]  K. Zierler.  Theoretical Basis of Indicator‐Dilution Methods For Measuring Flow and Volume , 1962 .

[14]  J B Michel.  Relationship between decrease in afterload and beneficial effects of ACE inhibitors in experimental cardiac hypertrophy and congestive heart failure. , 1990, European heart journal.

[15]  R. Millard,et al.  Indicator-dilution dispersion models and cardiac output computing methods. , 1997, The American journal of physiology.

[16]  B. Reichart,et al.  Intensive care unit procedures: cost savings and patient safety , 2000, Critical Care.

[17]  J. Douglas Faires,et al.  Numerical Analysis , 1981 .

[18]  K. Zierler.  Indicator Dilution Methods for Measuring Blood Flow, Volume, and Other Properties of Biological Systems: A Brief History and Memoir , 2000, Annals of Biomedical Engineering.

[19]  M. Labarbera.  Principles of design of fluid transport systems in zoology. , 1990, Science.

[20]  J. W. Barr,et al.  Fore-'n-aft triangle formula for rapid estimation of area. Dye dilution curve. , 1969, American heart journal.

[21]  H. Falsetti,et al.  Measurement of cardiac output in man with a nonrecirculating indicator. , 1971, Journal of Clinical Investigation.

[22]  D M Band,et al.  The shape of indicator dilution curves used for cardiac output measurement in man. , 1997, The Journal of physiology.

[23]  Wise Me,et al.  Tracer dilution curves in cardiology and random walk and lognormal distributions. , 1966 .

[24]  E. Olivier,et al.  Coherent oscillations in monkey motor cortex and hand muscle EMG show task‐dependent modulation , 1997, The Journal of physiology.

[25]  A. Coats,et al.  Measurement accuracy of cardiac output in humans: indicator-dilution technique versus geometric analysis by ultrafast computed tomography. , 1993, Journal of the American College of Cardiology.

[26]  S. Lakshminarayan,et al.  Comparison of estimates of cardiac output by indicator dilution and freon 22 uptake during gas mixing in dogs. , 1991, Cardiovascular research.

[27]  S. Jamieson,et al.  Thermal dye double indicator dilution measurement of lung water in man: comparison with gravimetric measurements. , 1987, Thorax.

[28]  B. Reichart,et al.  Reproducibility of double indicator dilution measurements of intrathoracic blood volume compartments, extravascular lung water, and liver function. , 1998, Chest.

[29]  J. Jansen,et al.  The thermodilution method for the clinical assessment of cardiac output , 1995, Intensive Care Medicine.

[30]  P. Lund-johansen,et al.  The dye dilution method for measurement of cardiac output. , 1990, European heart journal.

[31]  B. Reichart,et al.  Hemodynamic monitoring by double-indicator dilution technique in patients after orthotopic heart transplantation. , 2000 .

[32]  O. Picker,et al.  Determination of total blood volume by indicator dilution: a comparison of mean transit time and mass conservation principle , 2001, Intensive Care Medicine.

[33]  K. Zierler,et al.  Frequency Function of Transit Times through Dog Pulmonary Circulation , 1970, Circulation research.

[34]  C A Shanks,et al.  Recirculatory pharmacokinetic models of markers of blood, extracellular fluid and total body water administered concomitantly. , 1996, The Journal of pharmacology and experimental therapeutics.

[35]  F. Chinard,et al.  Indicator‐Dilution Studies with “Diffusible” Indicators , 1962, Circulation research.