A transfer function-based mathematical model of the fetal-placental circulation

Ultrasound in Medicine and Biology

Volumn 28, Issue 11-12, 2002, Pages 1421-1431

  Capper, W L ^a   Cowper, J G ^a   Myers, L J ^a  

^a UNIVERSITY OF CAPE TOWN   (South Africa)

Author keywords

Doppler waveform indices; Fetal circulation; Transfer function model; Ultrasound

Indexed keywords

BLOOD; ELECTRIC CURRENTS; FOURIER TRANSFORMS; MATHEMATICAL MODELS; TRANSFER FUNCTIONS;

HUMAN FETUS;

BIOMEDICAL ENGINEERING;

ARTERY DIAMETER; ARTICLE; BLOOD FLOW; DOPPLER FLOWMETRY; FETUS CIRCULATION; FETUS HEART RATE; FOURIER TRANSFORMATION; GESTATIONAL AGE; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; NONHUMAN; PLACENTA CIRCULATION; PRIORITY JOURNAL;

EMBRYONIC AND FETAL DEVELOPMENT; FEMALE; FETAL WEIGHT; FETUS; FOURIER ANALYSIS; GESTATIONAL AGE; HEART RATE, FETAL; HUMANS; MODELS, CARDIOVASCULAR; PLACENTAL CIRCULATION; PREGNANCY; PULSATILE FLOW; REGIONAL BLOOD FLOW; ULTRASONOGRAPHY, PRENATAL; VASCULAR RESISTANCE;

EID: 0036865983     PISSN: 03015629     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0301-5629(02)00658-0     Document Type: Article

References (61)

1. Adamson S.L., Langille B.L. Factors determining aortic and umbilical blood flow pulsatility in fetal sheep. Ultrasound Med Biol. 18:1992;255-266.
2. Adamson S.L., Morrow R.J., Langille B.L., Bull S.B., Ritchie J.W.K. Site dependent effects of increases in placental vascular resistance on the umbilical arterial velocity waveform in fetal sheep. Ultrasound Med Biol. 16:1990;19-27.
3. Adamson S.L., Whiteley K.J., Langille B.L. Pulsatile pressure-flow relations and pulse-wave propagation in the umbilical circulation of fetal sheep. Circ Res. 70:1992;761-772.
4. Battaglia F.C., Meschia G. Introduction to fetal physiology. 1986;Academic Press, Orlando, FL.
5. Benirschke K., Kaufmann P. Pathology of the human placenta. 2nd ed:1990;Springer-Verlag, New York.
6. Bergqvist G., Zetterstrom R. Blood viscosity and peripheral circulation in newborn infants. A study on resting flow. Acta Paediatr Scand. 63:1974;865-868.
7. Block B.S., Llanos A.J., Creasy R.K. Responses of the growth retarded fetus to acute hypoxaemia. Am J Obstet Gynecol. 148:1984;878-885.
8. Block B.S., Schlafer D.H., Wentworth R.A., Kreitzer L.A., Nathanielsz P.W. Intrauterine asphyxia and the breakdown of physiologic circulatory compensation in sheep. Am J Obstet Gynecol. 162:1990;1325-1331.
9. Capper WL, Myers LJ. Gestational age dependency of umbilical flow waveforms: An investigation using a lumped parameter model. Paper 5293-97775 in the digest of papers from the 2000 World Congress on Medical Physics and Biomedical Engineering, and the 22nd annual International Conference of the IEEE Engineering in Medicine and Biology Society, Chicago Navy Pier, July 23-28. 2000.
10. Chen H.Y., Chang F.M., Huang H.C., Hseih F.J., Lu C.C. Antenatal fetal blood flow in the descending aorta and in the umbilical vein and their ratio in normal pregnancy. Ultrasound Med Biol. 14:1988;263-268.
11. Eik Nes S.H., Brubakk A.O., Ulstein M.K. Measurement of human fetal blood flow. BMJ. 280:1980;283-284.
12. Erskine R.L.A., Ritchie J.W.K. Quantitative measurement of fetal blood flow using Doppler ultrasound. Br J Obstet Gynaecol. 92:1985;600-604.
13. Field D.R., Parer J.T., Auslender R.A., et al. Cerebral oxygen consumption during asphyxia in fetal sheep. J Dev Physiol. 14:1990;31-137.
14. Fitzgerald D.E., Stuart B., Drumm J.E., Duignan N.H. The assessment of fetal placental circulation with continuous wave Doppler ultrasound. Ultrasound Med Biol. 10:1984;371-376.
15. Giles W.B., Trudinger B.J., Baird P. Fetal umbilical artery flow velocity waveforms and placental resistance Pathological correlation. Br J Obstet Gynaecol. 92:1985;31-38.
16. Gill R.W., Trudinger B.J., Garrett W.J., Kossoff G., Warren P.S. Fetal umbilical venous flow measured in utero by pulsed Doppler and B-mode ultrasound. Am J Obstet Gynecol. 139:1981;720-725.
17. Goodlin R.C., Girard J., Hollmen A. Systolic time intervals in the fetus and neonate. Obstet Gynecol. 39:1972;295-303.
18. Guelke R.W., Bunn A.E. Transmission line theory applied to sound wave propagation in tubes with compliant walls. Acustica. 48:1981;101-106.
19. Guelke R.W., Bunn A.E. The propagation of sound in liquids confined in tubes with compliant walls. Acustica. 51:1982;131-134.
20. Guettouche A., Challier J.C., Ito Y., et al. Mathematical modeling of the human fetal arterial blood circulation. Int J Biomed Comput. 31:1992;127-139.
21. Hendricks S.K., Sorensen T.K., Wang K.Y., et al. Doppler umbilical artery waveform indices-normal values from fourteen to forty two weeks. Am J Obstet Gynecol. 161:1989;761-765.
22. Joern H., Funk A., Goetz M., et al. Development of quantitative Doppler indices for uteroplacental and fetal blood flow during the third trimester. Ultrasound Med Biol. 22:1996;823-835.
23. Kenny J.F., Plappert T., Doubilet P., et al. Changes in intracardiac blood flow velocities and right and left ventricular stroke volumes with gestational age in the normal human fetus A prospective Doppler echo-cardiographic study. Circulation. 74:1986;1208-1216.
24. Krebs C., Macara L.M., Leiser R., et al. Intrauterine growth restriction with absent end diastolic flow velocity in the umbilical artery is associated with maldevelopment of the placental terminal villous tree. Am J Obstet Gynecol. 175:1996;1534-1542.
25. Lingman G., Marsal K. Fetal central blood circulation in the third trimester of normal pregnancy-A longitudinal study. II Aortic blood velocity waveform. Early Hum Dev. 13:1986;151-159.
26. Low J.A. The current status of maternal and fetal blood flow velocimetry. Am J Obstet Gynecol. 164:1991;1049-1063.
27. Mackintosh T.F., Walker C.H.M. Blood viscosity in the newborn. Arch Dis Child. 48:1973;547-553.
28. Marsal K., Laurin J., Lindblad A., Lingman G. Blood flow in the fetal descending aorta. Semin Perinatol. 11:1987;322-334.
29. Maulik D., Arbeille P., Kadado T. Hemodynamic foundation of umbilical arterial Doppler waveform analysis. Biol Neonate. 62:1992;280-289. (Review).
30. Myers L.J., Capper W.L. Analytical solution for pulsatile axial flow velocity waveforms in curved elastic tubes. IEEE Trans BME. 48:2001;864-873.
31. Naeye R.L. Umbilical cord length Clinical significance. J Pediatr. 107:1985;278-281.
32. Nichols W.W., O'Rourke M.F. McDonald's blood flow in arteries. Theoretic, experimental and clinical principles. 3rd ed:1990;Lea & Febiger, London, Philadelphia.
33. Pattinson R.C., Theron G.B., Thompson M.L., Lai Tung M. Doppler ultrasonography of the fetoplacental circulation-normal reference values. S Afr Med J. 76:1989;623-625.
34. Pattinson R.C., Norman K., Odendaal H.J. The role of Doppler velocimetry in the management of high risk pregnancies. Br J Obstet Gynaecol. 101:1994;114-120.
35. Pearce J.M., Campbell S., Cohen-Overbeek T., et al. Reference ranges and sources of variation for indices of pulsed Doppler flow velocity waveforms from the uteroplacental and fetal circulation. Br J Obstet Gynaecol. 95:1988;248-256.
36. Peeters L.L.H., Sheldon R.E., Jones M.D., Makowski E.L., Meschia G. Blood flow to fetal organs as a function of arterial oxygen content. Am J Obstet Gynecol. 135:1979;637-646.
37. Pennati G., Fumero R. Scaling approach to study the changes through the gestation of human fetal cardiac and circulatory behaviours. Ann Biomed Eng. 28:2000;442-452.
38. Raymond S.P.W., Whitfield C.R. Systolic time intervals of the fetal cardiac cycle. Baillieres Clin Obstet Gynaecol. 1:1987;185-201. (Review).
39. Reed K.L., Meijboom E.J., Sahn D.J., et al. Cardiac Doppler flow velocities in human fetuses. Circulation. 73:1986;41-46.
40. Reed K.L., Anderson C.F., Shenker L. Changes in intra-cardiac Doppler blood flow velocities in fetuses with absent umbilical artery diastolic flow. Am J Obstet Gynecol. 157:1987;774-779.
41. Reuwer P.J., Nuyen W.C., Beijer H.J., et al. Feto-placental circulatory competence. Eur J Obstet Gynecol Reprod Biol. 21:1986;15-26.
42. Rudolph A.M. Distribution and regulation of blood flow in the fetal and neonate lamb. Circ Res. 57:1985;812-821.
43. Rudolph A.M., Heymann M.A. Fetal and neonatal circulation and respiration. Ann Rev Physiol. 19:1974;187.
44. Rudolph A.M., Heymann M.A., Teramo K.A.W., Barrett C.T., Raiha N.C.R. Studies on the circulation of the previable human fetus. Pediat Res. 5:1971;452-465.
45. Sahn D.J., Lange L.W., Allen H.D., et al. Quantitative real-time cross sectional echocardiography in the developing normal human fetus and newborn. Circulation. 62:1980;588.
46. Sherer D.M., Anyaeg-bunam A. Prenatal ultrasonographic morphologic assessment of the umbilical cord A review. Part 1. Obstet Gynecol Surv. 52:1997;506-514.
47. Skoll M.A., Fouron J.C., Sonesson S.E., et al. Doppler velocimetric indices from the abdominal and placental ends of the umbilical artery of growth restricted fetuses. J Clin Ultrasound. 25:1997;421-424.
48. Sonesson S.E., Fouron J.C., Drblik S.P., et al. Reference values for Doppler velocimetric indices from the fetal and placental ends of the umbilical artery during normal pregnancy. J Clin Ultrasound. 21:1993;317-324.
49. Stale H., Marsal K., Gennser G., et al. Aortic diameter pulse waves and blood flow velocity in the small for gestational age fetus. Ultrasound Med Biol. 17:1991;471-478.
50. St. John Sutton M, Gill T, Plappert T. Functional anatomic development in the fetal heart. In: Polin RA, Fox WW, eds. Fetal and Neonatal Physiology. vol. 1. London: WB Saunders, 1992:604.
51. Struijk P.C., Wladimiroff J.W., Hop W.C.J., Simonazzi E. Pulse pressure assessment in the human fetal descending aorta. Ultrasound Med Biol. 18:1992;39-43.
52. Theron G.B., Thompson M.L. A centile chart for birth weight for an urban population of the Western Cape. S Afr Med J. 85:1995;1289-1292.
53. Thompson R.S., Trudinger B.J. Doppler waveform pulsatility index and resistance, pressure and flow in the umbilical placental circulation An investigation using a mathematical model. Ultrasound Med Biol. 16:1990;449-458.
54. Thompson R.S., Trudinger B.J., Cook C.M., Giles W.B. Umbilical artery velocity waveforms Normal reference values for the A/B and Pourcelot ratio. Br J Obstet Gynaecol. 95:1988;589-591.
55. Todros T., Guiot C., Pianta P.G. Modelling the feto-placental circulation. 2 A continuous approach to explain normal and abnormal flow velocity waveforms in the umbilical arteries. Ultrasound Med Biol. 18:1992;545-551.
56. Trudinger B.J., Stevens D., Connely A., et al. Umbilical artery flow velocity waveforms and placental resistance The effects of embolization of the umbilical circulation. Am J Obstet Gynecol. 157:1987;1443-1448.
57. Van Lierde M., Oberweis D., Thomas K. Ultrasonic measurement of aortic and umbilical blood flow in the human fetus. Obstet Gynecol. 63:1984;801-805.
58. Wladimiroff J.W., Tonge H.M., Stewart P.A. Doppler ultrasound assessment of cerebral blood flow in the human fetus. Br J Obstet Gynaecol. 93:1986;471-475.
59. Wladimiroff J.W., Vosters R., Vletter W. Ultrasonic measurement of fetal and neonatal ventricular dimensions. Contrib Gynecol Obstet. 6:1979;109.
60. Womersley J.R. Oscillatory flow in arteries Effect of radial variation in viscosity on rate of flow. J Physiol. 127:1955;38-39P.
61. Womersley J.R. Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known. J Physiol. 127:1955;553-563.