Simulation and Analysis of Umbilical Blood Flow using Markov-based Mathematical Model

Full Text (PDF, 948KB), PP.41-50

Views: 0 Downloads: 0


Abdullah Bin Queyam 1,* Sharvan Kumar Pahuja 1 Dilbag Singh 1

1. Dr. B R Ambedkar National Institute of Technology, Jalandhar-144011, India

* Corresponding author.


Received: 12 Apr. 2016 / Revised: 15 Jul. 2016 / Accepted: 12 Oct. 2016 / Published: 8 Mar. 2017

Index Terms

Fetal circulation, umbilical blood flow, uterine artery, Markov model, mathematical model, simulation, Doppler indices


The intra-uterine development of the fetus depends on various factors, one such critical factor is umbilical blood flow because the quantity of oxygen delivered to the placenta and to the fetus is directly limited by umbilical blood flow rate. Since the measurement of the hemodynamic quantities such as blood pressure and blood flow rate is not possible in utero hence the use of patient-specific mathematical modeling is beneficial for the assessment of feto-maternal well-being. A Markov model based mathematical model of fetal circulation is developed by taking three node concept. The fetus, the umbilical cord, and the placenta represent the 3 nodes of Markov model. A LabVIEW-based virtual instrument is designed to simulate the mathematical model which results in waveform similar to Doppler blood flow velocimetry of umbilical artery. The model is simulated at various degree of conductivity of the umbilical cord to the oxygenated blood. Simulation results show that the umbilical artery blood flow velocity waveform depends on gestation age, fetal heart rate, uterine contraction and placental insufficiency. The Doppler indices calculated from simulation helps in predicting both fetal and maternal abnormalities at various degrees of the conductivity to the blood flow passage. Therefore, integrating patient-specific models along with established medical equipments will be helpful in identifying true intra-uterine growth restricted fetuses from normal fetuses and helps clinicians to take timely interventions.

Cite This Paper

Abdullah Bin Queyam, Sharvan Kumar Pahuja, Dilbag Singh,"Simulation and Analysis of Umbilical Blood Flow using Markov-based Mathematical Model", International Journal of Intelligent Systems and Applications (IJISA), Vol.9, No.3, pp.41-50, 2017. DOI:10.5815/ijisa.2017.03.06


[1]J. T. Queenan, C. Y. Spong, and C. J. Lockwood, “Protocols for High-Risk Pregnancies: An Evidence-Based Approach”. John Wiley & Sons, 2015.
[2]H. Joern, A. Funk, M. Goetz, H. Kuehlwein, A. Klein, and H. Fendel, “Development of quantitative Doppler indices for uteroplacental and fetal blood flow during the third trimester.,” Ultrasound Med. Biol., vol. 22, no. 7, pp. 823–35, Jan. 1996.
[3]D. Maulik, D. Mundy, E. Heitmann, and D. Maulik, “Evidence-based approach to umbilical artery Doppler fetal surveillance in high-risk pregnancies: an update.,” Clin. Obstet. Gynecol., vol. 53, no. 4, pp. 869–78, Dec. 2010.
[4]G. Pennati, M. Bellotti, and R. Fumero, “Mathematical modelling of the human foetal cardiovascular system based on Doppler ultrasound data.,” Med. Eng. Phys., vol. 19, no. 4, pp. 327–335, 1997.
[5]K. L. Reed, C. P. Appleton, D. J. Sahn, and C. F. Anderson, “Human fetal tricuspid and mitral deceleration time: changes with normal pregnancy and intrauterine growth retardation.,” Am. J. Obstet. Gynecol., vol. 161, no. 6 Pt 1, pp. 1532–5, Dec. 1989.
[6]E. Ferrazzi, M. Bellotti, A. Marconi, L. Flisi, A. Barbera, and G. Pardi, “Peak velocity of the outflow tract of the aorta: correlations with acid base status and oxygenation of the growth-retarded fetus.,” Obstet. Gynecol., vol. 85, no. 5 Pt 1, pp. 663–8, May 1995.
[7]Z. Alfirevic and J. P. Neilson, “Doppler ultrasonography in high-risk pregnancies: systematic review with meta-analysis.,” Am. J. Obstet. Gynecol., vol. 172, no. 5, pp. 1379–87, May 1995.
[8]R. S. Thompson, B. J. Trudinger, and C. M. Cook, “A comparison of Doppler ultrasound waveform indices in the umbilical artery--I. Indices derived from the maximum velocity waveform.,” Ultrasound Med. Biol., vol. 12, no. 11, pp. 835–44, Nov. 1986.
[9]R. S. Thompson, B. J. Trudinger, and C. M. Cook, “A comparison of Doppler ultrasound waveform indices in the umbilical artery--II. Indices derived from the mean velocity and first moment waveforms.,” Ultrasound Med. Biol., vol. 12, no. 11, pp. 845–54, Nov. 1986.
[10]R. S. Thompson, B. J. Trudinger, and C. M. Cook, “Doppler ultrasound waveform indices: A/B ratio, pulsatility index and Pourcelot ratio.,” Br. J. Obstet. Gynaecol., vol. 95, no. 6, pp. 581–8, Jun. 1988.
[11]B. J. Trudinger, W. B. Giles, and C. M. Cook, “Uteroplacental blood flow velocity-time waveforms in normal and complicated pregnancy.,” Br. J. Obstet. Gynaecol., vol. 92, no. 1, pp. 39–45, Jan. 1985.
[12]B. J. Trudinger and C. M. Cook, “Umbilical and uterine artery flow velocity waveforms in pregnancy associated with major fetal abnormality.,” Br. J. Obstet. Gynaecol., vol. 92, no. 7, pp. 666–70, Jul. 1985.
[13]A. A. Baschat, U. Gembruch, I. Reiss, L. Gortner, and K. Diedrich, “Demonstration of fetal coronary blood flow by Doppler ultrasound in relation to arterial and venous flow velocity waveforms and perinatal outcome--the ‘heart-sparing effect’.,” Ultrasound Obstet. Gynecol., vol. 9, no. 3, pp. 162–72, Mar. 1997.
[14]P. W. Callen, “Ultrasonography in Obstretrics and Gynecology,” 5th Edition, Elsevier, 2008.
[15]H. Joern, A. Klein, H. Kuehlwein, and W. Rath, “Critical comparison of indices and threshold values for assessing placenta performance using Doppler ultrasound.,” Ultrasound Med. Biol., vol. 23, no. 8, pp. 1179–83, Jan. 1997.
[16]F. Figueras and J. Gardosi, “Intrauterine growth restriction: new concepts in antenatal surveillance, diagnosis, and management.,” Am. J. Obstet. Gynecol., vol. 204, no. 4, pp. 288–300, Apr. 2011.
[17]U. Krishna and S. Bhalerao, “Placental insufficiency and fetal growth restriction.,” J. Obstet. Gynaecol. India, vol. 61, no. 5, pp. 505–11, Oct. 2011.
[18]D. Maulik and I. Zalud, “Doppler Ultrasound in Obstetrics and Gynecology,” 2nd Edition, Berlin, Germany: Springer-Verlag, 2005.
[19]W. B. Giles, “Vascular Doppler Techniques,” Obstetrics and Gynecology Clinics of North America, vol. 26, no. 4, pp. 595–606, Dec. 1999.
[20]M. Bellotti, G. Pennati, C. De Gasperi, M. Bozzo, F. C. Battaglia, and E. Ferrazzi, “Simultaneous measurements of umbilical venous, fetal hepatic, and ductus venosus blood flow in growth-restricted human fetuses.,” Am. J. Obstet. Gynecol., vol. 190, no. 5, pp. 1347–58, May 2004.
[21]R. S. Thompson, B. J. Trudinger, C. M. Cook, and W. B. Giles, “Umbilical artery velocity waveforms: normal reference values for A/B ratio and Pourcelot ratio.,” Br. J. Obstet. Gynaecol., vol. 95, no. 6, pp. 589–91, Jun. 1988.
[22]H. Konar, “DC Dutta’s Textbook of Obstetrics,” 7th Edition, JP Medical Ltd, 2014.
[23]C. Battaglia, P. G. Artini, P. A. Galli, G. D’Ambrogio, F. Droghini, and A. R. Genazzani, “Absent or reversed end-diastolic flow in umbilical artery and severe intrauterine growth retardation. An ominous association.,” Acta Obstet. Gynecol. Scand., vol. 72, no. 3, pp. 167–71, Apr. 1993.
[24]A. Valcamonico, L. Danti, T. Frusca, M. Soregaroli, S. Zucca, F. Abrami, and A. Tiberti, “Absent end-diastolic velocity in umbilical artery: risk of neonatal morbidity and brain damage.,” Am. J. Obstet. Gynecol., vol. 170, no. 3, pp. 796–801, Mar. 1994.
[25]P. Chanprapaph, C. Wanapitak and T. Tongsong, “Umbilical artery Doppler waveform indices in normal pregnancies.,” Thai J Obstet Gynaecol, vol. 12, pp. 103-107, June. 2000.
[26]A. Najafzadeh and J. E. Dickinson, “Umbilical venous blood flow and its measurement in the human fetus.,” J. Clin. Ultrasound, vol. 40, no. 8, pp. 502–11, Oct. 2012.
[27]A. Kaponis, T. Harada, G. Makrydimas, T. Kiyama, K. Arata, G. Adonakis, V. Tsapanos, T. Iwabe, T. Stefos, G. Decavalas, and T. Harada, “The Importance of Venous Doppler Velocimetry for Evaluation of Intrauterine Growth Restriction,” J. Ultrasound Med., vol. 30, no. 4, pp. 529–545, Apr. 2011.
[28]P. Garcia-Canadilla, P. A. Rudenick, F. Crispi, M. Cruz-Lemini, G. Palau, O. Camara, E. Gratacos, and B. H. Bijens, “A Computational Model of the Fetal Circulation to Quantify Blood Redistribution in Intrauterine Growth Restriction,” PLoS Comput. Biol., vol. 10, no. 6, p. e1003667, Jun. 2014.
[29]J. P. H. M. van den Wijngaard, B. E. Westerhof, D. J. Faber, M. M. Ramsay, N. Westerhof, and M. J. C. van Gemert, “Abnormal arterial flows by a distributed model of the fetal circulation,” Am. J. Physiol. - Regul. Integr. Comp. Physiol., vol. 291, no. 5, 2006.
[30]G. M. Sokol, E. A. Liechty, and D. W. Boyle, “Comparison of steady-state diffusion and transit time ultrasonic measurements of umbilical blood flow in the chronic fetal sheep preparation.,” Am. J. Obstet. Gynecol., vol. 174, no. 5, pp. 1456–60, May 1996.
[31]F. J. Huikeshoven, I. D. Hope, G. G. Power, R. D. Gilbert, and L. D. Longo, “Mathematical model of fetal circulation and oxygen delivery.,” Am. J. Physiol., vol. 249, no. 2 Pt 2, pp. R192–202, Aug. 1985.
[32]A. Costa, M. L. Costantino, and R. Fumero, “Oxygen exchange mechanisms in the human placenta: mathematical modelling and simulation,” J. Biomed. Eng., vol. 14, no. 5, pp. 385–389, Sep. 1992.
[33]A. Guettouche, J. C. Challier, Y. Ito, C. Papapanayotou, Y. Cherruault, and A. Azancot-Benisty, “Mathematical modeling of the human fetal arterial blood circulation,” Int. J. Biomed. Comput., vol. 31, no. 2, pp. 127–139, Aug. 1992.
[34]T. Todros, C. Guiot, and P. G. Piantà, “Modelling the feto-placental circulation: 2. A continuous approach to explain normal and abnormal flow velocity waveforms in the umbilical arteries,” Ultrasound Med. Biol., vol. 18, no. 6–7, pp. 545–551, Jan. 1992.
[35]P. M. Sá Couto, W. L. van Meurs, J. F. Bernardes, J. P. Marques de Sá, and J. A. Goodwin, “Mathematical model for educational simulation of the oxygen delivery to the fetus,” Control Eng. Pract., vol. 10, no. 1, pp. 59–66, Jan. 2002.
[36]M. B. van der Hout-van der Jagt, G. J. L. M. Jongen, P. H. M. Bovendeerd, and S. G. Oei, “Insight into variable fetal heart rate decelerations from a mathematical model.,”Early Hum. Dev., vol. 89, no. 6, pp. 361–9, Jun. 2013.
[37]L. J. Myers and W. L. Capper, “A transmission line model of the human foetal circulatory system.,” Med. Eng. Phys., vol. 24, no. 4, pp. 285–94, May 2002.
[38]C. Guiot, P. G. Piantà, and T. Todros, “Modelling the feto-placental circulation: I. A distributed network predicting umbilical haemodynamics throughout pregnancy,” Ultrasound Med. Biol., vol. 18, no. 6–7, pp. 535–544, Jan. 1992.
[39]A. Kleiner-Assaf, A. J. Jaffa, and D. Elad, “Hemodynamic model for analysis of Doppler ultrasound indexes of umbilical blood flow.,” Am. J. Physiol., vol. 276, no. 6 Pt 2, pp. H2204–14, Jun. 1999.
[40]K. V. Kumar and S. S. Kumar, “LabVIEW based Condition Monitoring of Induction Machines,” Int. J. Intell. Syst. Appl., vol. 4, no. 3, p. 56, 2012.
[41]A. Waugh and A. Grant, Ross & Wilson Anatomy and Physiology in Health and Illness. Elsevier Health Sciences UK, 2014.
[42]C. Lees, G. Albaiges, C. Deane, M. Parra, and K. H. Nicolaides, “Assessment of umbilical arterial and venous flow using color Doppler,” Ultrasound Obstet. Gynecol., vol. 14, no. 4, pp. 250–255, Oct. 1999.
[43]T. Kiserud and G. Acharya, “The fetal circulation,” Prenat. Diagn., vol. 24, no. 13, pp. 1049–1059, Dec. 2004.
[44]G. Acharya, T. Wilsgaard, G. K. R. Berntsen, J. M. Maltau, and T. Kiserud, “Reference ranges for serial measurements of umbilical artery Doppler indices in the second half of pregnancy.,” Am. J. Obstet. Gynecol., vol. 192, no. 3, pp. 937–44, Mar. 2005.
[45]P. Fogarty, B. Beattie, A. Harper, and J. Dornan, “Continuous wave Doppler flow velocity waveforms from the umbilical artery in normal pregnancy.,” J. Perinat. Med., vol. 18, no. 1, pp. 51–7, Jan. 1990.