Inverse Solution of the Fetal-Circulation Model Based on Ultrasound Doppler Measurements

Oded Luria, Jacob Bar, Josef Shalev, Michal Kovo, Abraham Golan, Ofer Barnea*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Fetal growth restriction (FGR) is one of the major contributors to adverse perinatal outcome. However, the diagnostic tools used for the assessment of fetal well-being are limited due to the great variability among fetuses. The purpose of this study was to estimate the dynamics of fetal circulation during the advanced stages of the gestational period. A methodology for estimating fetal hemodynamic parameters is presented. The method combines a mathematical model of the fetal circulation, optimization algorithm, and measurements of power-Doppler ultrasound. The model estimates fetal indices of the fetal circulation that are not accessible for direct measurement, aimed at the identification of the degree of circulatory compromise in fetuses diagnosed as FGR. The method was tested on a cohort of 20 normal and 22 growth-restricted fetuses. Model predictions indicated significant changes in the circulation of FGR fetuses compared to normal fetuses. Cardiac output was significantly lower in the FGR group compared to the control group (330 ± 52 mL min-1 kg-1 compared to 396 ± 52 mL min-1 kg-1, p < 0.001). Furthermore, placental blood flow was lower for the FGR group (145 ± 49 mL min-1 kg-1 compared to 181 ± 31 mL min-1 kg-1, p < 0.01). In the FGR fetuses with adverse outcome, both indices were reduced even further (297 ± 56 mL min-1 kg-1, p < 0.001 and 97 ± 46 mL min-1 kg-1, p < 0.001, respectively). In the adverse outcome group the model indicated also significant increase in cardiac output distribution towards the brain (9.6 ± 0.7%, compared to 8.0 ± 1.6%, p < 0.01) and an increase in the ratio of blood shunted by the ductus venosus (60.6 ± 17.7%, compared to 39.7 ± 14.8%, p < 0.01), indicating a severe brain sparing effect in these fetuses. In conclusion, patient-specific modeling may provide a reliable estimate of the important hemodynamic indices of the fetal circulation which may be clinically relevant for the management of FGR pregnancies.

Original languageEnglish
Pages (from-to)202-216
Number of pages15
JournalCardiovascular Engineering and Technology
Issue number2
StatePublished - May 2014


  • Fetal growth restriction
  • Inverse problem
  • Mathematical modeling
  • Parameter estimation


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