A computational model of the fetal circulation to quantify blood redistribution in intrauterine growth restriction

Abstract

Intrauterine growth restriction (IUGR) due to placental insufficiency is associated with blood flow redistribution in order to maintain delivery of oxygenated blood to the brain. Given that, in the fetus the aortic isthmus (AoI) is a key arterial connection between the cerebral and placental circulations, quantifying AoI blood flow has been proposed to assess this brain sparing effect in clinical practice. While numerous clinical studies have studied this parameter, fundamental understanding of its determinant factors and its quantitative relation with other aspects of haemodynamic remodeling has been limited. Computational models of the cardiovascular circulation have been proposed for exactly this purpose since they allow both for studying the contributions from isolated parameters as well as estimating properties that cannot be directly assessed from clinical measurements. Therefore, a computational model of the fetal circulation was developed, including the key elements related to fetal blood redistribution and using measured cardiac outflow profiles to allow personalization. The model was first calibrated using patient-specific Doppler data from a healthy fetus. Next, in order to understand the contributions of the main parameters determining blood redistribution, AoI and middle cerebral artery (MCA) flow changes were studied by variation of cerebral and peripheral-placental resistances. Finally, to study how this affects an individual fetus, the model was fitted to three IUGR cases with different degrees of severity. In conclusion, the proposed computational model provides a good approximation to assess blood flow changes in the fetal circulation. The results support that while MCA flow is mainly determined by a fall in brain resistance, the AoI is influenced by a balance between increased peripheral-placental and decreased cerebral resistances. Personalizing the model allows for quantifying the balance between cerebral and peripheral-placental remodeling, thus providing potentially novel information to aid clinical follow up.

Figure 1. Anatomical simplified configuration and equivalent lumped model of the fetal circulation.

(a) Anatomical configuration composed of 14 arterial segments and 8 vascular beds: (1) right and (2) left upper body, (3) right and (4) left brain, (5) right and (6) left lung, (7) peripheral and (8) coronary arteries. QaoV and QpV represent the aortic (left) and pulmonary (right) inflows respectively. (b) Electric circuit of the lumped model. The 14 blocks corresponding to the 14 arterial segments are highlighted in solid lines and include 1 resistor (R), 1 capacitor (C) and 1 inductor (L). The 8 blocks of vascular beds are highlighted in dashed lines and they consist of a resistor R_c in series with a capacitor C_p in parallel with a resistor R_p.

Figure 2. Doppler ultrasound data of the study individuals.

Doppler recordings from umbilical artery (UA) (top), middle cerebral artery (MCA) (middle) and aortic isthmus (AoI) (bottom) for the control and the three intrauterine growth restricted (IUGR) fetuses with present (PEDF), absent (AEDF) or reverse (REDF) umbilical artery end-diastolic flow. Red arrows indicated reversal flow in the AoI.

Figure 3. Measured and model-based flow and pressure waveforms of the control fetus.

Comparison between measured and model-based blood flow waveforms in (a) aortic inflow (used as left input in our model (Q_aoV)), (b) pulmonary inflow (used as right input in our model (Q_pV)), (c) aortic isthmus, (d) cerebral arteries, (e) ductus arteriosus and (f) ascending aorta. Dashed line indicates a blood flow of 0 ml·s⁻¹. (g) Model-based pressure waveform.

Figure 4. Model-based flow waveforms in the aortic isthmus and cerebral arteries.

Model-based flow waveforms in the (a) aortic isthmus and (b) cerebral arteries for different degrees of peripheral and brain resistance changes. R_per and R_brain represent the peripheral and brain resistances respectively, and and are their corresponding normal values. Dashed line indicates a blood flow of 0 ml·s⁻¹.

Figure 5. Plots of the aortic isthmus flow related indexes.

Plots illustrating the percentage of reversal flow (a,b), pulsatility index (PI) (c,d) and flow index (IFI) (e,f) in aortic isthmus (AoI) as a function of decrease and increase of brain (R_brain) and peripheral (R_per) resistances respectively, calculated as the ratio between the current and their corresponding normal values and . The plots in the left (a,c,e) show the variation of the three indexes as a function of all the possible combinations of R_per increase and R_brain decrease. The plots in the right (b,d,f) shows the variation of the three indexes when only one of the resistances was changed and the other was kept with a value of 1.

Figure 6. Plots of the cerebral arteries and descending aorta flow related indexes.

Plots illustrating the pulsatility index (PI) in cerebral arteries (a,b) and PI ratio of descending aorta (dAo) and cerebral arteries (CA) (c,d) as a function of decrease and increase of brain (R_brain) and peripheral (R_per) resistances respectively, calculated as the ratio between the current and their corresponding normal values and . The plots in the left (a,c) show the variation of the two indexes as a function of all the possible combinations of R_per increase and R_brain decrease. The plots in the right (b,d) shows the variation of the two indexes when only one of the resistances was changed and the other was kept with a value of 1. (e) Percentage of combined cardiac output (CCO) going towards the brain (solid line) and towards the lower body & placenta (dashed line) plotted as a function of decrease and increase of brain (R_brain) and peripheral (R_per) resistances respectively.

Figure 7. Measured and model-based flow waveforms and model parameters of the intrauterine growth restricted fetuses.

Comparison between measured (top) and model-based (bottom) blood flow waveforms in the aortic isthmus (a–c) and cerebral arteries (d–f) for the intrauterine growth restricted (IUGR) fetuses with umbilical artery (UA) present (PEDF), absent (AEDF) or reversed (REDF) end-diastolic flow. Dashed line indicates a blood flow of 0 ml·s⁻¹. (g) Percentage of estimated increase in peripheral-placental resistance (grey bars) and decrease in brain resistance (white bars) calculated for each individual. (h) Estimated percentage of combined cardiac output (CCO) towards the brain and towards the lower body and placenta for each individual.