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.
Intrauterine growth restriction (IUGR), predominately due to placental insufficiency, is one of the main causes of perinatal mortality and morbidity [1], [2], and defined as a birth weight below the 10th percentile for gestational age. IUGR fetuses, suffering from hypoxia and undernutrition, show Doppler changes in several arteries of the feto-placental circulation such as umbilical artery (UA), middle cerebral artery (MCA), and also in the aortic isthmus (AoI). These changes are assessed in clinical practice to stage the severity of IUGR and are thought to reflect blood flow redistribution due to increased peripheral resistance, with decreased brain resistance in order to maximize brain blood supply under an adverse environment. In IUGR fetuses, AoI diastolic forward flow usually decreases and can become reversed in the more severe cases reflecting blood redistribution from the ductus arteriosus towards the brain instead of the periphery. Reverse flow in the AoI is associated with worse perinatal and neurodevelopmental outcome [3]–[7]. However, which remodeling or redistribution processes in the cardiovascular system induce the observed changes in AoI flow in IUGR fetuses is not fully understood. It has been proposed that cerebral vasodilation plays a major role in decreasing diastolic flow in the AoI [8]. However, other clinical studies suggested that AoI flow pattern is influenced by simultaneous changes in both cerebral and peripheral-placental resistances [6], [9]–[11]. Moreover, some experimental studies in an ovine animal model [12]–[14] have quantified the influence of placental resistance increase in the AoI flow, showing a strong correlation between the increase in the placental resistance and the amount of diastolic reversal flow in the AoI. However, the cerebral vasodilation occurring as response to fetal hypoxemia also influences the flow patterns in the AoI, and this influence could not be isolated from those changes caused by the increase in placental resistance. Therefore, it would be of interest to be able to estimate the separate influence of the individual contributors, such as the cerebral vasodilation and placental resistance increase, on the AoI flow. This can further improve the understanding of the flow changes in IUGR and provide more targeted assessment of flow redistribution. For this, lumped computational models have been proposed to recreate and better understand hemodynamic changes in the fetal circulation [15]–[22]. These models are based on the idea that the flow in a tube is analogous to the current in an electrical circuit and flow properties such as viscosity, inertia and compliance can be modeled with resistors, inductors and capacitors respectively. Hence, the different parts of the fetal circulation, such as arteries or vascular beds, can be modeled with a set of electrical components. The parameters of the electrical components are calculated based on the cardiovascular system' s physical properties and dimensions together with physiological and imaging measurements, where possible. Thus, an equivalent electric circuit of the fetal circulation can be obtained. Computational models have the advantage that they enable to evaluate the effects of changes in individual parameters on the total system performance. For example, the influence of changes in placental and/or brain resistance on the AoI flow can be evaluated separately, which cannot be performed in a clinical or experimental setting. Previously published models of the fetal circulation focused either on the materno-fetal circulation, studying oxygen exchange [15], [17], [18]; only focused on the fetal circulation under normal conditions [16], [20]; lack the full complexity of the fetal circulation (such as the ductus arteriosus) to study the flow redistribution in the places connecting the specific segments present [18], [21]; or have used a simplified and non-measured and personalized flow waveform at the entrance of the aorta and pulmonary artery [19], [21], [22]. Therefore, we developed an extended lumped model of the fetal circulation, including all relevant components to study flow redistribution in IUGR that additionally can be tuned towards an individual fetus when blood flow measurements are available. This model was further used to help in better understanding the hemodynamic changes induced by altered conditions in the brain circulation, including the AoI and the MCA. The model was calibrated and validated using clinical measurements from a healthy control fetus. Next a parametric study was performed to specifically evaluate contributors to flow changes in the AoI and cerebral arteries (CA). Finally, the model was personalized with clinical data from three IUGR cases with different degrees of severity in order to show the individual contributors to flow redistribution.
In order to calibrate and validate the accuracy of the fetal circulation model, and to show its potential for personalization, clinical and Doppler data from one control and three IUGR fetuses with different degrees of severity were included. Eligible cases were singleton pregnancies that were selected from women who attended the Maternal-Fetal Medicine Department at Hospital Clínic de Barcelona. The study protocol was approved by the local Ethics Committee and patients provided written informed consent. IUGR was defined as an estimated fetal weight [23] and confirmed birth weight below the 10th percentile according to local reference curves [24] together with a pulsatility index (PI) in the UA above 2 standard deviations [25]. IUGR fetuses were classified in stages of severity based upon the end-diastolic flow (EDF) in the UA as: present (PEDF), absent (AEDF) or reversed (REDF) [26]. We selected one IUGR representative of each severity stage. All IUGR cases and the control fetus underwent an ultrasonographic examination between 31–34 weeks of gestation using a Siemens Sonoline Antares machine (Siemens Medical Systems, Malvern, PA, USA) which included estimation of fetal weight, standard obstetric Doppler evaluation and fetal echocardiography. Fetal echocardiography included the evaluation of flow velocities in the UA, MCA, AoI, ductus arteriosus and ascending aorta (only in the control fetus). The UA was evaluated in a free loop of the umbilical cord. The MCA was measured in a transverse view of the fetal skull at the level of its origin from the circle of Willis [27]. The cerebroplacental ratio was calculated by dividing MCA and UA PI [25]. PI was calculated as: systolic velocity minus diastolic velocity divided by time-averaged maximum velocity. Ductus arteriosus and AoI flow velocities were obtained either in a sagittal view of the fetal thorax with a clear visualization of the aortic arch or in a cross section of the fetal thorax at the level of the 3-vessel and trachea view [28]. The AoI flow velocity was quantified by measuring the AoI PI and flow index (IFI). The IFI was calculated as: (systolic + diastolic) /systolic velocity integrals. Aortic inflow velocity was imaged in an apical or basal 5-chamber view of the heart, and pulmonary artery inflow velocity was obtained in a right ventricular outflow tract view. Peak systolic velocities of both aortic and pulmonary artery inflows, ejection time and heart rate were measured. The diameters of the aortic and pulmonary valves were measured in frozen real-time images during systole by the leading-edge-to-edge method [29]. Additionally, Doppler recording from the ascending aorta was obtained in the control fetus. The angle of insonation was kept as close as possible to 0° and always below 30°. Doppler data are shown as crude values and z-scores by gestational age according to previously published normal values [25], [27], [28], [30]. Upon delivery, gestational age, birth weight, birth weight centile, mode of delivery, Apgar scores, presence of preeclampsia and length of stay at the neonatal intensive care unit were recorded.
Ultrasonographic and perinatal data are shown in Table 2. As expected, IUGR cases showed a higher UA PI and AoI PI, together with lower MCA PI, cerebroplacental ratio and IFI values as compared to the control fetus. Also, as expected, IUGR cases delivered earlier and had lower birthweight and birthweight centile as compared with the control fetus. There were no perinatal deaths with the exception of the most severe IUGR case (REDF) who died in utero. Fig. 2 shows the real measured flow velocity waveforms in UA, MCA and AoI for the control and the 3 IUGR fetuses. Reversed diastolic flow in the AoI can be appreciated in IUGR cases with AEDF and REDF. Model-based and measured flow waveforms from the aortic and pulmonary inflows, ascending aorta, AoI, MCA and ductus arteriosus of the control fetus after calibration are displayed in Fig. 3 highlighting their similarity. The model-based pressure waveform is displayed in the same figure (Fig. 3G). Furthermore, we confirmed that the amount of blood flow distributed towards each vascular bed was within the range of normal values, as shown in Table 3. The parameters values' of the vascular bed resistances and compliances are listed in Table 4. Fig. 4 displays model-based AoI and CA traces for different combinations of peripheral and brain resistance values, modeling different severity degrees of IUGR. It shows that as peripheral resistance increases and/or brain resistance decreases, late-systolic and diastolic flow in the AoI is reversed while blood flow in the CA increases. The amount of reversal flow in the AoI (Fig. 5A–B), PI in the AoI (Fig. 5C–D) and IFI (Fig. 5E–F) were plotted as a function of brain and peripheral resistances relative to their normal value. Both the individual increase in peripheral resistance and decrease in brain resistance seem to have similar effects on the AoI flow. PI in the CA (PICA) and the ratio between the PI in the dAo and CA (PIdAo/PICA) were plotted in Fig. 6 as a function of brain and peripheral resistances relative to their normal value. In the case of the CA, the decrease in brain resistance seems to have a bigger influence on decreasing PICA than the increase in peripheral resistance (Fig. 6B). Regarding PIdAo/PICA, up to a two-fold increase/decrease in peripheral/brain resistance, its relation with the corresponding resistance variation is similar (Fig. 6D). The increase in percentage of CCO towards the brain depends mainly on the reduction of brain resistance rather than peripheral changes, as shown in the graphs plotted in Fig. 6E. However the reduction of the amount of blood flow towards the lower body and the placenta was mainly produced by the increase in the peripheral resistance. The comparison between the measured and the patient specific fitting of the AoI and CA blood waveforms are displayed in Fig. 7A–F showing similar measured and model-based flow waveforms. Table 4 shows the values of vascular bed resistances and compliances and also the estimated peripheral and brain resistances after fitting for all individuals in the study. Table 5 shows the model-based parameters' values obtained for the four fetuses, which are similar to the clinical measurements shown in Table 2. The relative increase and decrease in peripheral and brain resistance respectively, estimated for each modeled case is plotted in Fig. 7G. In the IUGR fetus with UA-PEDF, the peripheral resistance was increased by 20% (×1. 2) while brain resistance remained almost equal (÷1. 08). In the most severe IUGR case, the peripheral resistance increased 274% (×3. 7) with −41% (÷1. 7) decrease of brain resistance. Therefore, in all three IUGR fetuses, the estimated variation in peripheral resistance is much higher than the variation in the brain resistance. The estimated amount of blood flow towards the brain and the lower body and placenta for the four fetuses is plotted in Fig. 7H showing that as the severity condition increases, the percentage of blood flow to the brain increases and the flow to the lower body and placenta is reduced.
We developed a realistic computational model of the fetal circulation to study blood redistribution in IUGR enabling both parametric studies to determine individual contributors to remodeling as well as personalization to quantify changes in an individual fetus. Using this approach, we show that AoI flow changes depend both on brain vasodilation and peripheral resistance increase, while MCA flow is mainly affected by changes in cerebral resistance. Furthermore we showed that individual IUGR fetuses show marked differences in their vascular components with an exaggerated change in peripheral-placental resistance as major determinant for observed changes in measured Doppler flows. For this, we implemented and calibrated a lumped model of the fetal circulation taking into account the main arteries of the fetal circulation, including the ductus arteriosus and the aortic isthmus. Previous approaches to model the fetal circulation focused mainly on the (oxygen) exchange within the placenta [15], [17], [18] or have only modeled fetal circulation under normal conditions [16], [20]. Some previous studies that investigated the influence of an increase in placental resistance on flow related indexes did not include the ductus arteriosus, thus limiting its comparison with in-vivo imaging and the translation to clinical practice [19], [21]. Therefore, to our knowledge, ours is the first attempt to evaluate the effect of peripheral and cerebral resistances on AoI flow by using a computational model of the fetal circulation. Another important difference from previously published models is that we use data from individual clinical imaging as boundary conditions for each modeled subject, instead of considering a single flow input with fixed values calculated from the literature. The reliability of our model was ensured by comparing the model-based flow waveforms with Doppler velocity profiles recorded in the control fetus. Moreover, the fraction of cardiac output distributed to the different peripheral regions of the fetus obtained with our model agrees with the cardiac output distribution measured in human fetuses [10], [46], [47], and also estimated in other models [16], [20]. We have comprehensively evaluated how the flow in AoI and CA are affected by changes in the vascular resistances. The increase in placenta vasculature resistance together with the vasoconstriction of the lower body arteries were modeled by increasing the peripheral resistance. The cerebral vasodilation that occurs as a compensatory mechanism to fetal hypoxia and undernutrition was modeled by decreasing brain resistance. We observed that, as increasing the modeled IUGR severity, diastolic flow in AoI decreases and, in very severe cases becomes markedly retrograde. This pattern of changes in AoI flow is consistent with the changes clinically described in IUGR cases [6], [9]–[11], [30]. We also found that the AoI flow changes observed in IUGR are influenced independently by both cerebral vasodilation and peripheral resistance increase. Previous reports suggested that the decrease in cerebral resistance plays a major role in determining the net AoI diastolic flow since MCA vasodilation precedes AoI flow abnormalization [8]. Other studies have described a correlation between the IFI and postnatal neurodevelopmental outcome [6], [7], supporting the impact of cerebral vasodilation in AoI flow changes. However, other studies [6], [9] indicated that since the AoI is connecting the two fetal circulations in parallel, AoI flow pattern reflects the existence of differences in vascular resistances, suggesting that both the increase in peripheral resistance and the cerebral vasodilation are responsible for AoI flow changes. Our results support this last hypothesis since we showed that not only cerebral vasodilation but also the increase in peripheral resistance altered the AoI flow pattern. These results are consistent with the consideration of AoI as a good predictor of not only the poor neurodevelopmental outcome [5], [6] but also of the high risk of adverse perinatal outcome and mortality [3], [7], [50]. Regarding the CA, we showed that the decrease in PICA is mostly related to cerebral vasodilation and much less influenced by changes in the periphery/placenta. This is also reflected in the amount of blood flow that is distributed towards the brain and towards lower body and placenta. For example, when brain resistance was decreased by 75%, the flow that went to the lower body and placenta was decreased by 57% but cerebral flow increased 150%, showing how cerebral vasodilation is the most responsible for the blood flow increase in CA. These results are in line with those previously reported by van den Wijngaard et al. [21] and consistent with MCA being a risk stratifying factor for suboptimal neurodevelopment in IUGR rather than perinatal complications [4], [50]. Finally, PIdAo/PICA showed a linear increase with the severity of IUGR, starting from a value about 1. 0 for the control fetus. This result was consistent with the data published by Makikallio et al. [9] that showed also a value of 1. 0 in control fetuses and an increase in the IUGR group. Next we constructed patient-specific models of three IUGR fetuses. We were able to reproduce the AoI and CA flow waveforms and also the model-based values for AoI PI, CA PI and IFI parameters were consistent with the measured ones, demonstrating that the developed lumped model of the fetal circulation not only is able to reproduce the hemodynamic changes that occur in fetus under normal conditions, but also with increased peripheral-placental resistance and vasodilation. This is helpful to estimate parameters that cannot be measured clinically such as the relative variation of the upper and lower body resistances who might be more directly related to the staging of the disease than only the measurements of PI, currently used in clinical practice. However, the presented lumped model has some limitations. Firstly, 0D lumped models only consider the temporal variation of pressure, flow and volume variables, assuming no variation of these parameters in the spatial dimension. However, since the aim of the study was to evaluate the hemodynamic interactions among the different cardiovascular parts, without considering flow phenomena or wave reflections, we think that 0D lumped models were accurate enough for our purpose. Also, the model is a simplified version of the fetal arterial tree because it only considers one artery and one peripheral bed for the lower body. However since the goal was to study the flow changes in the AoI and brain we considered that including or not all the lower arteries and organs would have the same effect on the AoI and cerebral flows. Secondly, the increase in right ventricular predominance observed in IUGR fetuses [10], [51], [52] was not taken into account for the parametric study as we decided to focus on the resistance variation and used the measurement of a normal fetus as input rather than changing the input for each combination of resistances. Thirdly, the fetal heart was not modeled. Nevertheless, since we used patient-specific Doppler waveforms at the ventricular outputs as the input of the model, we were indirectly considering the cardiac changes that may affect the cardiac output when studying the individual cases. Fourthly, our model does not take into account the major biochemical disorders created by placental circulatory insufficiency, such as low pH, hypoxia and respiratory acidosis, that can interfere with the normal cardio circulatory function and play a significant role in the hemodynamic changes during IUGR [53]. Fifthly, considering a venous pressure of 0 mmHg could have an effect, but mainly on the pressure values. However, we were interested only in flow waveforms and we were able to reproduce the measured Doppler traces in all cases. Finally, although we are not estimating all the parameters that may change between subjects and/or under pathological conditions, we still can consider our approach as a patient-specific modeling. We are using patient specific data to build the model and its boundary conditions (gestational age, fetal weight, heart rate, Doppler velocities and valve radius) to finally estimate the specific resistances variation for each individual. In conclusion, the proposed equivalent lumped model seems to be a good approximation to assess hemodynamic changes in the fetal circulation under abnormal growth conditions. Further developments of the model can be useful for assessing further vessels and their interactions under various clinical conditions, and the impact of interventions. Our results suggested that AoI flow is affected by peripheral-placental as well as cerebral resistances while CA flow mainly depends on cerebral resistance. Furthermore, when personalizing the model to IUGR fetuses we were able to estimate the specific vascular resistances variation, suggesting that the peripheral-placental resistance is the major determinant for observed changes in measured Doppler flows. This study supports the potential role of AoI as marker of adverse perinatal and neurological outcome since it is a central vessel connecting the two ventricular outputs and therefore its flow reflects the balance between ventricular output and upper/lower body vascular resistances. Personalizing the model shows promise to directly assess properties of the vascular bed rather than using indirect Doppler measurements.
Intrauterine growth restriction (IUGR) is one of the leading causes of perinatal mortality and can be defined as a low birth weight together with signs of chronic hypoxia or malnutrition. It is mostly due to placental insufficiency resulting in a chronic restriction of oxygen and nutrients to the fetus. IUGR leads to cardiac dysfunction in utero which can persist postnatally. Under these altered conditions, IUGR fetuses redistribute their blood in order to maintain delivery of oxygenated blood to the brain, known as brain sparing. 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. However, which remodeling or redistribution processes in the cardiovascular systems induce the observed changes in AoI flow in IUGR fetuses is not fully understood. We developed a computational model of the fetal circulation, including the key elements related to fetal blood redistribution. Using measured cardiac outflow profiles to allow personalization, we can recreate and better understand the blood flow changes in individual IUGR fetuses.
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A Computational Model of the Fetal Circulation to Quantify Blood Redistribution in Intrauterine Growth Restriction