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Effect of non-linearity in predicting Doppler waveforms through a novel model.

Gayasen A, Dua SK, Sengupta A, Nagchoudhuri D - Biomed Eng Online (2003)

Bottom Line: Normal pregnancy has been successfully modeled and the doppler output waveforms are simulated for different gestation time using the model.Both these results are established clinical facts.Total harmonic distortion (THD) is found to be informative in determining the Feto-maternal health.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Electrical Engineering, Indian Institute of Technology, New Delhi, India. gayasen@cse.psu.edu

ABSTRACT

Background: In pregnancy, the uteroplacental vascular system develops de novo locally in utero and a systemic haemodynamic & bio-rheological alteration accompany it. Any abnormality in the non-linear vascular system is believed to trigger the onset of serious morbid conditions like pre-eclampsia and/or intrauterine growth restriction (IUGR). Exact Aetiopathogenesis is unknown. Advancement in the field of non-invasive doppler image analysis and simulation incorporating non-linearities may unfold the complexities associated with the inaccessible uteroplacental vessels. Earlier modeling approaches approximate it as a linear system.

Method: We proposed a novel electrical model for the uteroplacental system that uses MOSFETs as non-linear elements in place of traditional linear transmission line (TL) model. The model to simulate doppler FVW's was designed by including the inputs from our non-linear mathematical model. While using the MOSFETs as voltage-controlled switches, a fair degree of controlled-non-linearity has been introduced in the model. Comparative analysis was done between the simulated data and the actual doppler FVW's waveforms.

Results & discussion: Normal pregnancy has been successfully modeled and the doppler output waveforms are simulated for different gestation time using the model. It is observed that the dicrotic notch disappears and the S/D ratio decreases as the pregnancy matures. Both these results are established clinical facts. Effects of blood density, viscosity and the arterial wall elasticity on the blood flow velocity profile were also studied. Spectral analysis on the output of the model (blood flow velocity) indicated that the Total Harmonic Distortion (THD) falls during the mid-gestation.

Conclusion: Total harmonic distortion (THD) is found to be informative in determining the Feto-maternal health. Effects of the blood density, the viscosity and the elasticity changes on the blood FVW are simulated. Future works are expected to concentrate mainly on improving the load with respect to varying non-linear parameters in the model. Heart rate variability, which accounts for the vascular tone, should also be included. We also expect the model to initiate extensive clinical or experimental studies in the near future.

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THD vs. pregnancy time
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Figure 7: THD vs. pregnancy time

Mentions: The documentation of the Doppler flow-velocity waveforms from the key peripheral uteroplacental vessels, the main functional site, is necessary to ascertain the underlying haemodynamic changes in pregnancy. The failure to obtain the information due to technological limitations as well as complex geometric pattern and variation existing in the system has been a major impediment to the advancement in knowledge [4,7,11]. Computer based algorithms and electrical transmission line analogy using mathematical model has been reported [5]. Simulations are done taking into consideration functions like lumped proximal and distal resistance, mean arterial pressure without explaining the geometric and the flow conditions. A definite pressure-flow velocity relation of the uteroplacental system considering its morphological and rheological changes, an important physiological parameter in pregnancy has not been considered as yet. In the absence of actual recording an alternative useful rational approach has been tried here linking the accessible proximal vessel to the unknown distal system using a theoretical MOSFET model. Normal pregnancy has been successfully modeled using the model. Output waveforms for increasing pregnancy time are shown in Fig. 5. It is observed that dicrotic notch disappears as pregnancy matures. Also, S/D ratio decreases with pregnancy time. Both these results are established clinical facts. As the pregnancy progresses, there is a gradual fall in the uteroplacental vascular resistance with increasing capacitance to accommodate extra blood volume necessary for the fetomaternal perfusion and exchanges. The Actual Doppler velocity profile recorded at the level of the uterine artery in the normally progressing pregnancy also shows a gradual fall in the Pulsatility and the resistance index [4,12,13]. In the present study, other than validating the non-linear electrical model, spectral analysis on these outputs showed some interesting results. Magnitudes of Fourier Coefficients of the outputs are plotted in Fig. 6. It is observed that the first harmonic is larger than fundamental frequency in early pregnancy. As pregnancy matures, the fundamental frequency component increases sharply and then shows somewhat linear fall as frequency (harmonics) increases. Similar relation is seen in hypertensive condition, where systolic (S) peak is higher and diastolic (D) is low (High S/D ratio), but the rise is comparatively and correspondingly lower compared to normal pregnancy. This result has been earlier observed using spectral analysis on actual Doppler data [14]. Also, Total Harmonic Distortion (THD) of the outputs is plotted vs. pregnancy time in Fig. 7. It is observed that the THD decreases as pregnancy matures. This too is expected, as it is known that low frequency components increase with pregnancy time [14]. Therefore, not only, we could generate similar type of variations in the FVW's profile as seen in the actual pregnancy condition, but also simultaneously, we found THD as an important diagnostic parameter that may be considered in future. A FVW's from mid pregnancy with high THD signifies high uteroplacental resistance and thus may predict impending pre-eclampsia and /or IUGR. The very fact that the results obtained from the mathematical model, the real time Doppler & spectral analysis and the non-linear electrical MOSFET simulation are in close approximation proves that the model is a novel one. The correspondingly similar simulated output that we obtained through this non-linear model by manipulating the terminal load and introducing the extra frequencies, the vital non-linear factor which greatly effects both the maternal and fetal haemodynamic is the biggest gain over the linear model.


Effect of non-linearity in predicting Doppler waveforms through a novel model.

Gayasen A, Dua SK, Sengupta A, Nagchoudhuri D - Biomed Eng Online (2003)

THD vs. pregnancy time
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC222923&req=5

Figure 7: THD vs. pregnancy time
Mentions: The documentation of the Doppler flow-velocity waveforms from the key peripheral uteroplacental vessels, the main functional site, is necessary to ascertain the underlying haemodynamic changes in pregnancy. The failure to obtain the information due to technological limitations as well as complex geometric pattern and variation existing in the system has been a major impediment to the advancement in knowledge [4,7,11]. Computer based algorithms and electrical transmission line analogy using mathematical model has been reported [5]. Simulations are done taking into consideration functions like lumped proximal and distal resistance, mean arterial pressure without explaining the geometric and the flow conditions. A definite pressure-flow velocity relation of the uteroplacental system considering its morphological and rheological changes, an important physiological parameter in pregnancy has not been considered as yet. In the absence of actual recording an alternative useful rational approach has been tried here linking the accessible proximal vessel to the unknown distal system using a theoretical MOSFET model. Normal pregnancy has been successfully modeled using the model. Output waveforms for increasing pregnancy time are shown in Fig. 5. It is observed that dicrotic notch disappears as pregnancy matures. Also, S/D ratio decreases with pregnancy time. Both these results are established clinical facts. As the pregnancy progresses, there is a gradual fall in the uteroplacental vascular resistance with increasing capacitance to accommodate extra blood volume necessary for the fetomaternal perfusion and exchanges. The Actual Doppler velocity profile recorded at the level of the uterine artery in the normally progressing pregnancy also shows a gradual fall in the Pulsatility and the resistance index [4,12,13]. In the present study, other than validating the non-linear electrical model, spectral analysis on these outputs showed some interesting results. Magnitudes of Fourier Coefficients of the outputs are plotted in Fig. 6. It is observed that the first harmonic is larger than fundamental frequency in early pregnancy. As pregnancy matures, the fundamental frequency component increases sharply and then shows somewhat linear fall as frequency (harmonics) increases. Similar relation is seen in hypertensive condition, where systolic (S) peak is higher and diastolic (D) is low (High S/D ratio), but the rise is comparatively and correspondingly lower compared to normal pregnancy. This result has been earlier observed using spectral analysis on actual Doppler data [14]. Also, Total Harmonic Distortion (THD) of the outputs is plotted vs. pregnancy time in Fig. 7. It is observed that the THD decreases as pregnancy matures. This too is expected, as it is known that low frequency components increase with pregnancy time [14]. Therefore, not only, we could generate similar type of variations in the FVW's profile as seen in the actual pregnancy condition, but also simultaneously, we found THD as an important diagnostic parameter that may be considered in future. A FVW's from mid pregnancy with high THD signifies high uteroplacental resistance and thus may predict impending pre-eclampsia and /or IUGR. The very fact that the results obtained from the mathematical model, the real time Doppler & spectral analysis and the non-linear electrical MOSFET simulation are in close approximation proves that the model is a novel one. The correspondingly similar simulated output that we obtained through this non-linear model by manipulating the terminal load and introducing the extra frequencies, the vital non-linear factor which greatly effects both the maternal and fetal haemodynamic is the biggest gain over the linear model.

Bottom Line: Normal pregnancy has been successfully modeled and the doppler output waveforms are simulated for different gestation time using the model.Both these results are established clinical facts.Total harmonic distortion (THD) is found to be informative in determining the Feto-maternal health.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Electrical Engineering, Indian Institute of Technology, New Delhi, India. gayasen@cse.psu.edu

ABSTRACT

Background: In pregnancy, the uteroplacental vascular system develops de novo locally in utero and a systemic haemodynamic & bio-rheological alteration accompany it. Any abnormality in the non-linear vascular system is believed to trigger the onset of serious morbid conditions like pre-eclampsia and/or intrauterine growth restriction (IUGR). Exact Aetiopathogenesis is unknown. Advancement in the field of non-invasive doppler image analysis and simulation incorporating non-linearities may unfold the complexities associated with the inaccessible uteroplacental vessels. Earlier modeling approaches approximate it as a linear system.

Method: We proposed a novel electrical model for the uteroplacental system that uses MOSFETs as non-linear elements in place of traditional linear transmission line (TL) model. The model to simulate doppler FVW's was designed by including the inputs from our non-linear mathematical model. While using the MOSFETs as voltage-controlled switches, a fair degree of controlled-non-linearity has been introduced in the model. Comparative analysis was done between the simulated data and the actual doppler FVW's waveforms.

Results & discussion: Normal pregnancy has been successfully modeled and the doppler output waveforms are simulated for different gestation time using the model. It is observed that the dicrotic notch disappears and the S/D ratio decreases as the pregnancy matures. Both these results are established clinical facts. Effects of blood density, viscosity and the arterial wall elasticity on the blood flow velocity profile were also studied. Spectral analysis on the output of the model (blood flow velocity) indicated that the Total Harmonic Distortion (THD) falls during the mid-gestation.

Conclusion: Total harmonic distortion (THD) is found to be informative in determining the Feto-maternal health. Effects of the blood density, the viscosity and the elasticity changes on the blood FVW are simulated. Future works are expected to concentrate mainly on improving the load with respect to varying non-linear parameters in the model. Heart rate variability, which accounts for the vascular tone, should also be included. We also expect the model to initiate extensive clinical or experimental studies in the near future.

Show MeSH
Related in: MedlinePlus