Limits...
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.

Show MeSH

Related in: MedlinePlus

Diagrammatic representation of the conversion of the spiral arteries into uteroplacental vessels
© Copyright Policy
Related In: Results  -  Collection


getmorefigures.php?uid=PMC222923&req=5

Figure 1: Diagrammatic representation of the conversion of the spiral arteries into uteroplacental vessels

Mentions: The biological system is highly non-linear. Therefore, the output of any simulated model will be near actual only when it includes various non-linearities. In such a case, unlike a linear system, minor variations in input may result in absolutely unpredictable outputs. In pregnancy, the local geometric vascular alteration is also accompanied by the systemic bio-rheological and haemodynamic change. Any abnormality in the system is known to trigger the onset of serious morbid conditions like pre-eclampsia and/or intrauterine growth restriction (IUGR). They are one of the leading causes of maternal and fetal deaths in both the developing as well as the developed countries. Precise Aetiopathogenesis is still not clear but the disorder has been linked to the endothelial dysfunction and the uteroplacental insufficiency, which in turn triggers systemic hypertension and sympathetic overactivity [1-3]. Studies by the standard biomedical technique have failed to improve our understanding of the rapidly altering uteroplacental blood flow dynamics during pregnancy (Fig 1). 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. Modeling is a known tool in the physiological fluid dynamics study. A validated non-linear mathematical model of the uteroplacental system has been developed which has also opened up a new frontier of research in the field of Doppler velocimetry analysis, modelling and image processing [4]. An electrical model can be easily simulated which can also incorporate various non-linearities present in the actual system. Earlier, Doppler FVW's have been analyzed by computer based algorithms using simple linearized first order differential equations transforming the functions into an R-C circuit commonly used in haemodynamic investigation [5]. Such a Transmission Line (TL) model [6] is linear, whereas, the actual system is non-linear and active. Blood flow velocity profile at the distal uteroplacental vessels (UPV) contains extra frequencies compared to the proximal uterine artery (UA). To analyze the FVW's mapped at the level of uteroplacental vessels, one has to separate it from the uterine artery, and it needs manipulation to see the effect of UPV on UA and vice-versa. Thus we need an active device that represents pregnancy time and change, which is not possible with TL model. Our group made an attempt to device a theoretical Junction field effect transistor (JFET) model earlier ([7,8]. MOSFET, field effect transistor, widely used in electrical engineering is flexible, and is nearer to the non-linear biological system. While using the MOSFETs as voltage-controlled switches, a fair degree of controlled-non-linearity has been introduced in the model. This is a distinct advancement and a major gain, more so in pregnancy, over the previously described passive linear models. In addition to the effect of the vessel elasticity and the blood density, the effect of blood viscosity is also simulated. Moreover, wide availability of several MOS models and extensive research in MOS fabrication justifies its selection as an ideal and a better model than the TL model. The simulation outputs are similar to the actual Doppler FVW's profiles obtained for some of the non-linear parameters by various authors [4,9]. However, we expect the present model and the simulation results to initiate extensive clinical or experimental studies involving various non-linear parameters in the near future. The feedback will help the scientist working in the field of modelling to further modify and improve the model significantly.


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

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

Diagrammatic representation of the conversion of the spiral arteries into uteroplacental vessels
© Copyright Policy
Related In: Results  -  Collection

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

Figure 1: Diagrammatic representation of the conversion of the spiral arteries into uteroplacental vessels
Mentions: The biological system is highly non-linear. Therefore, the output of any simulated model will be near actual only when it includes various non-linearities. In such a case, unlike a linear system, minor variations in input may result in absolutely unpredictable outputs. In pregnancy, the local geometric vascular alteration is also accompanied by the systemic bio-rheological and haemodynamic change. Any abnormality in the system is known to trigger the onset of serious morbid conditions like pre-eclampsia and/or intrauterine growth restriction (IUGR). They are one of the leading causes of maternal and fetal deaths in both the developing as well as the developed countries. Precise Aetiopathogenesis is still not clear but the disorder has been linked to the endothelial dysfunction and the uteroplacental insufficiency, which in turn triggers systemic hypertension and sympathetic overactivity [1-3]. Studies by the standard biomedical technique have failed to improve our understanding of the rapidly altering uteroplacental blood flow dynamics during pregnancy (Fig 1). 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. Modeling is a known tool in the physiological fluid dynamics study. A validated non-linear mathematical model of the uteroplacental system has been developed which has also opened up a new frontier of research in the field of Doppler velocimetry analysis, modelling and image processing [4]. An electrical model can be easily simulated which can also incorporate various non-linearities present in the actual system. Earlier, Doppler FVW's have been analyzed by computer based algorithms using simple linearized first order differential equations transforming the functions into an R-C circuit commonly used in haemodynamic investigation [5]. Such a Transmission Line (TL) model [6] is linear, whereas, the actual system is non-linear and active. Blood flow velocity profile at the distal uteroplacental vessels (UPV) contains extra frequencies compared to the proximal uterine artery (UA). To analyze the FVW's mapped at the level of uteroplacental vessels, one has to separate it from the uterine artery, and it needs manipulation to see the effect of UPV on UA and vice-versa. Thus we need an active device that represents pregnancy time and change, which is not possible with TL model. Our group made an attempt to device a theoretical Junction field effect transistor (JFET) model earlier ([7,8]. MOSFET, field effect transistor, widely used in electrical engineering is flexible, and is nearer to the non-linear biological system. While using the MOSFETs as voltage-controlled switches, a fair degree of controlled-non-linearity has been introduced in the model. This is a distinct advancement and a major gain, more so in pregnancy, over the previously described passive linear models. In addition to the effect of the vessel elasticity and the blood density, the effect of blood viscosity is also simulated. Moreover, wide availability of several MOS models and extensive research in MOS fabrication justifies its selection as an ideal and a better model than the TL model. The simulation outputs are similar to the actual Doppler FVW's profiles obtained for some of the non-linear parameters by various authors [4,9]. However, we expect the present model and the simulation results to initiate extensive clinical or experimental studies involving various non-linear parameters in the near future. The feedback will help the scientist working in the field of modelling to further modify and improve the model significantly.

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