title: Effect of non-linearity in predicting Doppler waveforms through a novel model.
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.
  
  
  METHODS
  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.
  
  
  CONCLUSIONS
  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.
  
  
  CONCLUSIONS
  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.
authors.affiliation: Department of Electrical Engineering, Indian Institute of Technology, New Delhi, India. gayasen@cse.psu.edu
authors.forename: Aman
authors.initials: A
authors.lastname: Gayasen
authors.forename: Sunil Kumar
authors.initials: SK
authors.lastname: Dua
authors.forename: Amit
authors.initials: A
authors.lastname: Sengupta
authors.forename: D
authors.initials: D
authors.lastname: Nagchoudhuri
mesh_terms: D001158:Arteries / Q000502:physiology; D001783:Blood Flow Velocity; D001809:Blood Viscosity / Q000502:physiology; D004548:Elasticity; D005260:Female; D006439:Hemodynamics; D006801:Humans; D008955:Models, Cardiovascular; D017711:Nonlinear Dynamics; D010920:Placenta / Q000098:blood supply; D011247:Pregnancy / Q000502:physiology*; D012212:Rheology; D016216:Ultrasonography, Prenatal; D014599:Uterus / Q000098:blood supply