title: Limitations of parametric modeling of the left ventricle using first harmonic analysis: possible role for gaussian modeling.
abstract: BACKGROUND
  Fourier (cosine) analysis of time activity curves (TAC) of radionuclide ventriculography (RVG) may oversimplify the TAC and has limitations.
  
  
  METHODS
  We identified 21 patients who had undergone 24 frame planar RVG with ejection fractions ranging from 8% to 76% (43% ± 19%). The TAC for each pixel was fitted to both a cosine and gaussian function then analyzed on a pixel-by-pixel basis then over the entire LV. Second, mathematical simulations were performed to analyze the stability of each fit in the presence of low amplitude and noise.
  
  
  RESULTS
  The fit was slightly but significantly better for the gaussian compared to the cosine function (RMS gaussian 13.0% ± 2.5% vs 13.5% ± 2.1% cosine; P = .016). There was near exact correlation with amplitude and between gaussian mu and cosine phase. The SD of phase from the cosine fit correlated strongly with the SD of the mu from the gaussian fit. The proposed new measure of dyssynchrony, the sigma parameter of the gaussian fit, correlated with the SD of the cosine phase (r = 0.520, P = .016). Simulations showed gradual but modest deviation of the sigma parameter from the gaussian fit with lower amplitudes whereas the deviation of the calculated SD of phase increased exponentially with decreasing amplitude.
  
  
  CONCLUSIONS
  First harmonic (cosine) fitting has significant limitations. Gaussian fitting is an alternative way to model the LV TAC. The sigma from the gaussian may provide additional information LV dyssynchrony and is less influenced by image noise. Gaussian fitting merits further evaluation for modeling LV function.
authors.affiliation: Section of Cardiology, Jefferson Heart Institute, Thomas Jefferson University, 925 Chestnut Street, Mezzanine, Philadelphia, PA, USA, christopher.hansen@jefferson.edu.
authors.forename: Christopher L
authors.initials: CL
authors.lastname: Hansen
mesh_terms: D006801:Humans; D008433:Mathematics; D008954:Models, Biological; D015635:Radionuclide Ventriculography / Q000379:methods*; D016277:Ventricular Function, Left