title: Mixture Models for Estimating Maximum Blood Flow Velocity.
abstract: OBJECTIVE
  A gaussian mixture model (GMM) was recently developed for estimating the probability density function of blood flow velocity measured with transcranial Doppler ultrasound data. In turn, the quantiles of the probability density function allow one to construct estimators of the "maximum" blood flow velocity. However, GMMs assume gaussianity, a feature that is not omnipresent in observed data. The objective of this work was to develop mixture models that do not invoke the gaussian assumption.
  
  
  METHODS
  Here, GMMs were extended to a skewed GMM and a nongaussian kernel mixture model. All models were developed on data from 59 patients with closed head injuries from multiple hospitals in the United States, with ages ranging from 13 to 81 years and Glasgow Coma Scale scores ranging from 3 to 11. The models were assessed in terms of the log likelihood (a goodness-of-fit measure) and via visual comparison with the underlying spectrograms.
  
  
  RESULTS
  Among the models examined, the skewed GMM showed a significantly (P< .05) higher log likelihood for 56 of the 59 patients and produced maximum flow velocity estimates consistent with the observed spectrograms for all patients. Kernel mixture models are generally less "robust" in that their quality is inconsistent across patients.
  
  
  CONCLUSIONS
  Among the models examined, it was found that the skewed GMM provided a better model of the data both in terms of the quality of the fit and in terms of visual comparison of the underlying spectrogram and the estimated maximum blood flow velocity. Nongaussian mixture models have potential for even higher-quality assessment of blood flow, but further development is called for.
authors.affiliation: From the Applied Physics Laboratory (C.M., P.D.M.) and Departments of Statistics (C.M., W.G.), Neurological Surgery (P.D.M.), and Bioengineering (P.D.M.), University of Washington, Seattle, Washington USA. marzban@stat.washington.edu.
authors.forename: Caren
authors.initials: C
authors.lastname: Marzban
authors.affiliation: From the Applied Physics Laboratory (C.M., P.D.M.) and Departments of Statistics (C.M., W.G.), Neurological Surgery (P.D.M.), and Bioengineering (P.D.M.), University of Washington, Seattle, Washington USA.
authors.forename: Wenxiao
authors.initials: W
authors.lastname: Gu
authors.affiliation: From the Applied Physics Laboratory (C.M., P.D.M.) and Departments of Statistics (C.M., W.G.), Neurological Surgery (P.D.M.), and Bioengineering (P.D.M.), University of Washington, Seattle, Washington USA.
authors.forename: Pierre D
authors.initials: PD
authors.lastname: Mourad
mesh_terms: D000293:Adolescent; D000328:Adult; D000368:Aged; D000369:Aged, 80 and over; D001783:Blood Flow Velocity / Q000502:physiology*; D002560:Cerebrovascular Circulation / Q000502:physiology*; D003198:Computer Simulation; D005260:Female; D016489:Head Injuries, Closed / Q000000981:diagnostic imaging* / Q000503:physiopathology*; D006801:Humans; D007090:Image Interpretation, Computer-Assisted / Q000379:methods; D008297:Male; D008875:Middle Aged; D008955:Models, Cardiovascular; D015233:Models, Statistical; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D017585:Ultrasonography, Doppler, Transcranial / Q000379:methods*; D055815:Young Adult
keywords: blood flow; brain; head injury; noninvasive; transcranial Doppler ultrasound