Mixture Models for Estimating Maximum Blood Flow Velocity.

OBJECTIVES: 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.

Earth before life.

BACKGROUND: A recent study argued, based on data on functional genome size of major phyla, that there is evidence life may have originated significantly prior to the formation of the Earth. RESULTS: Here a more refined regression analysis is performed in which 1) measurement error is systematically taken into account, and 2) interval estimates (e.g., confidence or prediction intervals) are produced. It is shown that such models for which the interval estimate for the time origin of the genome includes the age of the Earth are consistent with observed data. CONCLUSIONS: The appearance of life after the formation of the Earth is consistent with the data set under examination.

A double-gaussian, percentile-based method for estimating maximum blood flow velocity.

OBJECTIVES: Transcranial Doppler sonography allows for the estimation of blood flow velocity, whose maximum value, especially at systole, is often of clinical interest. Given that observed values of flow velocity are subject to noise, a useful notion of "maximum" requires a criterion for separating the signal from the noise. All commonly used criteria produce a point estimate (ie, a single value) of maximum flow velocity at any time and therefore convey no information on the distribution or uncertainty of flow velocity. This limitation has clinical consequences especially for patients in vasospasm, whose largest flow velocities can be difficult to measure. Therefore, a method for estimating flow velocity and its uncertainty is desirable. METHODS: A gaussian mixture model is used to separate the noise from the signal distribution. The time series of a given percentile of the latter, then, provides a flow velocity envelope. This means of estimating the flow velocity envelope naturally allows for displaying several percentiles (e.g., 95th and 99th), thereby conveying uncertainty in the highest flow velocity. RESULTS: Such envelopes were computed for 59 patients and were shown to provide reasonable and useful estimates of the largest flow velocities compared to a standard algorithm. Moreover, we found that the commonly used envelope was generally consistent with the 90th percentile of the signal distribution derived via the gaussian mixture model. CONCLUSIONS: Separating the observed distribution of flow velocity into a noise component and a signal component, using a double-gaussian mixture model, allows for the percentiles of the latter to provide meaningful measures of the largest flow velocities and their uncertainty.

A method for estimating zero-flow pressure and intracranial pressure.

BACKGROUND: It has been hypothesized that the critical closing pressure of cerebral circulation, or zero-flow pressure (ZFP), can estimate intracranial pressure (ICP). One ZFP estimation method used extrapolation of arterial blood pressure as against blood-flow velocity. The aim of this study was to improve ICP predictions. METHODS: Two revisions have been considered: (1) the linear model used for extrapolation is extended to a nonlinear equation; and (2) the parameters of the model are estimated by an alternative criterion (not least squares). The method is applied to data on transcranial Doppler measurements of blood-flow velocity, arterial blood pressure, and ICP from 104 patients suffering from closed traumatic brain injury, sampled across the United States and England. RESULTS: The revisions lead to qualitative (eg, precluding negative ICP) and quantitative improvements in ICP prediction. While moving from the original to the revised method, the ±2 SD of the error is reduced from 33 to 24 mm Hg, and the root-mean-squared error is reduced from 11 to 8.2 mm Hg. The distribution of root-mean-squared error is tighter as well; for the revised method the 25th and 75th percentiles are 4.1 and 13.7 mm Hg, respectively, as compared with 5.1 and 18.8 mm Hg for the original method. CONCLUSIONS: Proposed alterations to a procedure for estimating ZFP lead to more accurate and more precise estimates of ICP, thereby offering improved means of estimating it noninvasively. The quality of the estimates is inadequate for many applications, but further work is proposed, which may lead to clinically useful results.