A mathematical formula for prediction of gray and white matter volume recovery in abstinent alcohol dependent individuals

Department of Radiology and Biomedical Imaging, University of California, San Francisco, CA, USA.
Psychiatry Research (Impact Factor: 2.47). 09/2011; 194(2):198-204. DOI: 10.1016/j.pscychresns.2011.05.003
Source: PubMed


We propose a mathematical formula that predicts the trajectory of the recovery from lobar gray and white matter volume deficits in individuals with sustained abstinence from alcohol. The formula was validated by using MRI-measured volumetric data from 16 alcohol dependent individuals who had brain scans at three time points during abstinence from alcohol. Using the measured volumetric data of each individual from the first two time points, we estimated the individual's gray and white matter volume of the frontal, parietal and temporal lobes for the third time point using the formula. Similarly, using the measured data for the second and third time points, we estimated the first time point data for each individual. The data predicted from the formula were very similar to the experimentally measured data for all lobes and for both gray and white matter. The intra-class correlation coefficients between the measured data and the data estimated from the formula were >0.95 for almost all the tissues. The formula may also be applicable in other neuroimaging studies of tissue volume changes such as white matter myelination during brain development and white matter demyelination or brain volume loss in neurodegenerative diseases, such as Alzheimer's disease.

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Available from: Timothy C Durazzo, Apr 17, 2014
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    • "However, with this method, knowledge of the feeding habit of the fish is needed so that a feeding correction factor can be imposed on the regression estimates to achieve good prediction of age and/or growth rate of the fish. Recently, a simple mathematical formula was derived for prediction of human brain tissue volume re-growth/recovery in sustained abstinent alcohol dependent individuals (Mon et al., 2011) and for prediction of individual child growth (human growth) in both boys and girls across ethnically diverse children (Mon et al., 2013). For individual growth data, the formula relies on an intrinsic factor, known as growth rate factor or growth coefficient (k) to predict growth of the individual. "
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    ABSTRACT: Age determination or growth rate of fishes is a critical component of a proper fishery management. Current methods of fish age determination growth rate have several drawbacks, including, large numbers of fish needed over time for analyses, subjective interpretations during age determination or the use of expensive instrument for analysis. In this report, a simple theoretically derived mathematical formula is assessed for prediction of fish growth in length. Secondary data of length measures of 16 different species of tropical fish was used to assess the accuracy of the formula for predicting fish growth. The data comprised of relative length-at-age of 14 different fishes and absolute length of 2 other different fishes. For each species, two of the length measures together with the corresponding ages were used to estimate two constants in the formula and the formula used to predict the remaining lengths. The accuracy of the formula for prediction was assessed by evaluating the discrepancies between observed data and corresponding predicted data. The biasness as well as accuracy of the formula was also assessed. In all the species studied, discrepancies between observed data and the corresponding formula predicted values were minimal and fluctuated between negative and positive values. The mean signed value of the discrepancies (a measure of biasness) for all the 16 species was -0.2 ± 1.7, while the mean of the absolute discrepancies (a measure of accuracy) was 1.2 ± 1.4. The fluctuations of the discrepancies between negative and positive values demonstrate that the discrepancies are not systematic errors of prediction. The signed mean discrepancy of -0.2 is close to 0, thus indicating minimal biasness of prediction. Also the absolute mean discrepancy of 1.2 suggests prediction accuracy within 1 unit of actual measurement, indicating high accuracy.
    Full-text · Article · Mar 2015 · African journal of agricultural research
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    • "Consequently, little is known about the actual trajectory of regional volume changes during the first year of abstinence. Some studies suggest that treatment-seeking ALC experience more rapid brain volume increases over the first month of sobriety than during later months of sustained abstinence (Pfefferbaum et al. 1995; Agartz et al. 2003; Gazdzinski, Durazzo & Meyerhoff 2005; Yeh et al. 2007; Mon et al. 2011), which indicates that volume change is not necessarily linear over the first year of sobriety. Additionally , few studies have examined associations between changes in brain volume and neurocognition during early abstinence; therefore, the functional relevance of volume changes during this period is unclear. "
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    ABSTRACT: The trajectory of regional volume changes during the first year of sustained abstinence in those recovering from an alcohol use disorder is unclear because previous research typically employed only two assessment points. To better understand the trajectory of regional brain volume recovery in treatment-seeking alcohol-dependent individuals (ALC), regional brain volumes were measured after 1 week, 1 month and 7.5 months of sustained abstinence via magnetic resonance imaging at 1.5 T. ALC showed significant volume increases in frontal, parietal and occipital gray matter (GM) and white matter (WM), total cortical GM and total lobar WM, thalamus and cerebellum, and decreased ventricular volume over 7.5 months of abstinence. Volume increases in regional GM were significantly greater over 1 week to 1 month than from 1 month to 7.5 months of abstinence, indicating a non-linear rate of change in regional GM over 7.5 months. Overall, regional lobar WM showed linear volume increases over 7.5 months. With increasing age, smoking ALC showed lower frontal and total cortical GM volume recovery than non-smoking ALC. Despite significant volume increases, ALC showed smaller GM volumes in all regions, except the frontal cortex, than controls after 7.5 months of abstinence. ALC and controls showed no regional WM volume differences at any assessment point. In non-smoking ALC only, increasing regional GM and WM volumes were related to improving processing speed. Findings may indicate a differential rate of recovery of cell types/cellular components contributing to GM and WM volume during early abstinence, and that GM volume deficits persist after 7.5 months of sustained sobriety in this ALC cohort.
    Full-text · Article · Aug 2014 · Addiction Biology
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    • "Below we give a brief description of the human growth version of the original formula proposed for prediction of brain tissue volume recovery in abstinent alcohol dependent individuals (Mon et al., 2011). Suppose the height (H) of a child at time (t) is H (t) and that at a later time (t1s) is H (t1s) . "
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    ABSTRACT: The purpose of this study was to assess the applicability of a simple mathematical formula for prediction of individual child linear growth. The formula describes a square root dependence of height on age with only two constants, k and C. Retrospective serial height measurements of 137 healthy children (61 female), who attended clinic in the Pediatrics Department at the University of California, San Francisco were used. For each child, two of the initial measurements and their corresponding measurement times were used to determine the values of k and C. By substituting the determined values of k and C into the formula, the formula was then used to predict the trajectory of the child's growth. The 137 children were comprised of 20% Hispanic, 23% African-American, 27% Caucasian and 30% Asian. The formula predicted growth trajectories of 136 out of the 137 children with minimal discrepancies between the measured data and the corresponding predicted data. The mean of the discrepancies was 0.8 cm. Our proposed formula is very easy to use and predicts individual child growth with high precision irrespective of gender or ethnicity. The formula will be a valuable tool for studying human growth and possibly growths of other animals. Am. J. Hum. Biol., 2013. © 2013 Wiley Periodicals, Inc.
    Full-text · Article · Sep 2013 · American Journal of Human Biology
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