Psychiatry Research Neuroimaging 194 (2011) 198ndash204

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Psychiatry Research Neuroimaging

j ourna l homepage wwwe lsev ie rcom locate psychresns

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

Anderson Mon a Kevin Delucchi b Timothy C Durazzo a Stefan Gazdzinski c Dieter J Meyerhoff a

a Department of Radiology and Biomedical Imaging University of California San Francisco and Center for Imaging of Neurodegenerative Diseases Veterans Administration Medical CenterSan Francisco CA United Statesb Department of Psychiatry University of California San Francisco CA United Statesc Center for Imaging of Neurodegenerative Diseases Veterans Administration Medical Center San Francisco and M Smoluchowski Institute of Physics Jagiellonian University KrakowPoland

Corresponding author Center for Imaging of NeurodAdministration Medical Center Building 13 Mail Stop 11Francisco CA 94121 United States Tel +1 415 2212864

E-mail address AndersonMonucsfedu (A Mon)

0925-4927$ ndash see front matter Published by Elsevierdoi101016jpscychresns201105003

a b s t r a c t

a r t i c l e i n f o

Article historyReceived 14 September 2010Received in revised form 7 May 2011Accepted 15 May 2011

KeywordsBrainMRIAtrophyBrain recoveryNeurodegenerative diseaseAlcoholism

We propose a mathematical formula that predicts the trajectory of the recovery from lobar gray and whitematter volume deficits in individuals with sustained abstinence from alcohol The formula was validated byusing MRI-measured volumetric data from 16 alcohol dependent individuals who had brain scans at threetime points during abstinence from alcohol Using the measured volumetric data of each individual from thefirst two time points we estimated the individuals gray and white matter volume of the frontal parietal andtemporal lobes for the third time point using the formula Similarly using the measured data for the secondand third time points we estimated the first time point data for each individual The data predicted from theformula were very similar to the experimentally measured data for all lobes and for both gray and whitematter The intra-class correlation coefficients between the measured data and the data estimated from theformula were N095 for almost all the tissues The formula may also be applicable in other neuroimagingstudies of tissue volume changes such as white matter myelination during brain development and whitematter demyelination or brain volume loss in neurodegenerative diseases such as Alzheimers disease

egenerative Diseases Veterans4 M 4150 Clement Street San4810x6453 fax +1 415 668

Ireland Ltd

Published by Elsevier Ireland Ltd

1 Introduction

Alcohol use disorders (AUD) and other substance use disorders(SUD) are associated with alterations of brain structure and functionNeuroimaging studies have consistently demonstrated gray matter(GM) andor white matter (WM) loss and enlarged ventricles andsulci in AUD (Schroth et al 1988 Zipursky et al 1989 Jernigan et al1991 Sullivan et al 1995 Pfefferbaum et al 1996 Adalsteinsson andSpielman 1999 Gazdzinski et al 2005b) as well as with chroniccigarette smoking amphetamine cocaine and poly-substance usedisorders (Liu et al 1998 ONeill et al 2001 Brody et al 2004Durazzo and Meyerhoff 2007)

Brain morphometric abnormalities in AUD demonstrate variablelevels of recovery with sustained abstinence from alcohol (eg(Gazdzinski et al 2005a)) Cross-sectional magnetic resonanceimaging (MRI) studies of abstinent alcoholics demonstrated thatthose with smaller brain volumes at the inception of abstinence fromalcohol recover faster than those with larger volumes at inception

and longitudinally individual brain volume increases appear to begreater during short-term abstinence (ie the first few weeks) thanduring sustained long-term abstinence (Pfefferbaum et al 1995Gazdzinski et al 2005a) These two observations suggest a non-lineartrajectory of tissue volume recovery Themagnitude of volume changedemonstrated with various morphometric MRI methods during bothshort-term and long-term abstinence from alcohol has been linked tothe degree of tissue volume abnormalities at the beginning ofabstinence (Pfefferbaum et al 1995 Gazdzinski et al 2005aCardenas et al 2006 Yeh et al 2007) Specifically it was observedthat individuals with greater GM andor WM atrophy at the inceptionof abstinence (ie at baseline) generally showed greater volumeincreases over one month of abstinence from alcohol than those withless atrophy at baseline and that smaller lobar WM volumes wereassociated with greater lobar white matter volume increases withprolonged abstinence These observations highlight the dynamicneuroplastic changes that can occur after the removal of a chronicinsult such as chronic alcohol abuse

Although associations between brain volume at baseline andvolume changes during alcohol abstinence have been reported nomathematical formula has been advanced that predicts morphometricchanges that occur with sustained abstinence from alcohol Such aformula could be useful in further understanding abstinence-relatedbrain plasticity for predicting missing values in longitudinal studies

0 500 1000 1500200

205

210

215

220

225

230

Time (Days)

Vol

ume

(ml)

Fig 1 V(t) against t

199A Mon et al Psychiatry Research Neuroimaging 194 (2011) 198ndash204

and for predicting the trajectory of brain tissue volume recovery overdurations of abstinence that extend beyond the duration of mosttypical longitudinal neuroimaging studies Reliable projections ofbrain volume changes that accompany prolonged (ie years of)abstinence could have significant clinical and psycho-educationalrelevance and fuel future research applications

In this report using experimental serial volumetric MRI data fromthree different time points in the same alcohol-dependent individualswe propose and demonstrate the utility of a mathematical formulathat fairly reliably predicts individual changes in lobar gray matter(GM) or white matter (WM) volumes during abstinence from alcoholThe proposed formula is novel in that the prediction of individualbrain volumetric changes is not determined from the generalizedbehavior of a study group (as in statistical models that incorporategroup error terms) but is rather based on repeated measurements inthe same individual therefore incorporating the unique characteris-tics of the recovery of the individuals regional brain volumes

2 Theory

The amount of brain tissue volume (the volumetric sum ofneuronal microglial glial interstitial and vascular components)gained at any given time during abstinence in AUDSUD is dependenton the rate of tissue volume change during abstinence As the amountof brain tissue gained at a given time is directly proportional to thealcohol or substance induced atrophy at the beginning of abstinencethe rate of tissue volume change at any given time (t) during aninterval of abstinence is also directly proportional to the amount ofatrophy at t The amount of atrophy at a given time is inversely relatedto the volume of brain tissue present at that time (ie the greater theatrophy the lesser the amount of tissue and vice versa) Accordinglythe rate of change of the tissue volume at t should also be inverselyrelated to the volume of tissue at t From the foregoing argument itfollows that if the volume of brain tissue at t is V(t) and the atrophy issecondary to the effects of the chronically abused substance then

mathematically the rate of tissue volume gain denoted bydV teth THORNdt

at t

(measured from the onset of abstinence) can be expressed as

dV teth THORNdt

prop 1V teth THORN

or

dV teth THORNdt

=kiV teth THORN

eth1THORN

Here ki is a constant of proportionality unique to the i-thindividual that determines the rate of the individuals brain tissuevolume change ki can be referred to as the i-th individuals lsquorecoveryrate factorrsquo Factors such as age genetics environmental nutritionalgeneral medical condition etc which influence brain tissue recovery(or growth) all contribute to the value of the recovery rate factor ki Itshould be noted that this study is not intended to determine howmuch each of these factors contribute to the value of ki but rather todescribe the individualized trajectory of the brain tissue recoveryprocess An implicit assumption is that the same undeterminedfactors that govern ki in the fitted interval also govern ki in thetrajectory (ie if these factors are significantly different in these twotime periods prediction accuracy will be reduced)

Integration of Eq (1) yields

12V2

teth THORN = kit + Ci eth2THORN

where Ci is a constant of integration for the individual If t is in days kis in volume2dayminus1 and C in volume2

Fig 1 shows a plot of V(t) against t according to Eq (2) usingpractical values of C and k for frontal GM over an abstinence period of5 years The intercept on the V(t) axis equals (2Ci)

12 whichtheoretically is the volume of the tissue at the inception of abstinence

If V(t) is known from volumetric data at two different times t1 andt2 then it follows from Eq (2) that

ki =1

2 t2minust1eth THORN V2t2eth THORNminusV2

t1eth THORN

and C =V2

t1eth THORN2

minuskit1

Hence using the estimated values of ki and Ci the tissue volume atany other time t can be calculated from Eq (2) It is worth noting thatEq (2) ignores normal aging effects which is probably a goodapproximation for only short-term abstinence (eg not more than ayear) For longer abstinence periods it is necessary to add a normalaging factor (λ2) so that Eq (2) becomes

12V2

teth THORN = kit + Ciminusλ2i eth3THORN

where λi is the amount of brain tissue the individual lost due tonormal aging over the assessment intervalλ is best estimated from anage-matched longitudinal control sample Alternatively annual ratesof regional tissue volume lost due to normal aging have been reported(eg Resnick et al 2000 Resnick et al 2003 Scahill et al 2003Driscoll et al 2009) that λ can be estimated for an individual for agiven period of abstinence

3 Evaluation of the performance of the formula

We tested the formula using measuredMRI-derived regional braintissue volumes acquired from 16 abstinent alcohol dependentindividuals (13 males 3 females) with complete regional brain tissuevolume measures at three different time points (TP) The participantswere between 28 and 66 years of age (507plusmn119 years meanplusmnstandard deviation) and met DSM-IV criteria for alcohol dependencewith physiological dependence The male participants consumedmore than 150 alcoholic drinks per month the female participantsmore than 80 drinks per month (one standard alcoholic drinkcontains 136 g of pure ethanol) for eight or more years beforeenrollment into the study Participants were studied after55plusmn30 days (TP1) 364plusmn68 days (TP2) and 2223plusmn411 days(TP3) of sustained abstinence All participants gave formal writtenconsent for the research which was approved by the InstitutionalReview Boards of the University of California San Francisco and theSan Francisco Veterans Affairs Medical Center The MRI data were

200 A Mon et al Psychiatry Research Neuroimaging 194 (2011) 198ndash204

acquired in conjunction with an ongoing neuroimaging projectinvestigating the consequences of alcohol dependence on neurobio-logical and neurocognitive recovery during abstinence from alcoholThe data were acquired on a 15 Tesla clinical MR scanner (VisionSiemens Medical Systems Iselin NJ) using T2-weighted oblique-axialimaging (TR TE2=250080 ms 1times1 mm2 in-plane resolution 3 mmslice thickness no slice gap) with slices oriented 5deg to theorbitomeatal angle as seen on a midsagittal scout and T1-weightedcoronal imaging with a Magnetization Prepared Rapid AcquisitionGradient Echo sequence (TRTITE=93004 ms 1times1 mm2 in-planeresolution 15 mm slabs) oriented orthogonal to the long axis of thehippocampus Three-tissue intensity based segmentation (based onthe well-validated method of Van Leemput et al 1999) was appliedto the T1-weighted images to assign a set of probabilities of WM GMand cerebrospinal fluid (CSF) to each MRI voxel Intracranial volume(ICV) was calculated for each TP as the sum of all MRI voxels withinbrain The mean group difference in ICV for TP1 and TP3 was about02 ml The T2-weighted images were coregistered and re-sampled tothe T1 and used to mask out signal from non-brain tissue

We evaluated the performance of the formula using volumes forfrontal parietal and temporal GM and WM denoted here by fGMpGM tGM fWM pWM and tWM respectively Using these lobarvolumes for TP1 and TP2 of each participant as inputs we predictedthe corresponding TP3 lobar volumes for each participant Similarlyusing the TP2 and TP3 lobar volumes we predicted the individual TP1lobar volumes

For comparison we also estimated the individual tissue volumesfor TP1 and TP3 using themethod of multiple imputations (MI) (PROCMI in SAS version 92) (Schafer 1999) which is frequently used forimputing missing data in cost effectiveness analyses (Noble et al inpress) and in medical research (Sterne et al 2009) The MI method isthought to be better for imputing missing data than group meanreplacement or single imputation methods and can be used on bothcross-sectional and longitudinal data (Noble et al in press) (Sterneet al 2009) We did so by first deleting all TP1 values (ie settingthem to missing) and imputing those now missing ICV-correctedvolumes for each participant 10 times using data from TP2 and TP3Participant age and lifetimemeanmonthly alcohol consumption wereused as covariates as well (as they affect brain tissue volumes) theaverage of these 10 imputations was then calculated as theindividuals imputed tissue volume at TP1 This process was repeatedby deleting the TP3 data and imputing those values from TP1 and TP2The predicted data of the regional volumes derived from our formulaand from the MI approach were then compared with the experimen-

Table 1TP1 volumes frontal gray matter measured volumes and estimates from formula and mult

Participant V3measured V2measured V1measured V

1 25196 24370 242542 23060 23153 231563 20810 20342 202034 21535 21287 212135 24139 24142 239676 26995 26815 267227 23585 23871 239578 19169 18998 189509 26325 25850 2580110 21946 21885 2178611 20618 20351 2020912 27365 27101 2711213 21297 20921 2084414 23616 23422 2335115 19814 19806 1976616 18975 18957 19010MeanabsΔV1

V3measured V2measured and V1measured are the experimentally measured data V1formula=pr

method ΔV1=V1estimateminusV1measured

V1measured

times 100 and MeanabsΔV1 is the mean of absolute va

tally measured volumes for the corresponding TP using two statisticalapproaches i) calculating the percentage difference between mea-sured and predictedimputed data to compare the performances ofthe two methods and ii) calculating intra-class correlations betweenthe measured and predictedimputed data to compare the degree ofsimilarity between the volume estimates of each method with thecorresponding experimentally measured data We also performedpaired t-tests between TP2 observed data and TP3 observedpredicteddata and between TP2 observed data and TP1 observedpredicted datato evaluate the degree to which the statistical analysis that usedpredicted data gives statistical outcomes similar to that usingobserved data

4 Results

41 Percentage differences between measured and calculated data

Tables 1ndash3 show the measured volumes and the correspondingvolume estimates for TP1 from our formula and the MI for fGM pGMand tGM in all 16 participants For illustrative purposes Fig 2 showsrepresentative plots of experimental data for each TP and trajectoriesfor lobar GM volumes for eight of the 16 participants The circularmarks star marks and triangular marks show the measured frontalparietal and temporal GM volumes for the corresponding TP for eachindividual The curves show the trajectories derived from our formulausing the TP1 and TP2 volumes as inputs to predict the TP3 volumesfor each individual These plots allow appreciating the small deviationof the estimated individual TP3 volumes from the measured TP3volumes For brevity we did not include GM plots for all 16participants and we did not include plots and data for lobar WMvolumes instead we provide results from data of all the participantsfor both GM and WM analyses in the text

In Tables 1ndash3 columns 2 3 and 4 show the measured volumes(Vmeasured) for TP3 TP2 and TP1 respectively Columns 5 and 6 showthe volume estimates from the formula (Vformula) and the multipleimputations (VMI) respectively and columns 7 and 8 show thepercentage difference between Vmeasured and Vformula and betweenVmeasured and VMI respectively The group means (MeanabsΔV) werecalculated from the absolute values of individual percentage differ-ences of the predicted volumes from the measured volumes for all 16participants For TP1 MeanabsΔV1 for our formula were 010 021039 for fGM pGM tGM respectively and 001 004 and 051 forfWM pWM and tWM respectively The corresponding MeanabsΔV3for TP3 were 042 117 177 017 056 and 272 For comparison

iple imputations for individual study participants

1formula V1MI ΔVformula ΔVMI

24260 23780plusmn884 003 minus19523162 23027plusmn1251 003 minus05620277 20444plusmn1313 037 11921242 22091plusmn774 014 41424143 22894plusmn898 074 minus44826785 26029plusmn775 024 minus26023920 24975plusmn762 minus020 42118960 19986plusmn1015 005 54725746 25060plusmn1202 minus021 minus28721874 21993plusmn1229 040 09520287 21130plusmn862 039 45627059 27155plusmn706 minus020 01620813 20441plusmn747 minus015 minus19423360 23969plusmn1381 004 26519804 20348plusmn723 019 29418954 19953plusmn914 minus030 496

023plusmn018 285plusmn165

edicted data using the formula V1mult-imp=estimates from the multiple imputation

lues of the percentage errors

200 A Mon et al Psychiatry Research Neuroimaging 194 (2011) 198ndash204

acquired in conjunction with an ongoing neuroimaging projectinvestigating the consequences of alcohol dependence on neurobio-logical and neurocognitive recovery during abstinence from alcoholThe data were acquired on a 15 Tesla clinical MR scanner (VisionSiemens Medical Systems Iselin NJ) using T2-weighted oblique-axialimaging (TR TE2=250080 ms 1times1 mm2 in-plane resolution 3 mmslice thickness no slice gap) with slices oriented 5deg to theorbitomeatal angle as seen on a midsagittal scout and T1-weightedcoronal imaging with a Magnetization Prepared Rapid AcquisitionGradient Echo sequence (TRTITE=93004 ms 1times1 mm2 in-planeresolution 15 mm slabs) oriented orthogonal to the long axis of thehippocampus Three-tissue intensity based segmentation (based onthe well-validated method of Van Leemput et al 1999) was appliedto the T1-weighted images to assign a set of probabilities of WM GMand cerebrospinal fluid (CSF) to each MRI voxel Intracranial volume(ICV) was calculated for each TP as the sum of all MRI voxels withinbrain The mean group difference in ICV for TP1 and TP3 was about02 ml The T2-weighted images were coregistered and re-sampled tothe T1 and used to mask out signal from non-brain tissue

We evaluated the performance of the formula using volumes forfrontal parietal and temporal GM and WM denoted here by fGMpGM tGM fWM pWM and tWM respectively Using these lobarvolumes for TP1 and TP2 of each participant as inputs we predictedthe corresponding TP3 lobar volumes for each participant Similarlyusing the TP2 and TP3 lobar volumes we predicted the individual TP1lobar volumes

For comparison we also estimated the individual tissue volumesfor TP1 and TP3 using themethod of multiple imputations (MI) (PROCMI in SAS version 92) (Schafer 1999) which is frequently used forimputing missing data in cost effectiveness analyses (Noble et al inpress) and in medical research (Sterne et al 2009) The MI method isthought to be better for imputing missing data than group meanreplacement or single imputation methods and can be used on bothcross-sectional and longitudinal data (Noble et al in press) (Sterneet al 2009) We did so by first deleting all TP1 values (ie settingthem to missing) and imputing those now missing ICV-correctedvolumes for each participant 10 times using data from TP2 and TP3Participant age and lifetimemeanmonthly alcohol consumption wereused as covariates as well (as they affect brain tissue volumes) theaverage of these 10 imputations was then calculated as theindividuals imputed tissue volume at TP1 This process was repeatedby deleting the TP3 data and imputing those values from TP1 and TP2The predicted data of the regional volumes derived from our formulaand from the MI approach were then compared with the experimen-

Table 1TP1 volumes frontal gray matter measured volumes and estimates from formula and mult

Participant V3measured V2measured V1measured V

1 25196 24370 242542 23060 23153 231563 20810 20342 202034 21535 21287 212135 24139 24142 239676 26995 26815 267227 23585 23871 239578 19169 18998 189509 26325 25850 2580110 21946 21885 2178611 20618 20351 2020912 27365 27101 2711213 21297 20921 2084414 23616 23422 2335115 19814 19806 1976616 18975 18957 19010MeanabsΔV1

V3measured V2measured and V1measured are the experimentally measured data V1formula=pr

method ΔV1=V1estimateminusV1measured

V1measured

times 100 and MeanabsΔV1 is the mean of absolute va

tally measured volumes for the corresponding TP using two statisticalapproaches i) calculating the percentage difference between mea-sured and predictedimputed data to compare the performances ofthe two methods and ii) calculating intra-class correlations betweenthe measured and predictedimputed data to compare the degree ofsimilarity between the volume estimates of each method with thecorresponding experimentally measured data We also performedpaired t-tests between TP2 observed data and TP3 observedpredicteddata and between TP2 observed data and TP1 observedpredicted datato evaluate the degree to which the statistical analysis that usedpredicted data gives statistical outcomes similar to that usingobserved data

4 Results

41 Percentage differences between measured and calculated data

Tables 1ndash3 show the measured volumes and the correspondingvolume estimates for TP1 from our formula and the MI for fGM pGMand tGM in all 16 participants For illustrative purposes Fig 2 showsrepresentative plots of experimental data for each TP and trajectoriesfor lobar GM volumes for eight of the 16 participants The circularmarks star marks and triangular marks show the measured frontalparietal and temporal GM volumes for the corresponding TP for eachindividual The curves show the trajectories derived from our formulausing the TP1 and TP2 volumes as inputs to predict the TP3 volumesfor each individual These plots allow appreciating the small deviationof the estimated individual TP3 volumes from the measured TP3volumes For brevity we did not include GM plots for all 16participants and we did not include plots and data for lobar WMvolumes instead we provide results from data of all the participantsfor both GM and WM analyses in the text

In Tables 1ndash3 columns 2 3 and 4 show the measured volumes(Vmeasured) for TP3 TP2 and TP1 respectively Columns 5 and 6 showthe volume estimates from the formula (Vformula) and the multipleimputations (VMI) respectively and columns 7 and 8 show thepercentage difference between Vmeasured and Vformula and betweenVmeasured and VMI respectively The group means (MeanabsΔV) werecalculated from the absolute values of individual percentage differ-ences of the predicted volumes from the measured volumes for all 16participants For TP1 MeanabsΔV1 for our formula were 010 021039 for fGM pGM tGM respectively and 001 004 and 051 forfWM pWM and tWM respectively The corresponding MeanabsΔV3for TP3 were 042 117 177 017 056 and 272 For comparison

iple imputations for individual study participants

1formula V1MI ΔVformula ΔVMI

24260 23780plusmn884 003 minus19523162 23027plusmn1251 003 minus05620277 20444plusmn1313 037 11921242 22091plusmn774 014 41424143 22894plusmn898 074 minus44826785 26029plusmn775 024 minus26023920 24975plusmn762 minus020 42118960 19986plusmn1015 005 54725746 25060plusmn1202 minus021 minus28721874 21993plusmn1229 040 09520287 21130plusmn862 039 45627059 27155plusmn706 minus020 01620813 20441plusmn747 minus015 minus19423360 23969plusmn1381 004 26519804 20348plusmn723 019 29418954 19953plusmn914 minus030 496

023plusmn018 285plusmn165

edicted data using the formula V1mult-imp=estimates from the multiple imputation

lues of the percentage errors

Table 2TP1 volumes parietal gray matter measured volumes and estimates from formula and multiple imputations for individual study participants

Participant V3measured V2measured V1measured V1formula V1MI ΔVformula ΔV1MI

1 14175 13782 13674 13730 12535plusmn833 041 minus8332 13295 13270 13269 13267 12254plusmn606 minus001 minus7653 11156 11031 10995 11013 11434plusmn621 016 3994 11970 11725 11677 11681 11863plusmn498 004 1595 12409 12373 12347 12363 12265plusmn549 013 minus0666 13844 13647 13622 13614 13748plusmn628 minus006 0937 12632 12896 12906 12931 13352plusmn760 020 3468 10629 10653 10612 10659 10683plusmn880 044 0679 14048 13863 13774 13823 13259plusmn803 036 minus37310 11612 11486 11398 11462 11288plusmn803 056 minus09711 10373 10290 10283 10271 11423plusmn594 minus012 110912 13734 13829 13765 13843 14612plusmn464 057 61613 10198 10120 10072 10098 10930plusmn384 026 85214 13070 12971 12943 12939 12711plusmn803 minus003 minus17915 10922 10842 10826 10822 10916plusmn671 minus003 08416 10257 10236 10176 10232 10851plusmn425 054 663MeanabsΔV1 025plusmn020 419plusmn342

See Table 1 for abbreviations

201A Mon et al Psychiatry Research Neuroimaging 194 (2011) 198ndash204

the corresponding results of the MI approach were as followsMeanMIΔV1 for TP1 were 285 419 342 378 749 and 407 and forTP3 MeanMIΔV3 were 378 401 385 377 758 and 444 For eachlobar tissue type the MI estimates give much larger deviations fromthe measured volumes than the results obtained by our formula

Also as depicted in Fig 2 each curve passes close to theexperimental data at TP3 demonstrating that the formula describesthe individual time courses of brain volume re-growth very well

42 Intra-class correlations between measured and predicted data

The intra-class correlation coefficients between Vmeasured andVformula for TP1 were either 099 or 098 for fGM pGM tGM fWMpWM and tWM and the corresponding coefficients for TP3 were 098098 097 098 097 and 092 respectively The coefficients betweenVmeasured and VMI were 096 088 090 089 068 and 085respectively for TP1 and 091 090 088 092 073 and 087respectively for TP3 Here again the predictions from our formulashow closer relations to the measured data than the MI estimates

43 Paired t-test of Volumes between TPs

Tables 4 and 5 show results of the paired t-tests for TP1ndashTP2 andTP2ndashTP3 volumes respectively lsquoPair 1rsquo and lsquoPair 2rsquo of each row

Table 3TP1 volumes temporal gray matter measured volumes and estimates from formula and m

Participant V3measured V2measured V1measured V

1 15134 14944 14801 12 16213 16265 16236 13 13806 13549 13425 14 15359 15262 15321 15 16727 16771 16656 16 19057 18638 18580 17 15035 15050 15055 18 13839 13777 13694 19 17405 17385 17269 110 14372 14330 14313 111 14538 14320 14283 112 15853 15847 15876 113 13663 13891 13772 114 17469 17226 16976 115 13822 13819 13767 116 12614 12737 12672 1MeanabsΔV1

See Table 1 for abbreviations

constitute parallel analyses for the tissue indicated where lsquoPair 1rsquorepresents paired t-test between lsquoTP1 measuredrsquo and lsquoTP2 measuredrsquolsquoTP2 measuredrsquo and lsquoTP3 measuredrsquo and lsquoPair 2rsquo represents lsquoTP1predictedrsquo and lsquoTP2 measuredrsquolsquo TP2 measured and TP3 predictedrsquodata The predicted data from lsquoPair 2rsquo yielded t-statistics and P-valuesvery similar to those of the measured data from lsquoPair 1rsquo for all thetissues except tGM and tWM The differences in results between themeasured and predicted data for tGM and tWM may have to do withtemporal lobes experiencing magnetic field distortions and signal lossfrom susceptibility differences between brain and nearby ear canalwhich can lead to inaccurate segmentation

5 Discussion

The proposed mathematical formula describes the trajectory ofregional GM and WM volume recovery in AUD during sustainedabstinence from alcohol The regional brain volumes predicted fromthe formula very closely approximated the measured volumes for alltissues Similarly high consistency between the measured dataand the data derived from the formula were reflected in both thehigh intra-class correlation coefficients and the majority of the pairedt-tests Importantly the formula accounts for substantial individualvariability (through the recovery rate factor k) in the course andmagnitude of regional brain tissue volume changes during abstinence

ultiple imputations for individual study participants

1formula V1MI ΔVformula ΔVMI

4919 14870plusmn772 080 0466270 16063plusmn566 021 minus1973513 14090plusmn725 066 5705244 14703plusmn756 minus050 minus4036783 15624plusmn855 076 minus6208567 18547plusmn776 minus007 minus0185052 15723plusmn639 minus002 4443763 14177plusmn773 051 3537381 16603plusmn733 065 minus3864322 14289plusmn542 007 minus0164268 14437plusmn662 minus011 1075846 16849plusmn771 minus019 6133955 13639plusmn442 133 minus0977149 16787plusmn1451 101 minus1113818 13251plusmn851 037 minus3752760 14195plusmn592 069 1202

050plusmn037 342plusmn314

0 150 300

120

160

200

240

Days of Abstinence

Bra

in T

issu

e V

olum

e (m

l)

0 150 300

120

160

200

240

Days of Abstinence

Bra

in T

issu

e V

olum

e (m

l)

Fig 2 Plots of frontal parietal and temporal graymatter volumes against days of abstinence for 8 representative participants The curves represent our formulas trajectory of volumechange with time using TP1 and TP2 data as input The circular star and triangular marks represent the observed data for frontal parietal and temporal gray matter respectively

202 A Mon et al Psychiatry Research Neuroimaging 194 (2011) 198ndash204

from alcohol and does not rely on group data in theway that statisticalmethods such as MI do Since it is unclear to what extent agebiological differences genetic factors and other unknown factorscontribute to recovery rates basing our predictions on correlatedvolume measures at two time points gives us some protectionimmunity against unrealistic estimates The individually varyingrecovery rates demonstrated in Fig 2 adversely affect the accuracyof common imputation methods that are based on group datacharacteristics The larger deviations of the measured data from thatcalculated with the common MI approach versus data estimated byour formula support this assertion

51 Non-linear tissue volume increases in abstinent substance users

Simple linear trajectories were used previously to estimate braintissue recovery rates in abstinent alcoholics (Pfefferbaum et al 1995Gazdzinski et al 2005a) However linear recovery rates contradictresearch observations that brain volume gains decrease with duration

Table 4Paired t-tests between TP1 and TP2 data

TP2 volume versus TP1 volume t statistic P value (2-tailed)

fGM (pair 1) TP2 measuredndashTP1 measured 335 0004(pair 2) TP2 measuredndashTP1 predicted 378 0002fWM (pair 1) TP2 measuredndashTP1 measured 525 b0001(pair 2) TP2 measuredndashTP1 predicted 311 0007pGM (pair 1) TP2 measuredndashTP1 measured 384 0002(pair 2) TP2 measuredndashTP1 predicted 184 0086pWM (pair 1) TP2 measuredndashTP1 measured 105 0310(pair 2) TP2 measuredndashTP1 predicted 091 0380tGM (pair 1) TP2 measuredndashTP1 measured 153 0150(pair 2) TP2 measuredndashTP1 predicted 267 0032tWM (pair 1) TP2 measuredndashTP1 measured 340 0004(pair 2) TP2 measuredndashTP1 predicted 056 0580

of abstinence and the goodness of fit with our proposed formulaBased on longitudinal MRI volume data over seven months ofabstinence from alcohol we previously suggested that brain tissuevolume gains over that time period may be exponential (Gazdzinskiet al 2005a) However for the recovery process to be exponential therecovery rate at any time has to be directly proportional to theavailable brain tissue volume at that time (ie the smaller theavailable volume the slower the rate of recovery and vice versa)mdashthisis contrary to observations Therefore linear or exponential functionsare not expected to describe brain volume recovery processesappropriately as is indeed observed in our described analyses Onthe other hand our formula better describes brain volume trajectoriesduring short and long term abstinence because its derivation wasbased directly on the observations that cross-sectionally individualswith smaller tissue volumes at the inception of abstinence recovervolume faster than those with larger baseline volumes and thatlongitudinally short-term recovery rates are greater than long-termrecovery rates

Table 5Paired t-tests between TP3 and TP2 data

TP2 volume verse TP3 volume t statistic P value (2-tailed)

fGM (pair 1) TP3 measuredndashTP2 measured 320 0006(pair 2) TP3 predictedndashTP2 measured 273 0015fWM (pair 1) TP3 measuredndashTP2 measured 242 0029(pair 2) TP3 predictedndashTP2 measured 432 0001pGM (pair 1) TP3 measuredndashTP2 measured 214 0049(pair 2) TP3 predictedndashTP2 measured 377 0002pWM (pair 1) TP3 measuredndashTP2 measured 140 0183(pair 2) TP3 predictedndashTP2 measured 144 0169tGM (pair 1) TP3 measuredndashTP2 measured 273 0016(pair 2) TP3 predictedndashTP2 measured 227 0039tWM (pair 1) TP3 measuredndashTP2 measured 090 0382(pair 2) TP3 predictedndashTP2 measured 340 0004

203A Mon et al Psychiatry Research Neuroimaging 194 (2011) 198ndash204

We also tested the formula on lobar volume decreases inindividuals with dementia who had four MRI scans over two years(baseline six months 12 months two years) When using the twoinitial measurements to calculate the values of C and k in the formulathe deviations of our estimates from the measured data at 12 monthsand two years were less than 2 and similar for both TPs It appearsimportant however that the initial time interval is long enough to fitvolume change reliably (ie volume change should be large comparedto the measurement error) A case in point is that in our abstinentcohort of alcohol dependent individuals estimates from the formulawere much better when predicting TP1 data from TP2 and TP3 dataThe input data were separated by a longer scan interval than whenpredicting TP3 data from TP1 and TP2 data which were separated by ashorter scan interval In other words because MRI volume measuresare inherently noisy coupled with the fact that any physiologicalchanges during abstinence from alcohol are gradual processes thelonger the interval between the two measurements that are used toestimate k themore accurate k is for predicting volume changes If theinterval between TP measures used to estimate k is not long enoughthe performance of our formula is only somewhat better than MI asdemonstrated by the deviations of both methods for the determina-tion of TP3 volumes The MI results are insensitive to TP intervals (iesimilar error magnitudes for predicting TP1 and TP3) as the MIapproach is based only on the respective TPs group data

We expect that a similar trajectory of brain tissue volume changesmay be apparent in those who remain abstinent from substance(s)other than alcohol This is because during abstinence from substancespromotion of biologicalmorphometric homeostasis may be driven bysimilar basic mechanisms much more related to factors mediatingplasticity than to the nature of the abused substance per se Suchfactors and mechanisms of brain regeneration in alcoholism havebeen described and are thought to mimic general mechanismsinvolved in brain growth and plasticity (Crews and Nixon 2009)Brain tissue recovery depends on plastic adaptations which are likelymediated by a complex interplay among the individualsrsquo geneticepigenetic factors chronicity and magnitude of substance use andvarious environmental circumstances including general health anddisposition Further research in quantitative neuroimaging of absti-nent individuals with AUD and SUD is required to confirm thissupposition It is encouraging that the trajectory of longitudinalvolume loss in dementia appears also well represented by ourformula Together these data sets suggest that our formula describesboth brain growth and shrinkage well Furthermore it is of note thatMRI detected brain tissue volume changes with normal human agingdevelopment has been described to follow also a non-linear course(Bartzokis et al 2001 Ge et al 2002 Jernigan and Gamst 2005Lenroot et al 2007) as has myelination in several brain regions(Benes et al 1994 Bartzokis et al 2010)

52 Potential applications

The proposed formula has several potential clinical and researchapplications For instance for effective treatment and monitoring ofAUD and SUD patients it would be highly informative andmotivational to have a model that fairly reliably charts the courseand level of volume recovery over time Also these disorders arecharacterized by a chronically relapsingremitting course overlifetime (Baler and Volkow 2006) and relapse in AUD is associatedwith further brain tissue volume loss (Pfefferbaum et al 1995)However the degree to which the severity of the relapse is related tothe amount of volume lost is unclear (Gazdzinski et al 2005a) Theproposed formula may assist in the prediction of the amount of braintissue volume lost by an individual due to relapse by comparing thevolume of tissue measured at a given time during relapse to itsvolume predicted with the formula for that same time whichrepresents the volume had abstinence been sustained This will be

useful in educating recovering alcohol dependent individuals aboutthe potential neurobiological benefits of abstinence ultimatelyincreasing their motivation to stay abstinent The formula could alsobe useful in determining regional variability in the magnitude ofchange associated with abstinence or relapse as suggested by theindividually varying recovery rates for GM shown in Fig 2 Theapplication of our formula to longitudinal MRI volumetric data ofdementia patients over two years (see above) suggests that braintissue loss in dementia follows a trajectory reverse to the tissue gainobserved during alcohol abstinence Thus the proposed formula mayalso prove useful for estimating missing values in longitudinal studiesof dementia and mild cognitive impairment where brain volume losswith time is widely and promisingly used as a marker of diseaseprogression in clinical trials but where missing data is fairly commonand impeding trial data analyses

53 Our formula versus multiple imputations

As demonstrated this formula fairly accurately calculates missingdata points in longitudinal volumetric studies of brain tissue volumerecovery in individuals abstinent from alcohol (and hypotheticallyother substances) The conventional statistical imputation methodsrely solely on the generalized behavior of a group in the estimation ofindividual missing data for cross-sectionallongitudinal samples (eg(Schafer 1997)) with the goal to draw accurate inferences from andabout population quantities not to predict accurately individualmissing values Thus a major drawback of MI or similar modelingapproaches is that individual biological differences and other within-subject factors that may affect volumetric changes are obscured likelycontributing to higher estimation errors Furthermore conventionalmodeling methods cannot be used to predict brain volume changesbeyond the time frame of the study Our formula incorporates withinthe recovery rate factor k the biological and other characteristics ofthe individual that influence the recovery process and allow to predictfairly well not only the individuals missing data in a longitudinal dataset but also the brain volume trajectory beyond the duration of thelongitudinal study

54 Limitations

Limitations of this report are a relatively small sample size and acohort composed of predominantly male alcohol-dependent individ-uals Thus the study should be considered more of a proof of conceptSecond the demonstration of the goodness of fit with the proposedformula is highly dependent on the quality of theMRdata and its tissuesegmentation For instance poor contrast-to-noise or signal-to-noiseand artifacts such as motion can greatly affect image segmentationwhich will in turn affect the goodness of the fit of the formula Alsowith poor segmentation methods especially where the segmentationis not consistent across time points the formulawill not give a good fitFurthermore it is possible that an individual may experience erraticbrain volume recovery due to changes in any of the factors thatinfluence the recovery process and therefore ki In such cases theformula will not be accurate as it assumes continuity over theprediction interval Lastly we did not test the proposed formula onan independent sample of alcohol dependent individuals Ourpromising preliminary results on brain tissue loss in dementia patientshowever support the assertion that the formula is applicable also toother cohorts

In conclusion we have discussed a mathematical formula thatfairly accurately predicts the recovery of brain tissue volume inindividual long-term abstinent alcoholics The formula may beapplicable to other substances of abuse and to volumetric brainchanges in dementia Therefore we see important utilities for thesevolume estimations in clinical trials using repeated neuroimagingvolumetrics as outcome measures (whether to observe volume

0 150 300

120

160

200

240

Days of Abstinence

Bra

in T

issu

e V

olum

e (m

l)

0 150 300

120

160

200

240

Days of Abstinence

Bra

in T

issu

e V

olum

e (m

l)

Fig 2 Plots of frontal parietal and temporal graymatter volumes against days of abstinence for 8 representative participants The curves represent our formulas trajectory of volumechange with time using TP1 and TP2 data as input The circular star and triangular marks represent the observed data for frontal parietal and temporal gray matter respectively

202 A Mon et al Psychiatry Research Neuroimaging 194 (2011) 198ndash204

from alcohol and does not rely on group data in theway that statisticalmethods such as MI do Since it is unclear to what extent agebiological differences genetic factors and other unknown factorscontribute to recovery rates basing our predictions on correlatedvolume measures at two time points gives us some protectionimmunity against unrealistic estimates The individually varyingrecovery rates demonstrated in Fig 2 adversely affect the accuracyof common imputation methods that are based on group datacharacteristics The larger deviations of the measured data from thatcalculated with the common MI approach versus data estimated byour formula support this assertion

51 Non-linear tissue volume increases in abstinent substance users

Simple linear trajectories were used previously to estimate braintissue recovery rates in abstinent alcoholics (Pfefferbaum et al 1995Gazdzinski et al 2005a) However linear recovery rates contradictresearch observations that brain volume gains decrease with duration

Table 4Paired t-tests between TP1 and TP2 data

TP2 volume versus TP1 volume t statistic P value (2-tailed)

fGM (pair 1) TP2 measuredndashTP1 measured 335 0004(pair 2) TP2 measuredndashTP1 predicted 378 0002fWM (pair 1) TP2 measuredndashTP1 measured 525 b0001(pair 2) TP2 measuredndashTP1 predicted 311 0007pGM (pair 1) TP2 measuredndashTP1 measured 384 0002(pair 2) TP2 measuredndashTP1 predicted 184 0086pWM (pair 1) TP2 measuredndashTP1 measured 105 0310(pair 2) TP2 measuredndashTP1 predicted 091 0380tGM (pair 1) TP2 measuredndashTP1 measured 153 0150(pair 2) TP2 measuredndashTP1 predicted 267 0032tWM (pair 1) TP2 measuredndashTP1 measured 340 0004(pair 2) TP2 measuredndashTP1 predicted 056 0580

of abstinence and the goodness of fit with our proposed formulaBased on longitudinal MRI volume data over seven months ofabstinence from alcohol we previously suggested that brain tissuevolume gains over that time period may be exponential (Gazdzinskiet al 2005a) However for the recovery process to be exponential therecovery rate at any time has to be directly proportional to theavailable brain tissue volume at that time (ie the smaller theavailable volume the slower the rate of recovery and vice versa)mdashthisis contrary to observations Therefore linear or exponential functionsare not expected to describe brain volume recovery processesappropriately as is indeed observed in our described analyses Onthe other hand our formula better describes brain volume trajectoriesduring short and long term abstinence because its derivation wasbased directly on the observations that cross-sectionally individualswith smaller tissue volumes at the inception of abstinence recovervolume faster than those with larger baseline volumes and thatlongitudinally short-term recovery rates are greater than long-termrecovery rates

Table 5Paired t-tests between TP3 and TP2 data

TP2 volume verse TP3 volume t statistic P value (2-tailed)

fGM (pair 1) TP3 measuredndashTP2 measured 320 0006(pair 2) TP3 predictedndashTP2 measured 273 0015fWM (pair 1) TP3 measuredndashTP2 measured 242 0029(pair 2) TP3 predictedndashTP2 measured 432 0001pGM (pair 1) TP3 measuredndashTP2 measured 214 0049(pair 2) TP3 predictedndashTP2 measured 377 0002pWM (pair 1) TP3 measuredndashTP2 measured 140 0183(pair 2) TP3 predictedndashTP2 measured 144 0169tGM (pair 1) TP3 measuredndashTP2 measured 273 0016(pair 2) TP3 predictedndashTP2 measured 227 0039tWM (pair 1) TP3 measuredndashTP2 measured 090 0382(pair 2) TP3 predictedndashTP2 measured 340 0004

203A Mon et al Psychiatry Research Neuroimaging 194 (2011) 198ndash204

We also tested the formula on lobar volume decreases inindividuals with dementia who had four MRI scans over two years(baseline six months 12 months two years) When using the twoinitial measurements to calculate the values of C and k in the formulathe deviations of our estimates from the measured data at 12 monthsand two years were less than 2 and similar for both TPs It appearsimportant however that the initial time interval is long enough to fitvolume change reliably (ie volume change should be large comparedto the measurement error) A case in point is that in our abstinentcohort of alcohol dependent individuals estimates from the formulawere much better when predicting TP1 data from TP2 and TP3 dataThe input data were separated by a longer scan interval than whenpredicting TP3 data from TP1 and TP2 data which were separated by ashorter scan interval In other words because MRI volume measuresare inherently noisy coupled with the fact that any physiologicalchanges during abstinence from alcohol are gradual processes thelonger the interval between the two measurements that are used toestimate k themore accurate k is for predicting volume changes If theinterval between TP measures used to estimate k is not long enoughthe performance of our formula is only somewhat better than MI asdemonstrated by the deviations of both methods for the determina-tion of TP3 volumes The MI results are insensitive to TP intervals (iesimilar error magnitudes for predicting TP1 and TP3) as the MIapproach is based only on the respective TPs group data

We expect that a similar trajectory of brain tissue volume changesmay be apparent in those who remain abstinent from substance(s)other than alcohol This is because during abstinence from substancespromotion of biologicalmorphometric homeostasis may be driven bysimilar basic mechanisms much more related to factors mediatingplasticity than to the nature of the abused substance per se Suchfactors and mechanisms of brain regeneration in alcoholism havebeen described and are thought to mimic general mechanismsinvolved in brain growth and plasticity (Crews and Nixon 2009)Brain tissue recovery depends on plastic adaptations which are likelymediated by a complex interplay among the individualsrsquo geneticepigenetic factors chronicity and magnitude of substance use andvarious environmental circumstances including general health anddisposition Further research in quantitative neuroimaging of absti-nent individuals with AUD and SUD is required to confirm thissupposition It is encouraging that the trajectory of longitudinalvolume loss in dementia appears also well represented by ourformula Together these data sets suggest that our formula describesboth brain growth and shrinkage well Furthermore it is of note thatMRI detected brain tissue volume changes with normal human agingdevelopment has been described to follow also a non-linear course(Bartzokis et al 2001 Ge et al 2002 Jernigan and Gamst 2005Lenroot et al 2007) as has myelination in several brain regions(Benes et al 1994 Bartzokis et al 2010)

52 Potential applications

The proposed formula has several potential clinical and researchapplications For instance for effective treatment and monitoring ofAUD and SUD patients it would be highly informative andmotivational to have a model that fairly reliably charts the courseand level of volume recovery over time Also these disorders arecharacterized by a chronically relapsingremitting course overlifetime (Baler and Volkow 2006) and relapse in AUD is associatedwith further brain tissue volume loss (Pfefferbaum et al 1995)However the degree to which the severity of the relapse is related tothe amount of volume lost is unclear (Gazdzinski et al 2005a) Theproposed formula may assist in the prediction of the amount of braintissue volume lost by an individual due to relapse by comparing thevolume of tissue measured at a given time during relapse to itsvolume predicted with the formula for that same time whichrepresents the volume had abstinence been sustained This will be

useful in educating recovering alcohol dependent individuals aboutthe potential neurobiological benefits of abstinence ultimatelyincreasing their motivation to stay abstinent The formula could alsobe useful in determining regional variability in the magnitude ofchange associated with abstinence or relapse as suggested by theindividually varying recovery rates for GM shown in Fig 2 Theapplication of our formula to longitudinal MRI volumetric data ofdementia patients over two years (see above) suggests that braintissue loss in dementia follows a trajectory reverse to the tissue gainobserved during alcohol abstinence Thus the proposed formula mayalso prove useful for estimating missing values in longitudinal studiesof dementia and mild cognitive impairment where brain volume losswith time is widely and promisingly used as a marker of diseaseprogression in clinical trials but where missing data is fairly commonand impeding trial data analyses

53 Our formula versus multiple imputations

As demonstrated this formula fairly accurately calculates missingdata points in longitudinal volumetric studies of brain tissue volumerecovery in individuals abstinent from alcohol (and hypotheticallyother substances) The conventional statistical imputation methodsrely solely on the generalized behavior of a group in the estimation ofindividual missing data for cross-sectionallongitudinal samples (eg(Schafer 1997)) with the goal to draw accurate inferences from andabout population quantities not to predict accurately individualmissing values Thus a major drawback of MI or similar modelingapproaches is that individual biological differences and other within-subject factors that may affect volumetric changes are obscured likelycontributing to higher estimation errors Furthermore conventionalmodeling methods cannot be used to predict brain volume changesbeyond the time frame of the study Our formula incorporates withinthe recovery rate factor k the biological and other characteristics ofthe individual that influence the recovery process and allow to predictfairly well not only the individuals missing data in a longitudinal dataset but also the brain volume trajectory beyond the duration of thelongitudinal study

54 Limitations

Limitations of this report are a relatively small sample size and acohort composed of predominantly male alcohol-dependent individ-uals Thus the study should be considered more of a proof of conceptSecond the demonstration of the goodness of fit with the proposedformula is highly dependent on the quality of theMRdata and its tissuesegmentation For instance poor contrast-to-noise or signal-to-noiseand artifacts such as motion can greatly affect image segmentationwhich will in turn affect the goodness of the fit of the formula Alsowith poor segmentation methods especially where the segmentationis not consistent across time points the formulawill not give a good fitFurthermore it is possible that an individual may experience erraticbrain volume recovery due to changes in any of the factors thatinfluence the recovery process and therefore ki In such cases theformula will not be accurate as it assumes continuity over theprediction interval Lastly we did not test the proposed formula onan independent sample of alcohol dependent individuals Ourpromising preliminary results on brain tissue loss in dementia patientshowever support the assertion that the formula is applicable also toother cohorts

In conclusion we have discussed a mathematical formula thatfairly accurately predicts the recovery of brain tissue volume inindividual long-term abstinent alcoholics The formula may beapplicable to other substances of abuse and to volumetric brainchanges in dementia Therefore we see important utilities for thesevolume estimations in clinical trials using repeated neuroimagingvolumetrics as outcome measures (whether to observe volume

203A Mon et al Psychiatry Research Neuroimaging 194 (2011) 198ndash204

We also tested the formula on lobar volume decreases inindividuals with dementia who had four MRI scans over two years(baseline six months 12 months two years) When using the twoinitial measurements to calculate the values of C and k in the formulathe deviations of our estimates from the measured data at 12 monthsand two years were less than 2 and similar for both TPs It appearsimportant however that the initial time interval is long enough to fitvolume change reliably (ie volume change should be large comparedto the measurement error) A case in point is that in our abstinentcohort of alcohol dependent individuals estimates from the formulawere much better when predicting TP1 data from TP2 and TP3 dataThe input data were separated by a longer scan interval than whenpredicting TP3 data from TP1 and TP2 data which were separated by ashorter scan interval In other words because MRI volume measuresare inherently noisy coupled with the fact that any physiologicalchanges during abstinence from alcohol are gradual processes thelonger the interval between the two measurements that are used toestimate k themore accurate k is for predicting volume changes If theinterval between TP measures used to estimate k is not long enoughthe performance of our formula is only somewhat better than MI asdemonstrated by the deviations of both methods for the determina-tion of TP3 volumes The MI results are insensitive to TP intervals (iesimilar error magnitudes for predicting TP1 and TP3) as the MIapproach is based only on the respective TPs group data

We expect that a similar trajectory of brain tissue volume changesmay be apparent in those who remain abstinent from substance(s)other than alcohol This is because during abstinence from substancespromotion of biologicalmorphometric homeostasis may be driven bysimilar basic mechanisms much more related to factors mediatingplasticity than to the nature of the abused substance per se Suchfactors and mechanisms of brain regeneration in alcoholism havebeen described and are thought to mimic general mechanismsinvolved in brain growth and plasticity (Crews and Nixon 2009)Brain tissue recovery depends on plastic adaptations which are likelymediated by a complex interplay among the individualsrsquo geneticepigenetic factors chronicity and magnitude of substance use andvarious environmental circumstances including general health anddisposition Further research in quantitative neuroimaging of absti-nent individuals with AUD and SUD is required to confirm thissupposition It is encouraging that the trajectory of longitudinalvolume loss in dementia appears also well represented by ourformula Together these data sets suggest that our formula describesboth brain growth and shrinkage well Furthermore it is of note thatMRI detected brain tissue volume changes with normal human agingdevelopment has been described to follow also a non-linear course(Bartzokis et al 2001 Ge et al 2002 Jernigan and Gamst 2005Lenroot et al 2007) as has myelination in several brain regions(Benes et al 1994 Bartzokis et al 2010)

52 Potential applications

The proposed formula has several potential clinical and researchapplications For instance for effective treatment and monitoring ofAUD and SUD patients it would be highly informative andmotivational to have a model that fairly reliably charts the courseand level of volume recovery over time Also these disorders arecharacterized by a chronically relapsingremitting course overlifetime (Baler and Volkow 2006) and relapse in AUD is associatedwith further brain tissue volume loss (Pfefferbaum et al 1995)However the degree to which the severity of the relapse is related tothe amount of volume lost is unclear (Gazdzinski et al 2005a) Theproposed formula may assist in the prediction of the amount of braintissue volume lost by an individual due to relapse by comparing thevolume of tissue measured at a given time during relapse to itsvolume predicted with the formula for that same time whichrepresents the volume had abstinence been sustained This will be

useful in educating recovering alcohol dependent individuals aboutthe potential neurobiological benefits of abstinence ultimatelyincreasing their motivation to stay abstinent The formula could alsobe useful in determining regional variability in the magnitude ofchange associated with abstinence or relapse as suggested by theindividually varying recovery rates for GM shown in Fig 2 Theapplication of our formula to longitudinal MRI volumetric data ofdementia patients over two years (see above) suggests that braintissue loss in dementia follows a trajectory reverse to the tissue gainobserved during alcohol abstinence Thus the proposed formula mayalso prove useful for estimating missing values in longitudinal studiesof dementia and mild cognitive impairment where brain volume losswith time is widely and promisingly used as a marker of diseaseprogression in clinical trials but where missing data is fairly commonand impeding trial data analyses

53 Our formula versus multiple imputations

As demonstrated this formula fairly accurately calculates missingdata points in longitudinal volumetric studies of brain tissue volumerecovery in individuals abstinent from alcohol (and hypotheticallyother substances) The conventional statistical imputation methodsrely solely on the generalized behavior of a group in the estimation ofindividual missing data for cross-sectionallongitudinal samples (eg(Schafer 1997)) with the goal to draw accurate inferences from andabout population quantities not to predict accurately individualmissing values Thus a major drawback of MI or similar modelingapproaches is that individual biological differences and other within-subject factors that may affect volumetric changes are obscured likelycontributing to higher estimation errors Furthermore conventionalmodeling methods cannot be used to predict brain volume changesbeyond the time frame of the study Our formula incorporates withinthe recovery rate factor k the biological and other characteristics ofthe individual that influence the recovery process and allow to predictfairly well not only the individuals missing data in a longitudinal dataset but also the brain volume trajectory beyond the duration of thelongitudinal study

54 Limitations

Limitations of this report are a relatively small sample size and acohort composed of predominantly male alcohol-dependent individ-uals Thus the study should be considered more of a proof of conceptSecond the demonstration of the goodness of fit with the proposedformula is highly dependent on the quality of theMRdata and its tissuesegmentation For instance poor contrast-to-noise or signal-to-noiseand artifacts such as motion can greatly affect image segmentationwhich will in turn affect the goodness of the fit of the formula Alsowith poor segmentation methods especially where the segmentationis not consistent across time points the formulawill not give a good fitFurthermore it is possible that an individual may experience erraticbrain volume recovery due to changes in any of the factors thatinfluence the recovery process and therefore ki In such cases theformula will not be accurate as it assumes continuity over theprediction interval Lastly we did not test the proposed formula onan independent sample of alcohol dependent individuals Ourpromising preliminary results on brain tissue loss in dementia patientshowever support the assertion that the formula is applicable also toother cohorts

In conclusion we have discussed a mathematical formula thatfairly accurately predicts the recovery of brain tissue volume inindividual long-term abstinent alcoholics The formula may beapplicable to other substances of abuse and to volumetric brainchanges in dementia Therefore we see important utilities for thesevolume estimations in clinical trials using repeated neuroimagingvolumetrics as outcome measures (whether to observe volume

204 A Mon et al Psychiatry Research Neuroimaging 194 (2011) 198ndash204

increases or decreases) and in answering research questions aboutbrain tissue growth plasticity and recovery after discontinuation of achronic and damaging insult

Acknowledgements

We thank Drs Valerie Cardenas Karl Young Norbert Schuff DuyguTosun Susanna Fryer and Jong-Min Lee for their various intellectualcontributions in the preparation of this manuscript We also thank theSan Francisco VA Medical Center Research Service for logisticalsupport This work was supported by R01 AA10788 (DJM) and R21DA025202 (DJM)

References

Adalsteinsson E Spielman DM 1999 Spatially resolved two-dimensional spectroscopyMagnetic Resonance in Medicine 41 8ndash12

Baler RD Volkow ND 2006 Drug addiction the neurobiology of disrupted self-control Trends in Molecular Medicine 12 559ndash566

Bartzokis G Beckson M Lu PH Nuechterlein KH Edwards N Mintz J 2001 Age-related changes in frontal and temporal lobe volumes in men a magneticresonance imaging study Archives of General Psychiatry 58 461ndash465

Bartzokis G Lu PH Tingus K Mendez MF Richard A Peters DG Oluwadara BBarrall KA Finn JP Villablanca P Thompson PM Mintz J 2010 Lifespantrajectory of myelin integrity and maximum motor speed Neurobiology of Aging31 (9) 1554ndash1562

Benes FM Turtle M Khan Y Farol P 1994 Myelination of a key relay zone in thehippocampal formation occurs in the human brain during childhood adolescenceand adulthood Archives of General Psychiatry 51 477ndash484

Brody AL Mandelkern MA Jarvik ME Lee GS Smith EC Huang JC Bota RGBartzokis G London ED 2004 Differences between smokers and nonsmokers inregional gray matter volumes and densities Biological Psychiatry 55 77ndash84

Cardenas VA Studholme C Gazdzinski S Durazzo TC Meyerhoff DJ 2006Deformation based morphometry of brain changes in alcohol dependence andabstinence Neuroimage 34 879ndash887

Crews FT Nixon K 2009 Mechanisms of neurodegeneration and regeneration inalcoholism Alcohol and Alcoholism 44 115ndash127

Driscoll I Davatzikos C An Y Wu X Shen D Kraut M Resnick SM 2009Longitudinal pattern of regional brain volume change differentiates normal agingfrom MCI Neurology 72 1906ndash1913

Durazzo TC Meyerhoff DJ 2007 Neurobiological and neurocognitive effects ofchronic cigarette smoking and alcoholism Frontiers in Bioscience 12 4079ndash4100

Gazdzinski S Durazzo TC Meyerhoff DJ 2005a Temporal dynamics and determinants ofwhole brain tissue volume changes during recovery from alcohol dependence Drug andAlcohol Dependence 78 263ndash273

Gazdzinski S Durazzo TC Studholme C Song E Banys P Meyerhoff DJ 2005bQuantitative brain MRI in alcohol dependence preliminary evidence for effects ofconcurrent chronic cigarette smoking on regional brain volumes AlcoholismClinical and Experimental Research 29 1484ndash1495

Ge Y Grossman RI Babb JS Rabin ML Mannon LJ Kolson DL 2002 Age-relatedtotal gray matter and white matter changes in normal adult brain Part I volumetricMR imaging analysis AJNR American Journal of Neuroradiology 23 1327ndash1333

Jernigan TL Gamst AC 2005 Changes in volume with agemdashconsistency andinterpretation of observed effects Neurobiology of Aging 26 1271ndash1274discussion 1275ndash1278

Jernigan TL Butters N DiTraglia G Schafer K Smith T Irwin M Grant I SchuckitM Cermak LS 1991 Reduced cerebral grey matter observed in alcoholics usingmagnetic resonance imaging Alcoholism Clinical and Experimental Research 15418ndash427

Lenroot RK Gogtay N Greenstein DK Wells EM Wallace GL Clasen LS et al2007 Sexual dimorphism of brain developmental trajectories during childhoodand adolescence NeuroImage 36 1065ndash1073

Liu X Matochik JA Cadet JL London ED 1998 Smaller volume of prefrontal lobe inpolysubstance abusers a magnetic resonance imaging study Neuropsychophar-macology 18 243ndash252

Noble SM Hollingworth W Tilling K in press Missing data in trial-based cost-effectiveness analysis the current state of play Health Economics electronicpublication 15 December doi101002hec1693

ONeill J Cardenas VA Meyerhoff DJ 2001 Separate and interactive effects ofcocaine and alcohol dependence on brain structures and metabolites quantitativeMRI and proton MR spectroscopic imaging Addiction Biology 6 347ndash361

Pfefferbaum A Sullivan EV Mathalon DH Shear PK Rosenbloom MJ Lim KO1995 Longitudinal changes in magnetic resonance imaging brain volumes inabstinent and relapsed alcoholics Alcoholism Clinical and Experimental Research19 1177ndash1191

Pfefferbaum A Lim KO Desmond J Sullivan EV 1996 Thinning of the corpuscallosum in older alcoholic men an MRI study Alcoholism Clinical andExperimental Research 20 752ndash757

Resnick SM Goldszal AF Davatzikos C Golski S Kraut MA Metter EJ Bryan RNZonderman AB 2000 One-year age changes in MRI brain volumes in older adultsCerebral Cortex 10 464ndash472

Resnick SM Pham DL Kraut MA Zonderman AB Davatzikos C 2003Longitudinal magnetic resonance imaging studies of older adults a shrinkingbrain Journal of Neuroscience Research 23 3295ndash3301

Scahill RI Frost C Jenkins R Whitwell JL Rossor MN Fox NC 2003 Alongitudinal study of brain volume changes in normal aging using serial registeredmagnetic resonance imaging Archives of Neurology 60 989ndash994

Schafer JL 1997 Analysis of Incomplete Multivariate Data Monographs on Statisticsand Applied Probability 72 Chapman amp HallCRC London

Schafer JL 1999 Multiple imputation a primer Statistical Methods in MedicalResearch 8 3ndash15

Schroth G Naegele T Klose U Mann K Petersen D 1988 Reversible brainshrinkage in abstinent alcoholics measured by MRI Neuroradiology 30385ndash389

Sterne JA White IR Carlin JB Spratt M Royston P Kenward MG Wood AMCarpenter JR 2009 Multiple imputation for missing data in epidemiological andclinical research potential and pitfalls BMJ 338 b2393

Sullivan E Rosenbloom MJ Deshmukh A Desmond JE Pfefferbaum A 1995Alcohol and the cerebellum effects on balance coordination and cognitionAlcohol Health and Research World 19 138ndash141

Van Leemput K Maes F Vandermeulen D Suetens P 1999 Automated model-based tissue classification of MR images of the brain IEEE Transactions on MedicalImaging 18 897ndash908

Yeh PH Gazdzinski S Durazzo TC Sjostrand K Meyerhoff DJ 2007 Hierarchicallinear modeling (HLM) of longitudinal brain structural and cognitive changes inalcohol-dependent individuals during sobriety Drug and Alcohol Dependence 91195ndash204

Zipursky RB Lim KC Pfefferbaum A 1989 MRI study of brain changes with short-term abstinence from alcohol Alcoholism Clinical and Experimental Research 13664ndash666