f~s -'/' .

.

Undersea Biomedical Research . Vol . 15, No . 4 , I9A8

Use of the maximum likelihood method in theanalysis of chamber air dives

P. TIKl1ISIS, R .Y. NISHI, and P.K. Wk:A1'HF.RSaIY

DrJrnte and f'ivrl fn.trirulr ult.nwrornmrnrul Mrduine, lldi Shrppard Aie . W., 1'.11 . Nor 2DW, je W, Onrario .

<"anada M+M dB91P.T. . il YN .6 and ILS Nuvul Submartnr Mrdirul Hr .trnrch Laborarory, C)roron, ('7 06349, and

Naial Mrdiral Rrxrurr h hiulfutr, llrrhrrda . Ail) 20814 f 1'•K . W 1

"l'ikuisis P, Nishi RY, Weatheryby PK . Use of the maximurn Iikehhqud methrxi in the analysis

of chamber air dives . l)ndersea iiiomed Res 1988 ; 15(4) :301-,I11 .41'he method of maximum

likelihaxi was used to evaluate the risk of dccontpression sickness (iX,'S) for selected chambe rmodels for predicting UC"5 were opùmiteJ

air dives . The parameters of two mathematica l

until the best agreement (as measured by maximum likelncood) corresponding ►o the observed

DCS incidents from a series of dives was attained . The decompression data used consisted of

80(1 man-dives with 21 incidents of DCS and Cr occurrences of marginal symptoms . The firtit

model investigated was based on a nonlinear gas exchange in a aerier arrangement of four

compariments . The second model was based on a monoexponential gas exchange in a parallel

arrangement of two compartmentsjhc overall statistical success in describing the t3(X) man-

dives was quite similar for the two model•, Predictions of safety for dives not part of the

original data differed for the models uue to differences in gas kinetics . For short, no-

decompresxion dives, the series arrangement of compartments predicted a lower incidence of

IX'S . These predictions were more consistent with the outcome of subiequent testing than

were predictions of the parallel compartment model . Predictions of the series a rrangement

model were also similar to those of it single-companment, two-exponentral model that was

evaluated with over 17i11) man-dives by the U .S . Navy .

decompression sicknessdiv emaximum likelihood

modelstablesprobability

0

The variability in the occurrence of decompression sickness ([X 5) makes the

prediction of DCS difficult for any given dive profile . Conventional methods for

establishing the risk of [)(:S for a particular dive require a great number of man-

dives . For example, if in 1 00 man-dives for a particular trial, 5 incidents of DCS

occurred (5% occurrence), then the 95% confidence interval limits for this occurrence

indicate that the probability of DCS can be between 1 . 64 and 11 .28% (1) . To "tighten"

the prediction of the incidence of bCâ for this particular dive trial, many more man-

dives would be required . For example, 65 incidents of DCS Out of 1300 man-dives

(!c% occurrencer would narrow the 95% confidence interval to between 4 and 6% fo r

301

302 P. TIKUISIS, K .Y . NISF11, ANl) P .K, WhàATfIt:KSIT Y

a particular dive trial . Since most dive trials involve considerably fewcr than IIK)individuals, a melhod for combining dive trials in a .ringle analysis is required .

Weathershy et al . (2) suggested using the method of maximum likelihood (i) toevaluate the risk of I;X'S, "t"hi, method applies a predictive model for DCS to actualoutcomes from a series of dive trials, Inputs to the predictive model are a decompre .-sinn dose response function and any decompression model that can be vt .sted math-ematict+liy . The decompression close response function is a measure of the cumulativerisk of DCS for a dive, The parameters of the predictive model me iulJurted until thebest agreement or maximum likelihood corresponding to the DCS event% ofpast trials

is obtained . Once the parameters of the predictive model have been uptimi/ed usingany number of dives from different suurccs, the model can he applied to predict theprobability of DCS for any new (tested and un(tatC ►1) dive profile .

In addition,,difi'erent decompression models can lie tested tv determinc which

model best fits the data . In this study, the method ►► f nt .► xintrrm likelihood is used t ►►compare the prediction of DCS between a nantint!ar series c► rrnpnrtrn ►.:nts (N1 .S(')model (4, S), featuring four con ►purtments in scrï6s, and it m ►►nuexpuncntial parallelct►mpartments (M E. 1'(") m ►►del, used by Wcuthershy el al . (6), feattuir ►g two c.om-partmcntN in ptirt ► Ilcl, Although rn .rrry ►► thcr rno ► le'w involving rn ► ,rc: than twu con) .partments in parallel exist (4), they ►►ff4r little of' r„ ► statistical ,r ► ivtu ► tu g 4 ovV1 filetw ►►-cc►mpartment Mlïl`(' rnudvl in tl ► e prcticnt trnr► lytiiti ( tr), but may he. iustific ► I bylarger data sets (7) . The methu ►t of maximum likelihood has nut been previurrrlyapplied to compartments in serie.s such as the NI .S(' model . The derornpressiunmodel that gives fhe hrrrCrst rnuximurn likelihood value is defined as the e ►n4 that hestfits the data . For specific classes of models, f►► rrm ► I statistical tests allow rigur ► ru .,comparison of model p,'edictic ►n, (2, 1), A desirable fetrture of the method o[ maximumlikelihood is that any set ut'dive data can he used for the comparison ,rnwng rn ►►del . .For inutt,nce, the MEPt:' model can he tested against dive trials that fi ► llifwed thedecompression procedures governed by the gas kinetics of' the Nl .ti(' model, andvice verra .

In summary, a probabilistic model uptimi>ed by maximum likelihood can he usedto test decompression procedures and to predict ► he probability of I)C .'ti . It ►:.un heused as an optimiting tool for determining the pi*! ►°t►meters of decompression mudel,,and as an evaluative tcn►1, but the prediction must he tested and the actual incidencemust be established by experiment . This study examines the use of the method of'maximum likelihood as applied to the NI .tiCand Mt:f'(' models in optimi/ing modelparameters, evaluating dive profiles, and comparing the prediction rit' DCS for pt ► r-ticular dive tables ,

I .IKI:I.IN(X)I) CtZI'l'F;filt)N

The variability in (X"S can be described in terms of probabilities . The probabilityof IX'S is a function of the dive profile and the decc ►mpre!rgi ►►n model te .r-ted, i .e . ,

N,K , - f (time, depth, madel), (1 )

where f is the deccimpression dose response function . It follows that the probabilityof no DCS is

USE <)F'rHE MAXIMUM t .IKk;LIHOC)t) Mt:i Ht)1) 30 3

I - /' r. S . (2 )

if Y is the actual outwtr ,► c of fX.'S for it dive, then the predicted probability of theactual c► utcc►me or t► b%,.rvt+tirm i s

A •ulu)n1a , (/~IK 0 ► ( I - P1X S) I I , (3 )

where Y - t) if UCS does not occur, and Y+o I if C)C'ti does occur . For those divesthat defy a definitive diagnosis (sometimes called marginal tiymptonyti or nigfZleti) anassignment of Y - 0 .5 can h e made, In other analyses such it choice has not beenshown to affect the ultimrrte conclusions of the analysis (2 . 8) .

Assuming that the outcome t ►f euch dive is independent, the total predicted pruh-ahility uf aFl the known outcomes is giver, by the likelihood functit ► rt ,

, „ 11 ,,,,n v ,!, ftIlf' (4)whcrc n is the total number or man-dives, I . is utiu,tlly it very Small numhcr, butgreater than zero, because it is th4 ProduGt of rnuny nunihcrs less than I, It iscu.rtomary to use the naturttl h ►garilhm of I ., or 1j, (log likelillood) ,

1 .1, - (5)Y ( rt l's,,,~,,,„,. .

Since 1 . is less thz ► n I, 13, is negative . 'l'hi„. rni►ximunt likelihuud value, which definetithe best lit hetw4en the mutlcl and da1u, is givcn by the smallest ;rl ► salutc value of 14.(or smallest negative valuc) as shown in Fig. 1, '1 tic modified M .u-Nuurdt ulgt►rithm(9) was used to obtain this value by v ;nyini; the n anrantetcrti of thc f► rrtJi4tivc mati e ltint il the bctit ;lgrcllncnt with the data was fi ►txl .

_100

-t100 .0 O,R 1.0 1 .5 2 .0

ittee Coefficient, 104 C

hi y . I . Log maximum tik e tthoixt, C.F., ptattnd t4geinwt the riak c«CiNwtenr, l', for the Nt .SC mo fel .SoliJ ufrrlos indicatc the 951 confidence litnit+ hseed on the LiketihoMx1 kuhri1'eht t3),

3()4 P. TIKUISIS, R .Y . NI5H1, AND P .K . WFATH<~(tSB Y

To use the method of maximum likelihood, the decompression dose responsefunction or /',x•s (see Eq . 1) must be defined . The function that was adopted for thisstudy is known as the "risk" function (z, b, 10) ,

rrws - I - exp ( - jrdf), (6)

where r is the measure of risk and t is time. If r is lar ge, then over a period of timethe probability of DCS approaches I . For each decompression model examined, r isdefined empirically and its value is dependent on the actual decompresvion profile(see Decompression Models) . Generally, r is non-zcro when a state of inert gassupcrsaturation occurs . L;epending on the degree and length of this state, N,x s willincrease accordingly . The calculation of P,,(w is continued until r falls below /eru, atwhich p,)int the value of /',ws represents the predictcd cumulative probability of 1)(vSfor the dive .

For models that can he cxpressed as simplified or more general versions of othermodels, a formal L .ikelihood Ratio Test can establish whether a model is a significantimprovement over another in .cscribing a data set (2, 3) . For example, to justifyincreasing the generality of it model by estimating one, two, three, etc ., additicmal

parameters, the l.L must increase by at least 1 .92, 30), 3 .91 units, etc ., respectively .

L)h;CüMt"REtiS1ON MOI)F;L.S

1 . Nonlinear serfes compartments mode l

The NL .St' mcKicl foi air diving (4, S) consists of four compartments in seriesrepresenting tissues having different rates of gas exehange, The rate crf change ot' gaspressure in the four compartments is described by the following set of 4 nonlinear

differential e(luations :

df',ldt - A((G1 + l'o + PJ(i'„ - I',) - (tl + i', + f' ;.)(P, -- P M, (7)

d/'zldr - A((H + /', + Pz)(l', - /',) "- ( B tl's 4 I'J(P: - l',)1 . (8)

df'Jdr - AI(1! + P, + /',)(N2 - t',) - (B + !', + l'~1tN, - f',)1, (9)

dPJdt - A((ll ~ P, + P4 ) ( Ni - l',). (lU)

where P, is the total gas pressure in comparlment i, I'„ is the current ambient pressure,and A and B are constants ((1 .(X)26 min '- A°I"A' and 8 .31 A'I'A, respectively) .

F?quations 7-I0 are those that control the uptake and elimination of gas for the originalKidd-Stubbs pneumatic analogue decompression computer model (4), the Kidd-Stubbs 1971 decompression tables ( I 1), and the current Defence and Civil Instituteof Environmental Medicine (DCIEM) 1983 decompression tables (12) . The only

differences among these 3 cases are in the safe ascent criterion for each comp.rrtnlent .The measure of risk for the present likelihood analysis is defined a s

roof, + rt + r, + r4, ( l l)

where, following the method of Weathersby et al . (b), the risk for compartment i is assumedto be

USE OF 't'HF: MAXIMUM L .IKELIF1OO[) MF?TN(3b 305

r, - ('(0 .7yP, - Pu)lP, (12)

and where C is the risk coefficient to be estimated . The risk defined by Eq. /2 isproportional to the relative supersaturation of the N2 component, hence the factor0.79 . If r, < 0, then r, is set to 0 . The value o f C is estimated by fitting the model tothe actual time-depth profile data for each dive until the maximum value of [ .l. isobtained . The m odel constants, A and B, can also be optimized using the maximumlikelihood method ; however, time constraints did not allow this .

F i gure 2 graphically demonstrates the NLSC model with C - O .O(X)154 - min ' toa single dive . This dive, to I85 fsw (5 .60 ATA) with a bottom time of 125 min, had 4divers and no incidence of t)('S. At the end of decompression ( r - 827 min), thepredicted incidence of tX'S is 5 .97 % , white r is still greater than ze ro owin g to thesupersaturation of N ; in the model compartments . After I I(x) min, r acc.ording to Eq .12, becomes zero and the final predicted incidence of DCS is 7 .04 * 1 .55% (95%confidence limit) .

2. Mono-exponential, parallel c.ornparttnentx modp l

The MF1'C' ttwtlt;l is baticit on in arrangement of single exponential compartmentsin parallcl . Wettthcrsby et al, (6) found that twra camptutmcnts were adequate to fitthe present data in their stuily . iiencc, in this study a two-compartment mono-exponential model Imodel 3 in (6)j is used . The exchange uf inert gas in each of thetwo compartments is described by the following linear diffc.rential equation :

tt

0300 600 A00 1800

Time (min )

piS . 2 . Measure of risk of DCS, r . and the probability of incidence of DCS, Pws, predicted by theNLSG model for a dive to 193 fsw for 125 min plotted as a function of time . The time-depth profile of thedive end the average gas pressure of the four cctmpwriments of the NLSC model are also shown,

306 P. TIKUISIS, R .Y . N1SH1 . ANI:) P .K . WEAfHERSB Y

dPNJdt - - (PN, -- 0.79P„)/k„ (1.1)

where P,, is the pressure of the N2 component of gas in compartment i and k, is thetime constant of the N2 uptake and elimination of compartment i .

The measure of risk is defined as

r R r,+ r 2

where

r, '0 C' ,(Ptv. w Po)/Po, (15)

and C, is the risk coefficient of compartment i . The values of C, and k, were estimated

by fitting the model to the data until the maximum value of 1,1 . was obtained .

RESULTS

The dive ► tata were obtained from the CANI)11) (Canadian Dive Data) data bank(13) and are the same data used in data set "I)" in (6) . The data used consist of 163air dive profiles in it hyperharic chamber totaling 8(Kl rnun-dives that were conductedduring I967-I968 with the Kidd-Stuhhy pneumrUie analogue decompression computerand other decr► tt ►prestiion criteria (4) . The (five ►Icplhs f►►r this data set ranged front99 to 300 fsw (3 .(1() to 9 .08 A`l'A) and the hotuum times ranged front 6 to 360 min .Th, .rc were 21 incidents of DCS and 6 occurrences of maiginal syniptorns of 1)(SIncidents of DCS were assigned in outcome ►►f Yto 1 .0 and marginal cases wereassigned an outcome of Y- 0 .5 .

Using these data, the values of LL are plotted against the risk coefficient, C, forthe NLSC model in Fig . I . The maximum value of H. ( = - 1(12 .57) was obtainedwith C = 0 .(XX)154 • min ' . This value was used to generate Fig . 2 . For the ME:NCmodel, the maximum value of lJ . -- I(N1 .63) was obtained with k, - 3 .91 min, k,- 382 min, (', = 0.(x)615 • min and C'~ - 00)126 - min '(6) . The values oflikelihood for the 2 models are close enough that the additional three estimatedparameters of the Mf:PC model would not he .justified by the Likelihood Ratio Testif it could he applied . Since the models are not suitahle for this test, then withincurrent limits of statistical theory, the retiult, can only he declared its similar . _ _

It is interesting to compare the predictions of these 2 models under differentcategories of risk of DCS. Figure 3 shows the results of the 2 models after separatingthe predictions of DCS (using F:y . b) into four categories : <2!xt, 2-5r/, 5-1(l''lr~, and> 10%r . For example, the NI,SC model predicted it L)C'S incidence of less than 211r,for 312 out of the >';(x') man-dives in the data set . Of these 312 dives, the averagepredicted incidence was 1 .471A and the average observed incidence was 1 .44''%r, . Inco ► nparison . the MEPC model predicted a DCS incidence of less than 2'%! for 23K outof the 800 man-dives, and of these the average predicted incidence was 1 .36% whilethe average observed incidence was 0 .84% . No dives were predicted to have a DCSincidence of > 10°l, using the NI.,SC model in contrast to the 15 man-dives predictedto exceed I(Ml., DCS incidence by the MEPC model . Despite these differences, thechi-square goodness-of-fit test for agreement between model prediction and actualoutcome for all 4 categories is 0 . 60 for the NLSC model and 1 .29 for the MEPCmodel , these low values indicate that both models predict outcome of DCS equallywell .

USE OF l'HN MAXIMUM LIKFt .IH(X)U METHOD 307

40

30

to

o NISC Model

0 MEPC Model

.

.-

oo 6 10 to 20

Predicted 9 DCS

Fig . 3 Avetage ub>erved in4idence of 1)('S plot (cd ag+nrrtit the averagC predirled incidence Of I)('S

for the NI .SC mtnkl ( ulo rn rir ( fr~_~) and M{iP(' model ( .tinlid rirt•1<~ .tl in four categories : <~2lr, . il~ . 5 ...

I(YT , and ~ , IOr/ . Rroi;en line shows the line of a+}Ircemcnt and vertical lines indicate the 951/( confidence

interval on the observed binary outcome .

sertesNr gas uptake and elimination in the compartments of the 2 models . Inc

Application of Theory

Once the parameters of the predic:tive model have been up6misr,ed, the mode! can

be used to predict the probability of I)('S for a series of difï'erent hut related dives .

Figure 4 shows the probability of DC:S preciicted by both the NLSC and MEPC

models for the [X 1EM no-decompression air diving limits (12) as shown in Table I .

These no-decompression limits are more conservative than those from the USN

Standard Air Decompressiun 'Fables (14, 15) (also shown in Table 1) . For depths of

30 to 40 fsw (0 .91 and 1 .21 A'l'A), which have not been tested, the predicted probability

of DCS is noticeably higher than that for deeper depths ; hence, according to this

analysis the nu-decompression limits (12) from these shallow depths entail a greater

risk of DCS .Dives deeper than 50 fsw (1 .51 ATA) have been tested according to the DCIt ;M

no-decompression air diving limits . No instances of 1)CS occurred in the 131 man-

dives considered here (16), an outcome that has 95% confidence limits of 0 to 2 .3%

DCS (I ) . In this depth range the Nt,SC model predicts a uniformly low probability

of DCS averaging 0 .2%, which is quite consistent with the outcome . This behavior

is not too surprising since the dive limits were obtained by a nunpr()habilistic modelwith the same kinetic constants as the present NLSC model (5, 12) . On the other

hand, the MEPC model predicts a logarithmically increasing probability of [)(:.S with

depth that averages 3 .1 % , or slightly outside the observed outcame . The reason for

the contrasting trend between the 2 models lies with the difference in the kinetics of

308 P TIKUISIS, R,Y . NISHI, AND P .K . WEATHERSB Y

TABLE ICOMPARISON OF NO-DF?COMPRESS ION AIR DIVIN(, i ..IMITti

Depth, fswMaximum Bottom Time, min

DCILiM* USN~30 380

40 175 2t)r)50 75 10060 50 6070 35 5080 25 4090 20 30

100 15 25110 12 20120 10130 IS

8 10140 7 10150 7

5160 6 5170 5 5180 5 S

'T'hese dive hmits have been te % ted from 50 to 1 9 0 frw at I)CIEM ,

compartmental structure of the NLS(' model leads tu a slower rate uf gas uptake inthe compartments, whereas the "fast" compartment (k, - 3 .91 min) of the MIrPC:model saturates quickly . It is this fast compartment that increases the calculatedmeasure of risk substantially more than do the compartments of the N1 .SC model .

Figure 4 also shows the predictions of model 5 in (6), a single-c ompartment, two-exponential model evaluated with over 1700 man-dives used to estimate the risk ofbends for different air dec ompression tables (15) . In the depth range of greater than50 fsw ( 1 .51 ATA), the average prediction is 1 .2% DCS which, along with the NLSCmodel, is consistent with the outcome for the present test dives .

Differences in model predictions are not as pronounced for dives with decompres-sion stops because the slower compartments predominate . Dives with decompressionstops are usually long enough for the gas pressure in the compartments of the NLSCmodel to increase the measure of risk to a degree similar to that predicted by theMEPC model . For example, of the ftUU man-dives examined earlier, the averagepredicted incidence of DCS for the NLSC model was 2 .92% and that for the MEPCmodel was 2 .97% . However, there are still some important differences between thepredictions of the 2 models for dives with decompression stops .

This is demonstrated in Fig . 5, where the probability of DCS predicted by both theNLSC and MEPC models for standard air dives to 150 fsw (4 .54 ATA) from theDCIEM 1983 decompression tables ( 12) is shown as a function of bottom time at 150fsw. The NLSC model predicts a monotonically increasing probability of DCS withincreasing bottom time . The MEPC model, on the other hand, predicts a high prob-ability of DCS for a short bottom time of 7 min, then decreasi ng probabilities until a

USE OF THE MAXIMUM LIKEC.tHOC)n METHO D

L

309

0 40 60 00 100Bottom Time (min )

Fig . 4 . l'robabihty of the incidence of IX'S plotted against depth for the 1)('II :M no-ifecumpressi,mair diving limits showing the difference between the NI .S(` modtl ( sufid line), the MI'.P(:' nux)el Ihrukerfine), and model 5 in (6) (dutted line) predictions .

minimum is reached at a bottom time of 25 min, followed by increasing probabilitiesthereafter . In all cases, the MF PC model predictions of DCS are higher than thosefor the NI .SC model . It is interesting to note that the two model predictions are inclose agreement in the mid-range of bottom time, say 25 to 55 min, which is the regionwhere data were available (in the data, dives between 145 and 155 fsw averaged 30min in bottom time) but diverge outside this range, This difference results from thedifferent gas kinetics of the 2 models discussed above . Actual testing of these profiles(17) produced I case of DCS out of 20 man-dives with 20 and 30 min bottom times(95%confidence limits of0.1 to 25% DCS) . Both NLSC and MEPC model prWictionsare consistent with that outcome .

Also shown in Fig . 5 are the predictions (15) for model 5 in (6), which are alsoconsistent with the outcome cited above (17) . These values follow a 4imilar trend tothe MEPC model prediction but with much lower values around 20 min bottom timeand progressively much higher values for bottom times beyond 35 min . These differ-ences are attributed to the different configuration (I-exponential 2-compartment vs .I-compartment 2-exponential) and data set (800 vs . > 1700 man-dives) used to estab-lish the MEPC model and model 5 in (6), respectively .

Finally, the method of maximum likelihood is used to compare the predicted riskof DCS among different decompression tables . Figure 6 shows a comparison of theprobabilities of DCS predicted by the NLSC model for standard air diving to 150 fsw(4 .54 ATA) based on the DCIEM 1983 air decompression tables (12), the Kidd-Stubbs1971 air decompression tables (11), and the USN standard air tables (14) as a functionof the bottom time . (Table 2 lists the decompression times as a function of bottom

31 0 P . TIKUISIS, R .Y . NISHI, ANC) P .K . W@ATWF.RSBY

10

8

6

MFf'C Mode l

Model 5 (Ref . G) . . . . . . . . . . .... . . . . . . . . . . . . . . .

. . . . . . . . . . . . .

N .4( ; Mode l

30 60 90 120Depth ( ( ew')

150 1() 0

Fig . S . Probability of incidence of t)('ti ttv it funcUon of hottum time for standard air 411ve.s Iri I SO Lw

front the IXI({M 198 1 lubies +howing the diffcrence hetween the NI .S(' model ( .%ulid linr) . he M1 :1'('

model throArrt lino. und model S in Iblldnrtrd bric) predictium .

time front all 3 tables .) All decompression procedures produce similar predictions forbottom times up to 30 min . The Kidd-Stuhbti I 9 71 decompression time s are mute

conservative than the IX.'IF?M I 983 tables for bottom times exceeding 45 rnin, but

less conservative in the moderat e bottom time range. Therefore, one would expect a

smaller /'t,, s, for the longer bottom times and a larger /',K y for the moderate bottom

time~ . This predicted behavior is shown in F ig . fi ; however, the differences are not

very large . Similarly, the predicted Ptx , using the F)CIF:M 19 8 3 tables are lower than

.hat using the USN table s , both by this analysis a nd that of (I5) . This is consistent

with the longer, and more conservative, decompression times of the DC1F:M 198 3

tables .A powerful application of the method of maximum likelihood is the calcula tion of

decompression tables of equal PI), s . Weathershy et al . (6, 18) have used this method

to establish a set of air decompression tables based on model 5 in (6) . A similar setcould be developed for any model, including the N LSC model, although this is beyond

the scope of the present study .

SUMMARY AND CONCLUSIO N

tively . The decompression data that were used consisted of 800 man-dives with 2 1were the NLSC and MEPC based on compartments in series and in parallel, respec-

The method of maximum likelihood was applied to compare two dit%rent gasexchange models used to establish safe decompression procedures . These model s

incidents of DCS and 6 occurrences of marginal symptoms of DCS . A comparison of

USE OF THEMAXIMUM I.IKEI..IH(X)t) MF.THUI) 31 1

à. g .~ r . .~ ...~

20 40 60

©Ot t OrTl Tinte ( rrllrl )

80 t00

t•iK . 6 . rr o htrhihty o f indden c e o r I)CS I,red i o. ted by the Nl .S ( ' rnudcl a . :r (li oc tiun of hutluar IUme lur

standard air dives to I SO t,w fromthe U(Yh :M I 4Ri table s( wlid linrl, he Ki d d-St+rhb s 19 71 whlc+IhruArn

line), and the t1SN Standard Air I ables (Jurre-d linr ) .

TABLE 2C UMt'AKISON OF TOTAL DI?(' :2M1'Kl•.SSION T IMh.S FOR 51 ANI)AKI) AIR I)Ivi?S

A'II501S W

Total [)ccompres5iun Timc., m in

Hottom'l'imrr, min [)('ItN 1983 KS-197

1 7 2.5 610 9 13IS Itt 2320 25 3125 43 3 830 57 4840 88 7450 128 16960 17tS 23870 228 291ü(1 271 35 5

IJSN

3.53 .55.5

11 .5

23 .5

34.559.5

8K.5112.5

146.5173 . 5

the NLSC and MEPC model predictions for DCS showed no sigr,ificant diti'erencebetween the two and so either model appears equally suitable for predicting DCSwith this limited data set . Use of a IargEr data set would improve the predicti ons,

312 P. TIKUISIS, R,Y . NISHI, AND P.K . WEATHERSBY

allow for more optimized parameters, and perhaps statistically distinguish the pre-dictive capabilitv of different models .

A striking result with the use of the maximum likelihood method is the differencein the predicted probabilities of DCS between the 2 models for no-decompression airdives in the range of 54-18 0 fsw (1 . 5 1--5 .45 ATA) and :,rort-bottom-time air dives to150 fsw (4 .54 ATA). Because of the nonlinear gas kinetics of the NLSC model, alower probability of DCS is predicted for these dives with this model than with theMEPC model . Subsequent testing indicated consistency with actual outcome for theNLSC model applied to the no-decompressiuct air dives and for both models appliedto the short-bc)ttom-time air dives . Further studies must be conducted to test differ-ences iu prediction between the 2 models and to validate the extrapolation of modelparame er values to dives that t'all outside the range of the data set used to establishtheir values, as done in this case .

'The authryrs µrratefnlly acknowkdae the advice of f)r . It C F.atoxk in the prep,yrahun of th i ti paper . IX'Ih:M t'uhhtennn88-1' 20 -Man as, ripr rrr~ei t rd / ehrunrY IUNN, urrrplyd Mai f9R8 .

Tikusis P, Nishi RY, Weatheraby l'K . l :niplui de la méthode de prubahilité max :m<r~e dans,l'analyse de plongées a l'air cri caisson . Undersea t3iumcd Rea 1988 ; 15(4) :301 ~31 1 ---Laméthode de probabilité maximale fut utilisée pour évaluer le riyque de maladie de .)écumpreti-viun (M[)(') pour un choix de plongées tl l'air cri caisson, I .ea paramètres de deux modèlesmathématiques pour prédire la MUC furent uptimati~és,iucyu' t l'obtention du meilleur assen•timent (tel que mesuré par la probabilité maximale) correspondant aux incidents de MI)Cobservés d,.tnv une série de plongéeti . Les données de décompression employées provenèrentde 8(X) plongées humaine% contenant 21 incidents de MU(' et 6 cas tic Nytiiptoiiies marginaux .Le premier modèle étudié était basé sur le principe des échange,, galeux mono-Cxponcriticisdans 2 compartiments montés en parallèle . [ .a réussite statistique globale a décrire les S(X)plongées humaines fut très similaire pour les deux modèles . Les prédictions de sécurite pourles plongées ne faisant pas partie des données originales étaient différentes de celles desmodèles à cause des variations dans la cinétique de-, ga / . Pour le s plongées courles, .an .décompression, les compartiments montés en série prédisent une moins grande incidence deM[X.' . Ces prédictions étaient plus consistantes (%'accurdaient mieux) avec W : evxais subsé-quents que les prédictions avec le modèle des compartiment-, cri parallele . Les prédiction,., dumr•,+t[e avec compartiment en série étaient aussi similaires à celles obtenues avec le modèleà compartiment simple qui fut évalué par la Marine américaine avec plus de 170(1 plongéeshumaines .

Tikuisis P, Nishi RY, Weathersby PK . Empico del metodo de probahilidad maxima en CIanalisis de r mersiones de camara con aire . Undersea Biomed Rer 1988 ; 15(4) : :101-313 .---Seempleo el metodo de prubabilidad maxima para evaluar el riesgo de enfermedad por des-compresiun (EPD) en inmersionex de camara con aire elcctivay . Se optimixo lus parametrosde dos modelos matematicuti para predecir la [iPl), hasta que se alcanto cl mejor criterio(medido pur la probabilidad maxima) correspondiente a los incidentes pur FI'[) observadosen una serie de inmersiones . l .os dato . de descompresion empteados consistian de 8(X)inmersiones de humanos, con 21 casus de [iPU y la inc :dencia de 6 con siniomas marginales .El primer mtxlelo estudiado se basaba en un intercamhio gaseoso no lineal en un arreglo enserie de cuatro compartimientos . El segundo modelu se hasaba en un intercambio gaseosomonoexponencial, en un arreglo en paralelo de dos compartimientos . El exito estadisticuglobal para describir las inmersianes de 800 humanos fue similar para ambos modelos, Laspredicciones de seguridad para inmersiones que no formaban parle de los datos originales,fue distinta para los dos modelos debido a la diferencia de la cinctica de los gases . La seriede arreglo en compartimientos predjjo una incidencia mener de EPD, para inmenionei; de nodescompresiôn cortas . Estas predicciones fueron mas consistentes con el resultado de pruebas

USE OF THE MAXIMUM I .IKF:LIHt`X)1) MF`.1°HOU 31 3

subsecuentes, que las del modelo de compartimientos en paraiclo, Las prediccirines del modelode arreglo r.n serre, tambien resultaron similares a las del modelo de un campartimientosencillo, dos exponencial, que se evaluo con mas de 1700 inmersione% de humanos por laU.S . Navy .

REFFRF.;NCE,.S

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1 6 . l.auckner ( ,R, Ni,hi RY, I::dock BC . Hvahratian o f the lX'IF?M 198 3 decompression model forcompresscd air diving ( series ( i•K) . IX'II :M report 84-R•7 1 , Ik>wnsview, Ontario : O e fence andCivil Institute of Environmental Medicine, 1984 .

17, Lauckner ( ;R, Nishi RY, Ciat oc k BC, 1;valu d tion of ► he IX'1[?M 1 9 ri1 decompre,r s ion model forcompressed air diving ( series A' P ) . lX'1l :M repo rt K4-R-7 2 , t)ownaview, Ontario : Ckfence andCivil Institute of F. nvironmental Medicine, 1984 .

18 . Weathershy PK, Hays JR . Survan,hi SS, of al Statistically based dcccrmpre s .iun tabler 11,Equal risk airdiving decctmpres .iun .chedule s . Naval Medical Re s earch Imtittnc report NMRI8 5 .17, F3etlre .da, Ml), Nasal Medic A Research In s trtute, l98 i,