the pd2i flow chart shown in fig4 begins with the data ( top ) and from this the i - and j - vectors are made and subtracted from one another ( i - j diff ). these vector difference lengths are entered , according the their value ( x , 1 to 1000 ), into the mxaray at the embedding dimension used ( m , 1 to 12 ). the entry is made as an increment of a counter at each location of the mxaray . after completion of the making of the vector difference lengths , the counter numbers ( 3 , 7 , 9 , 8 , 2 , 6 , 7 , 4 . . . ) are then used to make the correlation integrals for each embedding dimension ; this is done by making a cumulative histogram as a function of x , at each m i , and then making the log log plot of their cumulative values vs r ( plot log c ( n , r ) vs log r ). then each correlation integral is examined by the lc to find the longest segment of the second derivitive that falls within the limits of the set parameter ( lc = 0 . 30 means within a + to - deviation of 15 % of the mean slope ); this iterative lc test will find a range above the &# 34 ; floppy tail &# 34 ; ( i . e ., the smallest log - r region that is unstable because of finite data length ) and run up the correlation integral until the lc criterion is exceeded ( bold section of top correlation integral ). if a segment is found within the criterion , then the correlation integral scaling region is reset by the pl criterion ; this value is set from the smallest data point in the correlation integral to its criterion value ( e . g ., 15 %, bracket in second from top correlation integral ). the upper and lower limits of this region are observed to see if they have at least the number of data points required by the minimum scaling ( ms ) criterion . and finally the selected regions of all correlation integrals ( m = 1 to m = 12 ) are plotted and examined by the cc to see if convergence occurs at the higher embedding dimensions ( e . g ., m = 9 to m = 12 ); that is , to see if the selected regions have essentially the same slopes in which the standard deviation around the mean is within the limits set by the cc ( i . e ., cc = 0 . 40 means that the deviation around the mean is within + to = 20 % of the mean value ). if the cc is passed , then the mean slope and standard deviation are stored to file . if failure occurs at any of the earlier criteria ( lc , pl , ms ), then the program will exit and move the pd2i reference vector to the next data point and then start all over . if failure occurs at the cc , the mean and standard deviation are saved without exiting , for it may be the case that later the cc is desired to be changed ; i . e . the cc is a filter that determines whether or not the pd2i ( i . e ., the mean slope of m = 9 to m = 12 ) will be plotted in later graphical routines . initially , the concept of &# 34 ; chaos &# 34 ; is characterized by a type of dynamics that is neither stable , exploding or imploding , but rather characteristically has mathematical divergence of adjacent points plotted in phase space ( i . e . in an embedding dimension ). divergence means that as time goes on , the distance between the two adjacent points becomes larger and larger . this divergence was later found to be quantitated by a positive lyapunov exponent . none of these &# 34 ; chaos &# 34 ; concepts , however , is concerned with an often overlooked fundamental feature , that is , they are deterministic as opposed to stochastic . deterministic dynamics ( and their measures ) presume that the fine grain of the variation of data points is caused , and is not random variation due to uncertainty . the presumption of caused variation is an important distinction in signal analysis . for stochastic measures , such as the mean , standard deviation , t - value , f - value , fourier transform , power spectrum , and so on , the presumption is that there is always random variation about a mean for any sampled data - point . the data are considered inherently noisy . when deterministic newtonian models failed to account for results in particle physics , neils bohr invented a stochastic model of the universe and this led to the field of quantum physics . the stochastic models posit random variation of all observable events ( i . e . uncertainty ) as a feature of the positivistic universe . modern thinking adds that any incapacity to carry out those calculations ( any uncertainty in the results of those calculations ) is necessarily an epistemic uncertainty . it is often said that chaos enables free will to exist in a completely deterministic universe . predictability ( determinism ) exists in chaotic systems only in the short - term , because of the rapid divergence within the system ; in the long - term any divergence creates an inability to calculate what will happen ( ergo , stochasticism ). the universe may indeed be completely deterministic , but there are &# 34 ; calculation barriers &# 34 ; that make long - term deterministic measurement a real problem . &# 34 ; determinism &# 34 ; is an algorithm that examines a signal and tells how predictable things are in the short - term . if the measure is near 0 , then the average predictability of a point in phase space from its previous location is poor , as would occur with random noise ; if the measure is near 1 , then the predictability is high , as would occur for example with sine - wave data . if the data are nonstationary , then the accumulated algorithmic predictability cannot be accurately determined . most known deterministic measures are unable to quantify , on a data - point by data - point basis , what is happening in time to the output of the system ( i . e . generator ) if the data are nonstationary . only the present pd2i , which treats the problem of data nonstationary can do this in a highly accurate manner . deterministic measures are inherently more accurate than a comparable stochastic one if there is some short - term structure in the data and the data are stationary . thus , if the data are stationary , mean pd2i can tell you something about a change in the state of the generator of the signal that the stochastic mean of the data cannot . this is also true regarding the standard deviation , power spectrum or any other stochastic measure used on the same data . this greater sensitivity , presumably of the short - term variation , has been shown to be useful in detecting changes in biological data that the stochastic measures cannot make . for example , analysis of the rr intervals of the electrocardiogram of a group of pigs undergoing experimental myocardial infarction showed significant differences in mean pd2i before and after occlusion , whereas neither the rr mean nor the rr power spectrum were able to detect such differences . these same results were found when comparing rr intervals from human patients who manifested fatal ventricular fibrillation that day and matched controls who only manifested non - fatal ventricular tachycardia during the next 3 years . this greater sensitivity leads to greater individual specificity and the latter is the main reason why chaos theory has important implications for biology and medicine . this disclosure teaches that a fundamental difference in sensitivity of measurement occurs when one posits that the variation in the data is caused , as opposed to being random . even without a perfect way to define what chaos is , or how to determine whether or not it is in the data , one still finds that the determinism - based measures are sensitive to changes in the generator of the data that the stochastic measures cannot probe . fig1 plots log c ( r , n , nref ★) versus log r and depicts the crucial idea behind the pd2i algorithm . it is only the smallest initial part of the linear scaling region that should be considered if data nonstationarities exist . in this case the data were made by concatenating 1200 point data subepochs from a sine wave , lorenze data , a sine wave , henon data , a sine wave , and random noise . the reference vector was in the lorenz subepoch . for the correlation integral where the embedding dimension m = 1 , the segment for the floppy tail (&# 34 ; ft &# 34 ;) is avoided by a linearity criterion of lc = 0 . 30 ; the linear scaling region for the entire interval ( d2i ) is determined by plot length pl = 1 . 00 , convergence criterion cc = 0 . 40 and minimum scaling ms = 10 points . the species specific scaling region where the i - and j - vectors are both in the lorenz data ( pd2i ) is set by changing plot length to pl = 0 . 15 or lower . note that at the higher embedding dimensions ( e . g . m = 12 ) after convergence of slope vs embedding dimension has occurred , the slope for the pd2i segment is different from that of d2i . this is because the upper part of the d2i segment ( d2i - pd2i ) is contaminated by nonstationary i - j vector differences where the j - vector is in a nonstationary species of data with respect to the species the i - vector is in . fig2 shows a flow diagram of the invention applied to a cardiac patient or a normal subject undergoing cardiac evaluation . electrocardiographic data ( ecg ) from the subject is made by a conventional amplifier , digitized , and then given as input to a computer for analysis . first rr and qt intervals are made from the ecg data ; then they are analyzed by the pd2i software ( pd2 - 02 . exe ) and qtvsrr - qt software ( qt . exe ). the point correlation dimension is then calculated as a function of time and displayed ; the qt vs rr - qt plot is also made and displayed . graphics reports are then made for assessing risk . the digitized ecg is offloaded for storage . fig3 shows the invention applied to an epilepsy patient or normal subject undergoing neural analysis . electroencephalographic data ( eeg ) from the subject is made by a conventional amplifier , digitized , and then given as input to a computer for analysis . the point correlation dimension is then calculated as a function of time by the pd2i software ( pd2 - 02 . exe ) and displayed . a graphics report is then made for assessing location of epileptic focii and / or alteration of cognitive state . other similar applications of the invention are possible . the source of the electrophysiological signal will be different , and the structure of the graphics report ( s ) will be specific to the medical and / or physiological objectives . all analyses will use the pd2i algorithm , in some software form , and may be accompanied by other confirmatory analyses . an electrophysiological signal is amplified ( gain of 1 , 000 ) digitized ( 1 , 000 hz ) and then analyzed by the pd2i , a deterministic dimensional algorithm that is insensitive to data nonstationarities and can be used on data that have both linear and nonlinear structures . once the signal is digitized , it may be further reduced ( e . g . conversion of ecg data to rr interval data ) prior to processing . analysis of rr interval data has been repeatedly found to enable risk - prediction between large groups of subjects with different pathological outcomes ( e . g . ventricular fibrillation &# 34 ; vf &# 34 ; or ventricular tachycardia &# 34 ; vt &# 34 ;). in a study ( see examples below ) using sampled rr data from high risk patients , it was found that pd2i could discriminate those that later went into vf from those that did not . several nonproprietary algorithms were also used as comparative studies on physiological data . none of these algorithms could discriminate risks that the pd2i is capable of making . in the electrocardiographic analyzer apparatus contemplated in the present invention , the qt subinterval of each rr interval will be made by the qt . exe software described herein . the calculation of the qt interval enables a joint plot of the qt vs rr - qt subintervals , which can predict risk of fatal arrhythmias such as vf in high - risk patients all of whom exhibit ventricular vt , when the dynamics enter a previously defined exclusion area for that patient . the rationale for this prediction is based on a theory linking the subintervals to mathematical models as presented below in example 4 . the method and apparatus used to examine entry of the joint subinterval dymanics into the exclusion area for predicting risk of dynamical arrhythmogenesis in both cardiac patients and normal subjects is one embodiment of the present invention . once the pd2i and qtvsrr - qt values are calculated , as a function of time , they can be presented in a variety of graphics modes that will summarize the current results and provide a clinically useful predictor . these graphic reports provide visualization of the outputs of the pd2i and qtvsrr - qt algorithms . the pd2i algorithm has been applied to rr intervals of the electrocardiograms of 60 cardiac patients in a blinded , controlled , retrospective study , and pd2i &# 39 ; s & lt ; 1 . 2 were found to discriminate risk of imminent fatal arrhythmias ( i . e . the onset of ventricular fibrillation , vf , within 24 - hrs ), among high - risk control subjects ( i . e . patients with documented ventricular tachycardia , vt , who lived for more than 3 years and had pd2i &# 39 ; s & lt ; 1 . 2 ; sensitivty = 100 %, specificity = 86 %, p & lt ; 0 . 01 ). tables 2 , 3 and 4 , below , shows the composite data in human cardiac patients . table 2__________________________________________________________________________point - d2 and clinical data : the minimum point - d2 ( min pd2 ) ofthe heartbeat intervals ( r -- r ; a , b , c samples , 24 - h holter - tapes , 512 hz a / d ) discriminates among patients with nonsust - ained ventricular tachycardia those who will manifest ventric - ular fibrillation ( vf ) from those who will not ( ns - vt ). ambulatory nonsymptomatic patients with edit clin pvcs pvcs excurs r -- r holter - diag min min pd2 & lt ; 1 . 2 . sup . 6 sds . sup . 7 tape . sup . 8pt . sup . 1 tf / np . sup . 2 arr . sup . 3 pd2 . sup . 4 pd2 . sup . 5 a b c a b c tl vf hosp__________________________________________________________________________1 tp vf 1 . 2 nc 01 01 11 19 16 16 8 21 : 00 i2 tp vf 1 . 1 nc 11 11 01 6 18 15 9 21 : 00 i3 tp vf 1 . 0 1 . 1 11 11 11 25 14 18 21 07 : 30 i4 tp vf 0 . 7 nc 01 01 11 7 7 5 24 06 : 30 i5 vf 0 . 5n nc na 1 11 134 133 018 18 10 : 00 o6 tp vf 0 . 4 0 . 5 11 11 1 4 5 69 24 09 : 30 i7 tp vf 0 . 5 0 . 6 11 11 11 9 10 24 4 15 : 45 i8 vf 0 . 9n na 11 11 11 33 37 21 3 14 : 00 i9 tp vf 1 . 0 nc 11 01 11 6 18 6 14 11 : 00 i10 vf 0 . 9n na 11 11 11 10 14 na 9 19 : 45 i11 tn ns - vt 1 . 4 1 . 6 00 00 00 25 24 26 23 i12 tn ns - vt 1 . 5 nc 00 00 00 15 14 12 24 i13 tn pvc 1 . 5 nc 00 00 00 14 18 22 24 o14 tn ns - vt 1 . 6 nc 00 00 00 17 28 14 24 o15 tn ns - vt 1 . 9 nc 00 00 00 32 17 23 23 i16 tn ns - vt 1 . 6 nc 00 00 00 28 44 54 24 o17 tn ns - vt 1 . 5 nc 00 00 00 37 38 38 24 i18 tn ns - vt 1 . 4 nc 00 00 00 85 7 17 24 i19 tn ns - vt 1 . 4 nc 00 00 00 7 14 9 23 i20 tn ns - vt &# 39 ; 2 . 2 nc 00 00 00 21 24 26 24 i21 ns - vt 1 . 3n na 00 00 00 37 74 na 24 i22 tn pvc 1 . na 00 00 00 14 17 18 24 o23 tn pvc 1 . 4 1 . 5 00 00 00 11 13 14 24 o24 tn pvc 1 . 3 na 00 00 00 15 19 16 24 o25 pvc 1 . 8n na 00 00 00 19 50 63 24 o26 tn pvc 3 . 0 nc 00 00 00 18 22 19 21 o27 pvc 1 . 6n na 00 00 00 100 41 57 24 o28 tn pvc 1 . 3 na 00 00 00 20 15 20 24 o29 tn pvc 1 . 4 1 . 5 00 00 00 24 22 15 24 o30 tn pvc 1 . 4 na 00 00 00 24 16 14 20 o31 tn pvc 1 . 6 nc 00 00 00 24 16 21 24 o32 tn pvc 2 . 0 na 00 00 00 23 26 23 24 i33 tn pvc 1 . 6 nc 00 00 00 40 19 32 24 o34 fp ns - vt 0 . 4 nc 11 1 - 11 6 7 4 11 i35 fp ns - vt 0 . 5 0 . 6 11 11 11 15 17 10 24 o36 fp ns - vt 0 . 6 0 . 5 11 10 11 7 9 6 24 i37 fp ns - vt 0 . 8 nc 11 11 11 7 11 14 i38 vf 3 . 3n na na na na 133 131 124 2 10 : 40 i39 tp vf * 0 . 6 0 1 1 17 4 1440 tp vf * 0 . 6 1 1 1 29 6 1541 tp vf * 0 . 6 1 1 1 4 8 542 vf 4 . 2n 0 0 0 54 45 4443 tp vf * 0 . 7 0 1 0 30 33 4144 vf 1 . 9n 0 0 0 -- -- -- 45 vf 1 . 2n 1 0 0 -- -- -- 46 tp vf * 0 . 5 1 1 1 10 10 647 tp vf * 0 . 6 1 1 1 9 4 -- 48 vf 0 . 5n 1 1 0 78 15 -- 49 tp vf * 0 . 7 0 1 1 19 15 1150 tp vf * 0 . 5 1 1 1 3 6 751 tp vf * 0 . 6 1 1 1 16 62 2052 tp vf * 0 . 6 1 1 1 23 49 753 tp vf * 0 . 5 1 1 1 6 6 854 vf 0 . 8n 1 1 1 72 -- 9955 tp vf * 0 . 5 1 1 1 9 3 -- 56 tp vf * 0 . 8 1 1 0 8 19 5357 tp vf * 0 . 5 1 1 1 6 5 958 vf 0 . 6n 1 1 1 37 4 1359 vf 6 . 6n 0 0 0 -- -- -- 60 tp vf * 0 . 6 0 1 0 13 7 1761 tp vf * 0 . 6 1 1 1 30 5 -- __________________________________________________________________________ note : specificity of pd2i & lt ; 1 . 2 predicting vf outcome ( patients 1 - 61 ) = 86 %. sensitivity for pd2i & lt ; 1 . 2 predicting vf outcome ( patients 1 - 61 ) = 100 % ( & lt ; . 001 ). table 2 , end notes . sup . 1 patient number : pts 1 - 21 ( 1st study , blinded ) pts 22 - 38 ( 2nd study doubleblinded ); for pts 39 - 61 ( 3rd study , blinded ); for pts 62 - 80 ( 4th study , doubleblinded ); ( 15 min , prior to inducibility testing ). . sup . 2 t = true , f = false , n = negative , p = positive , where true = vf and positive = pd2 & lt ; 1 . 2 ; omitted entry means ps2 could not be calculated . sup . 3 clin diag arr = clinically diagnosed arrhythmias ; vf = nonsustaine ventricular tachycardia ending in ventricular fibrillation ; nsvt = nonstained ventricular tachycardia ; pvc = premature ventricular complexes norm = normal . . sup . 4 minpd2 = minimum point correlationdimension ( in dimensions , n = probably not a valid estimate because more than 75 % of estimates rejected ); arrhythmias and artifacts not removed from the r -- r data ; pd2 software from neurotech laboratories , inc ., 399 autumn drive , bangor , pa . . sup . 5 same as above , but artifacts and arrhythmias removed by digital overwritting with 5point copies from neighborhood ; nc = no change ; na = not available / applicable . . sup . 6 excurs pd2 & lt ; 1 . 2 = excursions of pd2 & lt ; 1 . 2 ; 1 = at least one excursion occurred during the 6 . 5 min epoch ; 0 = no excursion occurred ; two adjacent 6 . 5 min epochs comprise one a , b or c epoch ; a = initial epoch , b = mid epoch , c = final epoch . . sup . 7 r -- r sd = standard deviation of r -- r intervals ( msec ) during a 2 t 3 min stationary period without arrhythmias or artifacts ; a = initial epoch , b = mid epoch , c = final epoch . vf , nsvt , pvc not significantly different ( f = 1 . 6 , df = 109 ). . sup . 8 holter tape ; tl = tape length in hours ; vf = time of occurrence of vf ; hosp = hospital inpatient ( i ) or outpatient ( o ). * statistics : vf versus nsvt + pvc significantly different ( minpd2 , p & lt ; . 001 , f = 9 . 4 , df = 36 , pts 1 - 38 ); nsvt vs pvc not significantly different ; s + vf vs s + vt not significantly different ( pts 62 - 80 ); s + vf vs nsvt and s + vt vs nsvt significantly different ( p & lt ; . 01 ); oneway analysis of variance , with multipletests alphaprotection ; true epistat software , epistat services , richardson , tx . logistic regression model ( no vf vs vf , pts 1 - 38 ) show minpd2 ( p & lt ; . 001 ), ejfr ( p = not significant ), minpd2 and ejfr ( p & lt ; . 002 ); software from stata computing resource center los angeles , ca . table 3__________________________________________________________________________symptomatic patients , off drugs with editclin pvcs pvcs excurs r -- r holter - diag min min pd2 & lt ; 1 . 2 . sup . 6 sds . sup . 7 tape . sup . 8pt . sup . 1 tf / np . sup . 2 arr . sup . 3 pd2 . sup . 4 pd2 . sup . 5 a b c a b c tl vf hosp__________________________________________________________________________62 ( tp ) s + vf * 0 . 4 table 3 legend63 s + vf -- n s = previously documented syncope64 s + vf -- n vf = previously documented vf - converted65 ( tp ) s + vf * 0 . 5 vt = previously documented vt66 ( fp ) s + vf * 1 . 1 tp = true positive predicting prev . vf67 ( fp ) s + vf * 0 . 6 fp = false positive predicting prev . vt68 ( fp ) s + vf * 0 . 5 note : only 10 of 19 had ectopy rates69 ( fp ) s + vf * 1 . 0 low enough to enable valid pd2i calcu - 70 s + vf 1 . 7n lation ; pd2i & lt ; 1 . 2 predicts symptomatic71 ( tn ) s + vf * 1 . 4 condition in 9 of 10 vf / vt patients72 ( fp ) s + vf * 0 . 673 ( fp ) s + vf * 0 . 474 s + vf 2 . 4n75 s + vf 1 . 1n76 s + vf 1 . 2n77 s + vf 1 . 3n78 s + vf 3 . 0n79 s + vf 2 . 8n80 ( fp ) s + vf * 0 . 8normal controls 1 tn norm 1 . 8 -- 0 0 0 86 94 80 -- -- 33 m12 tn norm 1 . 7 -- 0 0 0 86 98 84 -- -- 25 m25 tn norm 1 . 6 -- 0 0 0 71 55 56 -- -- 50 m__________________________________________________________________________ table 3 , end notes : see end notes for table 2 , page 38 , supra . table 4__________________________________________________________________________ej pvc / history . sup . 15pt . sup . 1 fr . sup . 9 hr . sup . 10 a . sup . 11 s . sup . 12 meds . sup . 13 coronary anatomy . sup . 14 mi an hf ht dm__________________________________________________________________________1 na 84 65 m p na + + - - - 2 28 33 56 m dhsf 50 % lm + + + - - 3 50 10 52 f vn min + + - - - 4 60 80 61 f dhe min not applicable5 32 270 73 m pprdf 60 % rc - - + - + 6 33 407 63 f ndvf min - + + - - 7 60 900 42 m dcof min + - - - + 8 35 506 57 m din na + + - - - 9 na 105 80 m ndq na - + - - - 10 na 200 79 m fd 70 % lad , 30 % lm , 30 % rc + - + + - 11 67 114 58 m mp 50 % rc + - - + - 12 50 188 63 m dinhe 99 % rc + + - + - 13 61 2 57 m din na not applicable14 na 61 na m nfddife na not applicable15 25 45 53 m ddi tvd 30 + + - - 16 87 1 53 f di na not applicable17 50 2 66 m qd 100 % rc , 50 % lm , 70 % cx - + - - + 18 50 29 68 m qpnfd 100 % rc , 100 % lad - + - - - 19 32 108 63 m ncnfd 99 % lad , 99 % cx - + - + - 20 14 1152 59 m nfd na + + - + - 21 na 984 50 m qnnf na - + - - - 22 28 229 64 m didn na + + - + + 23 37 13 68 m dinp na + + - + - 24 30 72 49 m nnfp na + + - + - 25 32 24 51 m nfmpdn 95 % lad , 95 % rc + + + + - 26 32 11 57 f nfdi na + - - - - 27 21 12 59 f mpcn na + - - + - 28 23 77 64 m dinfc na + + - - - 29 39 7 55 m nfmp na + + - - - 30 25 1173 61 m cdnfn na + + - + - 31 32 6 72 m ndi na + + - + - 32 64 15 67 m nddi 75 % rc , 95 % lad + + - + + 33 22 6 53 m cdn na + - + + - 34 na 3 47 m dimp 80 % lad , 80 % rc + - - + - 35 20 360 63 m dn na not applicable36 29 60 64 m pcmxdi 100 % lm , 100 % rca , - + - + - opgrrca37 29 12 62 m atdi 90 % lad , 90 % rc - + - + - 38 14 86 55 m edb na + + + + + 39 - 80 records na101 na na 33 m na na na112 na na 25 m na na na125 na na 50 m na na napt . sup . 1 comments . sup . 16__________________________________________________________________________1 type ii aortic aneurysm2 heart failure3 - 5 days after back surgery4 evaluation of ventricular arrhythmias ; resuscitated in hospital5 evaluation of ventricular arrhythmias6 heart failure7 1 day after mitral commisurotomy , resuscitated in hospital8 10 days after non - q infarction9 4 days after exploratory laparotomy10 meningeoma ; autopsy consistent with ant . lat . ischemia ; old septalinfarct11 3 weeks after mi12 post - mi stratification13 na14 na15 coronary artery bypass graft16 na17 coronary artery bypass graft , pre work up18 coronary artery bypass graft , pre work up19 na20 weeks post - mi ; a single vt - triplet was observed21 coronary artery bypass graft , post 10 days , work up for palpitations22 5 days after mi23 5 days after mi24 1 week after mi25 3 months after mi26 2 weeks after mi27 5 weeks after mi28 2 weeks after mi29 10 months after mi30 5 days after mi31 1 week after mi32 1 week after unstable angina33 1 month after mi34 6 weeks after mi35 na36 work up for angina37 coronary artery bypass graft , pre work up38 post - mi stratificationtable 4 , end notes : for end notes . sup . 1 - 8 for table 4 , see end notes for table 2 , page 38 , supra .. sup . 9 ej fr = ejection fraction ( in percent ); vf , ns - vt , pvc notsignificantlydifferent ( f = 0 . 48 , df = 31 ).. sup . 10 pvc / hr = premature ventricular complexes per hour , averaged overthe fulllength of the holter - monitored electrocardiogram ( marquette , inc . ); vf , ns - vtand pvc not significantly different ( f = 0 . 45 , df = 37 ).. sup . 11 age . sup . 12 gender m = male ( 81 %), f = female ( 19 %), b = black ( 23 %), w = white ( 66 %), h = hispanic ( 5 %), a = asian ( 5 %).. sup . 13 medications at time holter tape made ; pts 39 - 61 had no medicalrecords available ; pts 62 - 80 were off medication , for more than 7 half - lives of drug , priorto cardiacelectrophysiology assessment of vt - inducibility ; for normals , na = notapplicable , no statistically significant drug - effects are detectable for this numberofsubjects . abbreviations : at = atenolol , b = bumetanide , c = captopril , co = coumadin , d = digoxin , di = diltiazem , e = enduronyl , f = furosamide , h = hydralazine , he = hetz , mp = metroprolol , mx = mexilitine , n = nitrates , nf = nifedipine , p = propranolol , pc = procainamide , pr = prazosin , q = quinidine , s = spirono - lactone , v = vasopresin .. sup . 14 coronary anatomy ; percentage occlusion on coronary angiography ; rc = right coronary ; lm = left main ; lad = left anterior descending ; cx = circumflex ; tvd = triplevessel disease ; opgrrc = open graft to right circumflex ; min = minimalcoronary disease .. sup . 15 history = medical history ; mi = myocardial infarction ; an = angina ; hf = heart failure ; ht = hypertension ; dm = diabetes mellitus .. sup . 16 comments written on medical records . additional preliminary data show that the separation in time of the recording and prediction and the actual time - of - occurrence of vf can be as much as 42 days and still exhibit high sensitivity and specificity . table 5 , below , shows these data . table 5______________________________________blinded 24 - hour study of the point - d2 ( pd2i ) of the heartbeatsin patients from the cardiac arrhythmia pilot study .. sup . 1 the r -- rintervals were made at a resolution of 128 - hz for the digitizingrate of the ecg .. sup . 2 days separating type of prediction actual predition out - by pd2i . sup . 3 event . sup . 4 from event come . sup . 5______________________________________note : - lived & gt ; 1000 tnhalf of the - lived & gt ; 881 tnfp &# 39 ; s may be - died 336 rfndue to a + died 231 rtplow digitizat - - died 149 rfnion rate for + died 42 rtpthe ecg + died 37 tp + died 9 tp + died 7 tp +* died 1 tp +* died 1 tp +* died 1 tp +* died 1 tp +* died 1 tp +* died 1 tp +* died 1 tp + lived & gt ; 1086 fp + lived & gt ; 1062 fp + lived & gt ; 904 fp + lived & gt ; 1020 fp ++* lived & gt ; 1000 fp ++* lived & gt ; 1000 fp +-# lived & gt ; 1000 tn +-# lived & gt ; 1000 tn______________________________________ table 5 , end notes . sup . 1 r -- r interval files made with marquette scanner by thomas bigger ( columbia university , new york ). . sup . 2 only 24 of 51 files could be examined because of low 128hz resolution . . sup . 3 + = minpd2 & lt ; 1 . 2 ; - = minpd2 & gt ; 1 . 2 ; * = same result obtained using 512hz digitizing rate for the ecg ; # = opposite result obtained using 512hz digitizing rate . . sup . 4 vf was cause of death . . sup . 5 predicted outcome : tn = true negative ; tp = true positive ; fp = false positive ; fn = false negative ; rfn = criticalrange false negative ; rtp = criticalrange true positive ( i . e ., this range exhibits prediction divergence and is the probable limit of the interval over which pd2prediction can be expected to work ). not only is the pd2i useful in analyzing physiological time series data such as the electrocardiogram ( e . g . rr intervals made from the ecg ), but it is also capable of analyzing the electroencephalogram ( eeg ). it has been applied to simultaneously - recorded scalp - eeg &# 39 ; s and electrocorticography - eeg &# 39 ; s obtained from 5 patients will epilepsy . it was found that the scalp electrodes nearest the suprapial cortical electrodes that were the earliest to show paroxysmal activity during an epileptic seizure ( i . e . the leads that by the electrocorticography method locate the epileptic focus ) had a statistically significantly larger pd2i variance ( standard deviation ) than any of the other scalp leads including the perifocal ones . these data are shown in fig5 . fig5 shows pd2i of eegs recorded simultaneously from the pia ( pia ) and scalp ( scalp ) in a conscious human with documented epilepsy . recordings were made from the surface of the cortex with electrocorticography electrodes and from the scalp with conventional scalp electrodes . data were recorded from two sites one minute before a seizure , ( 1 ) above the epileptic focus as defined by the electrocorticography lead that showed the earliest high frequency activity prior to the seizure , and ( 2 ) 2 - cm away from the focus ; the scalp leads were placed immediately above the selected electrocorticography leads . the mean pd2i and its standard deviation are shown for each of the preseizure epochs indicated . analysis of the eeg &# 39 ; s from both animals ( cats ) and humans show evoked alterations in the baseline pd2i of the eeg that persists in time between a memory storage event and a memory recall event . for example , when a group of 10 humans were instructed that a shock would be &# 34 ; strong ,&# 34 ; the resulting pd2i of the baseline eeg was reduced compared to the condition in which each of the same subjects was instructed that a shock of the same physical intensity would be &# 34 ; weak .&# 34 ; thus , from the time of the instruction onward the baseline pd2i maintained an altered value . as the shocks were of the same intensity , the evoked eeg potentials were of the same amplitude , for all components , but an altered pd2i of the same event - related potentials showed statistically significantly different components . thus , the results from the transient pd2i responses confirmed those of the tonic baseline - effects . a similar baseline eeg alteration was noted in 4 cats undergoing classical conditioning to a tone . the baseline pd2i was reduced during shock reinforcement of the tone , that is , as compared to the condition in which the tone was presented without reinforcement . thus , the pd2i of the eeg provides electrophysiological evidence of a persistent &# 34 ; engram &# 34 ; which bridges the time gap between the presentation of a learned stimulus and its later recall . the data from the above described human study are shown in fig6 . fig6 shows the effects of insrtuctional set ( expectancy ) on the event - related potential ( erp ) and the pd2i of the same potentials . the data are computer averages of 10 trials in 10 human subjects for two sessions in which a warning stimulus ( s1 , a moderate intensity flash ) preceded by 0 . 5 sec the occurrence of a moderate intensity skin shock ( s2 ). the subject had been instructed prior to each session to expect either a &# 34 ; weak &# 34 ; or a &# 34 ; strong &# 34 ; shock ; the s2 &# 39 ; s were equal in intensity and previously judged by the subject to be &# 34 ; moderate &# 34 ;. there were no effects of instructional set on the erp components ( ns ), but the pd2i &# 39 ; s showed a statistically significantly lower baseline for the expect &# 34 ; strong &# 34 ; shock condition and a significantly earlier and larger post - s2 response . each epoch length is 2 secs ; the amplitude of the verticle scale is 200 microv (- up ); eeg digitization rate was 200 hz . it has been demonstrated that in 7 of 7 normal human volunteers a combination of individualized psychological stress plus mild exercise results in arrhythmogenesis or ectopy ( pvcs , vt ) in the normal heart ; these arrhythmias occur within a few minutes following recovery from exercise , during which time the dynamics of the subinterval plots ( i . e . in the qt vs rr - qt plane ) traverse a previously defined exclusion area , the latter of which is a dynamical zone into which the data never go with exercise alone ( see plate below ). additionally , results in 20 high - risk patients with documented vt show that in 10 subjects who later manifest vf within 24 - hrs , there is an excursion of the joint subinterval plots into a previously defined qt vs rr - qt exclusion area , an excursion that does not occur in either the high - risk vt controls ( who lived for more than 3 years ) or in the normal volunteers ( with the exception noted above in which stress is superimposed upon recovery from mild exercise ). the theoretical explanation for the above findings is that any excitable - medium model will produce , during computerized simulation , premature beats , rotating spiral waves , and ventricular fibrillation ( i . e . arrhythmogenesis , ectopy ), but only when specific dynamical conditions are met . these dynamical conditions are known physiologically after remapping the qt and rr - qt subintervals onto the variable planes of any excitable - medium model . three physiological predictions are made from such models each of which was satisfied in the empirical data above , ( a ) an exclusion area must be found in the qt vs rr - qt plane that keeps the dynamics out of a specific central region where ectopy would otherwise be evoked ( i . e . mathematically ), ( b ) a breakdown of this exclusion area must occur , as ectopy is possible in the normal heart ( a breakdown under the influence of one or more factors associated with neurocardiac risk , such as psychologic stress , myocardial ischemia , etc . ), and ( c ) cardiac arrhythmo - genesis or ectopy will occur only when the qt vs rr - qt dynamics are coaxed into the exclusion area after its breakdown . because the two - dimensional exclusion area requires two degrees of freedom to be drawn , its breakdown must be associated with heartbeat pd2i &# 39 ; s & lt ; 2 . 0 . the data to support this example are shown in the schematics depicted in fig7 . the schematics shown in fig7 depicts the prediction of risk of arrhythmogenesis in a normal healthy heart by constructing a deterministic model subsequent to the measurement of the dimension of the heartbeat generator . after finding that the mean dimension of the heartbeat generator was approximately 3 , a modification of the 3 - dimensional deterministic model of a heartbeat generator by arthur winfree was made , as shown at the right ; it is the thickness of the shaft and the flutes near the shaft that makes this a 3 - dimensional model . the modified model predicts time - uncertainty for heartbeat points ( b2 , b3 ) falling within or near the shaft ( asterisks ). this predicted phenomenaon is actually observed in a joint plot of each qt ( the interval between the the q - wave and the r - wave in each heartbeat ) vs rr - qt interval in the serial beats ( thick arrows , upper row ). to cause the heartbeat dynamics to span the 2 - dimensional projection of the variable field , the subject was mildly exercised on a bicycle and then allowed to recover . recovery time is indicated at the lower left by plotting successive numbers of heart - beat points ( pts ). in a similar experiment , but with the subject psychologically stressed by keeping him waiting for one hr while he was supposed to be somewhere else , the point - d2 of the heartbeats was reduced to 1 . 2 , as indicated by a nearly 1 - dimensional recovery trajectory . this trajectory then traveled across the previously protected area ( i . e . where no points fell ) and 8 premature ventricular beats were evoked . if the trajectory had landed on the &# 34 ; point singularity &# 34 ; ( i . e . the infinitely thin shaft ) then ventricular fibrillation would have been evoked according to the excitable - medium model . this sequence illustrates the benefit of the deterministic measure ( pd2i ) which can reconstruct from the data important information regarding the generator . stochastic measures cannot reconstruct such information . in four patients with documented sleep apnea and in four normal controls , it was found that the pd2i of the sleeping eeg ( stages 1 - 3 of slow wave sleep ) had more low - dimensional excursions in the apnea subjects than in the controls . there were no significant differences detected in the power spectrum of these same eeg records . thus , a pathology in the sleeping eeg can be descriminated between the true sleep apnea patient and the normal control through the use of the pd2i algorithm . these data are presented in fig8 . the pd2i &# 39 ; s of the sleeping eeg of sleep apnea patients ( apn ) show more low - dimensional excursions ( dark arrows , white arrow ) than those in control subjects also presenting with a sleep disorder . the vertex electrocencephalogram ( eeg ), point - d2 ( pd2 ), histogram of pd2i &# 39 ; s ( hst ), neck - muscle electromyogram ( emg ), electrocardiogram ( ecg ), respiration ( rsp ), air flow ( afl ) and blood po 2 ( po 2 ) are shown for the control ( left column ) and apnea subjects ( right column ). by attaching the output of the pd2i algorithm to a software filter that recoginizes , rr - interval pd2i &# 39 ; s & lt ; 1 . 2 or eeg - pd2i &# 39 ; s from an epileptic focus with a standard deviation greater than that from a perifocal lead , an electrophysiological precursor of an untoward electrophysiological event ( e . g . ventricular fibrillation or epileptic seizure ) can be predicted at a time that would be soon enough for a clinician to prevent the undesireable occurrence of the event . both fatal arrhythmogenesis and hypertension are linked to the same underlying neurocardiac mechanisms : blockade of descending projections from the frontal lobes and amygdala will not only prevent ventricular fibrillation following coronary artery constriction in psychologically - stressed animals , but it will also normalize blood - pressure elevations in several animal models of experimental hypertension . thus , neurophysiological or electrocardiac abnormalities can be detected by pd2i analyses of the meg or ecg in hypertensive patients . the present invention can also be used to determine cognitive processes . it is known through event - related potential research that there are eeg correlates of intelligence , motor performance and perception . since the pd2i of event - related potentials is more sensitive than the event - related potential itself to certain types of perception ( e . g . the alteration of perception produced by the instructional set , demonstrated in example 3 , for expectancy of &# 34 ; weak &# 34 ; and &# 34 ; strong &# 34 ; sensory stimuli that are physically the same ), the pd2i of other types of event related eeg potentials , evoked in other stimulus paradigms , are more sensitive than the event - related potentials themselves to the underlying cognitive process . certain types of autonomic electrophysiological responses have been associated with lie detection . more recently the possession of secret knowledge has been revealed through analysis of event - related potential components ( e . g . enhancement of the p3 component of a &# 34 ; target &# 34 ; stimulus ). because the pd2i of electrophysiological potentials regulated by both the central and autonomic nervous system has been shown to be more sensitive and specific in the detection of underlying pathology than any of a variety of stochastic analyses of the same data , it would be expected that the pd2i of electrophysiological potentials evoked in a paradigm to reveal secret knowledge would similarly be more sensitive and specific , and hence to enhance the lie - detection method . in data from conscious pigs , not only did pd2i reduction show sensitivity to imminent risk of vf ( as described in human patients in example 1 ) but also to myocardial ischemia . table 6 below shows that mean pd2i reduction during the first minute following complete left anterior descending coronary occlusion is indeed predictive of vf , but additionally that the pd2i reduction is monotonically reduced as a function of time following acute coronary artery occlusion , and that pd2i reduction is monotonically reduced as a function of the percent occlusion of the coronary artery . thus , pd2i reduction is proportional to the degree of myocardial ischemia , both as it accumulates in time and as it is related to the degree of coronary artery constriction . table 6__________________________________________________________________________ complete * 100 % occcontrol * partial severe whole first last0 % occ 50 % occ 90 % occ epoch min # min # pig mean sd mean sd had mean sd had mean sd mean sd mean sd hadid pd2i pd2i pd2i pd2i vf pd2i pd2i vf pd2i pd2i pd2i pd2i pd2i pd2i vf__________________________________________________________________________1 3 . 9 0 . 84 2 . 9 0 . 95 no early vf yes2 3 . 7 0 . 82 3 . 5 0 . 86 no 3 . 0 1 . 44 no early vf yes3 1 . 6 0 . 87 1 . 2 1 . 10 1 . 22 0 . 30 1 . 08 0 . 13 yes4 2 . 0 1 . 09 1 . 4 1 . 11 1 . 39 0 . 34 1 . 08 0 . 14 yes5 2 . 7 0 . 65 2 . 3 1 . 14 no 1 . 7 1 . 11 1 . 60 0 . 77 0 . 93 0 . 22 yes6 1 . 3 0 . 85 1 . 2 0 . 86 no 1 . 2 0 . 86 1 . 27 0 . 44 0 . 87 0 . 19 yes7 3 . 3 0 . 69 1 . 8 1 . 22 2 . 43 1 . 36 1 . 39 0 . 22 yes8 1 . 5 0 . 67 early vf yesmean 2 . 5 0 . 81 1 . 4 1 . 08 1 . 58 0 . 64 1 . 07 0 . 18__________________________________________________________________________ * student &# 39 ; s paired ttest , t = 6 . 4 , df & gt ; 100 , twotailed alpha , p & lt ; . 01 # student &# 39 ; s paired ttst , t = 7 . 6 , df & gt ; 100 , twotailed alpha , p & lt ; . 01 replications of the 50 % occlusion experiments for pigs 1 and 2 were : 2 . 5 0 . 81 , no ; 3 . 2 , 1 . 56 , no . table 6 tabulates the effects of left anterior descending coronary artery occlusion of various degrees ( 100 %, 90 %, 50 %) on the mean point - d2 of rr intervals in the conscious pig . each pig was stressed by the unfamiliar laboratory . the control data ( 8 . 3 min ) were recorded immediately before complete coronary occlusion . during complete occlusion experiments , pigs 1 , 2 and 8 showed short - latency ventricular fibrillation ( vf latecy : 1 . 0 , 3 . 0 , 1 . 2 min ); this prevented sufficient data acquisition to calculate the pd2i . in the other pigs the vf latency was 7 . 0 to 11 . 7 minutes . after vf , the coronary occlusion was released and the heart electro - converted . additional experiments were performed in some pigs , on separate days ; both 50 % and 90 % occlusion experiments were performed ( 15 min in duration , no vf , pulsed - doppler ultrasound assessemnt of coronary blood velocity ). after 24 - hrs of recovery from the last experiment each pig was euthanized with pentobarbital and the excised heart examined for histochemical evidence of myocardial ischemia ( hbfp stain ) and coronary stenosis ; no heart showed evidence of myocardial ischemia or any coronary anolomies , thus indicating normal myecardial conditions under which all experiments were performed . the illustrated embodiments have proven to be useful in many applications for this art . further modifications based on the disclosure will occur to persons skilled in the art . these modifications are within the scope and spirit of the present invention as defined by the following claims .
disclosed is a method and a device in which electrophysiological signals are acquired and analyzed to provide a basis of prediction of clinical outcomes such as sudden cardiac death and cerebral epilepsy .