W~94/04219 ~ 2 ~ 2 9 PCT/US93/0~09 .-:.' REAL TIME CARDIAC ARRHYTHMIA
BACKGROUN _ OF THE INVENTION
This invention relates in general to monitoring,analyzing and modifying the pulsating behavior of active systems, and in particular that of living cardiac 5 tissue. ~ ;
The realization that many activities of an apparently random nature are actually examples of a ~ `;
deterministic phenomenon known as chaos offers a new ~``
approach to analysis and modification of complex ~ ~
l0 systems. Phenomena that have been shown to exhibit ~;-chaos include the transition to turbulence in f~luids,~
;many mechani~al vibrations, irregular oscillations in i~
chemical reactions, the~rise and fall of epidemics and ~-the irregular dripping o~ a faucet. Several studies 15 have~ argued that certain cardiac arrhy hmias are also examples of an irregular pul~ating behavior characterizable as ch~os.
Until recently the ~ain strategy for deali~ng~ with a~system exhibiting~chaos was to develop a model of the system sufficiently ~detailed to identify the ~key~
parameters and then ~o;change those parameters enough to take the~system~out of the chaotic regime. ~owever that strategy is limited~to systems for which a theoretical model is known~and which do not display irreversible ~
25 parametric changes~(often the very changes causing the `;~ ' chaos) ~ such ! as ~aging. ~ Recently,~ al~strategy was de.veloped which~does;not attempt~to take the system~;out~
o~the~chaotic~egime~but uses~the chaos~to control~ he sys~em.~The iri~tica1 ~eature v~chaos~believed to~make 30~ this~possib1e; is~the~ extreme sensitivity of cha~otic~
systems to~ pe~rtu~ba~tions~of~heir initial~conditions.
The~key~to such~stra~egy~ lies~ in the~fact~that~haotic motion~includes~;an~infinite number of unstable periodic~
mot~i~ons. ~;A~ch~aotic sysXem never~remains~long~ in any;~of W094/042~9 Z1L~2 ~9 PCT/US93/0~09 '~`''~"' ''~. ~ "
such unstable motions ~ut continually switches ~rom one periodic motion to another, thereby giving the appear~nce of randomness. It was conjectured that it should be possible to stabilize a chaotic system around 5 selected periodic motions. Such syste~ stabilizing - -theory and approach was first applied experimentally (a) to contr~lling the chaotic vibrations of a magnetoelastic ribbon and t~) subsequently applied to a diode resonator circult and (c) in the chaotic outpu~ of lasers. Such chaos controlling strategy involved development of a real-time measurement of the current ., ,. :~
system state and identification of an unstable fixed point of interest on a plot along with its stable and unstable manifolds. Such fixed point and its accompanying manifolds shift in response to changes in system-wide parameters. Thus, a feedback providing algorithm was developed tending to move the fixed point and manifolds toward the system state point on the aforementioned plot in response to corrective control of the` selected system-wide parameter. Unfortunately, a system-wide parameter capable of being changed with sufficient rapidity to implen~ent corrective control in accordance with the foregoing strategy was not found to be suitable in ce~tain cases for stabilization purposes.
It is therefore an important object o~ the present invention to provide a method and apparatus for manipulating chaotic behavior based on the aforementioned study of chaotic regimes by intervention ': ' at irregular times determined~ from real `t'ime 3~ calculations involving` data obtained by monitoring a selected observable system behavior.
`-~ ~SUMM~RY 9F THF I~V NTION
In accordance with the present i~Yention r a procedure for stabilization of living tissue pulsations . . .
W~94/04~1~ 2 1 ~ ~ ~ 2 9 PCT/U~93~09 involves monitoring the timing of intervals between pulsation beats and experimental determination of interbeat intervals in response to a single stimulus intervention pulse. Interbeat interval monitoring is performed during a learning phase typically lasting approximately 5 to 60 seconds in order to determine by real time calculation the approximate locations of t~e unstable fixed point of a chaotic regime at the intersection of its stable and unstable directions (manifolds) plotted as a function of the observable interbeat interval change. When the learning phase is completed, an intervention waiting period is instituted based on the close approach of interbeat interval timing to the unstable fixed point, such intervention ~eing based on switching of the chaotic regime to a periodic condition according to natural system behavior. Thus at the end of such waiting period, intervention by premature in~ection of a stimulus pulse causes a shi~t to an interbeat interval system state point as a variable, lying on the stable manifold path from which it monotonically approaches the unstable fixed point, by exclusive increase or decrease of such variable. An important aspect of the present invention therefore involves real time measurement and exploitation o~ the aforesaid natural behavior without any theoretical model.
The aforementioned intervention waiting period is terminated by said premature injection of the stimulus ; l ' pulsei causing advance of the interbeat interval 'and movement of the system` state point onto the stable manifold toward the unstable fixed point~ If the;next spontaneous pulse beat corresponds to ~an interbeat interval point close to the unstable fixed point, the intervention phase is terminated and the ~behavior stabilization program is recycled. Otherwise, another intervention stimulus pulse is injected before recycllng.
W094~04~9 PCT/VS93/0~09 2 ~ ~2r~
The foregoing behavior stabilization program of ~;
monitoring interbea~ intervals, performing real time ".
calculations and delaying prematur~ injection of ;~
stimulus pulses, if applied by way of ~xample to the control system of a cardiac pacemaker should restore or res~me peri~dic frequency beat.control activity~ Such ;~`
a behavior ~tabilization program is based on the recogniti~n that the chaotic regime of cardiac tissue is ~:~
characterized by natural moti~n of interbeat interval ` :.. :
points along unstable paths toward or away from the unstable fixed point and such chaos is controllable by ~ `
a properly delayed intervention of injected stimulus ;~
pul~es tending to shorten the interbeat interval.
Other objects, advantages and novel features of the ,,:
15 invention will bPcome apparent from the following ~.
detailed dascription of tha invention when considered in ~.
conjunction with the accompanying drawings. ~
. -RIEF DESCRIPTION OF DRAWING FIGURES
FIGS. lA, lB, lC and lD are yraphical p~ots of monophasic action potentials characterizing spontaneous periodic beating of cardiac tissue ~t a constant interbeat interval (lA), higher order periodîcities (lR, lC) and chaotic (lD) patterns.
FI~. 2 is a block dia~ram illustrating a :chaos : controlling system in accordance with one embodiment of : the invention.
FIG. 3 is a flow chart diagram of the software pro~ram associated ~ith the~computer~diagrammed ini'FIG.
FIG~ 4 is a graphical interbeat i~terval plot orPoin are map of the aperiodic phase of the induced : ~ ~` arrhythmia of animal cardiac tissue to which the present invention was applied.
FIGS. 5A and 5B are exemplary interbeat interval plots cor~esponding to FIG. 4,~ depicting: a chaos controlling sequence~
.. . .
2 ~ ~ 2 6 2~i :
WO94/04219 PCTiUS93/o~o9 `~
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DETAILED DESCRIPTION OF PREFERRED EMBODIMENT
In accordance with one embodiment of the invention, living tissue preparation in the form of an isolated wel}-perfused portion of the interventriciular septum from a rabbit heart was arterially perfused through a septal branch of its coronary artery with a physiologic oxygenated Kreb's solution at 37C. The tissue was stimulated by injection o~ 3 ms constant voltage pulse into a ~Grass SD9 stimulator connected to platinum electrodes in contact with the preparation and triggered by computetir control. Electrical activity was monitored to record monophasic action potentials through Ag-~gCl wires on the surface of the tissue. Monophasic action potentials and~a stimulus marker tracing were~recorded on a modified videocassette recorder (Model 4~0, A.R.
Vetter, Inc.) and one of the monophasic action potential: ,.,,t,~
traces was simultaneously digitized at 2 ~Hiz by a 12-bi~
A-D converter board (National Instruments Model~AT-MO-16). The digitized trace was processed on-line by:a 486 computer to detect the activation time:of each beat from the maximum of the first derivative of the vol~age:
Arrhythmias were~induced in the tissue by adding 2-5 ~M ouabain with or without 2-10 ~lM epinephrine~:to the arterial perfusate. :The mechanism of ouabain/epinephrine-induced arrhythmias;is probably a combination ~:of triggered actiYity and non~triggeretd ~utomaticity caused by progressive intracellular Ca2+
overload~ ~ ~from Na+ pump inhiibi~tion an~d incre~sed ~ lCa2+
30 current. The~ ressu~ltant oscillations ~in~ intracellul~air ; :~:: ~Ca2+ ~ caused spontaneous beating ~ by ~activating~
: ~ a~rhythmogenic inward currents from electrogenic ~Na~-Ca2t~
: exchan~e and;Ca2+ activated nonselective cation channels.
Typically the~ouaba:in/epinephrine combination ;induced 35 spontaneous: beatingl initially~ at a` cc~nstant interbeat interval :as~ graph;ically plotted ~ in: FI(;. lA, then : progressing to bigeminy:and high order periodicity,-~as W~94/042l9 PCT/US93/0~09 , ~4~77~9 6 ~
depicted in FIGS. lB and lC, before development of a highIy irregular aperiodic pattern of spontaneous ac~tivity in 85~ of the preparations as shown in FIG. l~.
The duration of the aperiodic phase was variable, lasting up to several minutes before electrical activity ceased, probably corresponding to progressive ~evere membrane depolarization`from Na~ pump inhibition. The spontaneous activity so induced showed a number of features symptomatic of chaos. Most importantly, in progressin~ from spontaneous beating at a fixed interbeat interval to highly aperiodic behavior, the arrhythmia passed through a series of transient stages that involved higher order periodicities. The arrhythmia then progressed to an aperiodic stage characteristic of a chaotic rather than a random process~
FIG. 2 diagrams a typical hardware arrangement associated with the foregoing embodiment of the invention, wherein tissue 10 hereinbefore ~escribed and arterially perfused, exhibited a pulsating behavioral activity. The concomitant electrical signal was detected by a monophasic action potential (MAP) type sensor 12 for digitization through an analog~to-digital converter 14. The output data of the converter 14 was ~ ....
fed to a chaos behavior controlling computer ~6 as diagrammed in FIG. 2. Chaos control by computer 16 was effected under a software program for monotonic intervention involving delivery of a stimulus pulse into tissue lOiafter a spontaneous pulse ~eat by mieansl'of a digital-to-analog converter 18 actuating a tiss~e stimulator and isolator 20 to energize a stimulus injector 22. Consequently, the intervening stimulus injection through injector 22 requiredi the computer 16 ~ to predict the timing of the next beat in order to anticiipate and shorten the interbeat interval.
Injection of the intervening stimulus by the hardware arrangement as diagrammed in FIG. 2, is under ~: .
WO94/0~219 P~T/US~3/0~09 ~`
. 7 control of the computer software program as diagrammed in FIG. 3. The tissue stimulator 20 may alternatively be a~tuated by a fixed periodic beat controller 30, such as a cardiac pacemaker, that is disabled by a chaos control switch 32 as also diagrammed in FIG. 2.
The software progxam of computer 16 consists of a learning phase section 34 and a control phase section 36 as diagrammed in FIG. 3. Entry of measurem2nt input data from probe 12 through converter 14 to computer 16 initiates the learning phase for real time calculation in accordance with the computer algorithm. Thus, interbeat interval data f~om converter 14 is repeatedly monitored in the computer 16 pursuant to step 40 of the software program until chaotic beating ocdurs. The interval data is then plotted pursuant to program step 42 to initiate the learning phase 34. Plotting of the intervals between chaotic beats involved use of delay indicating coordinates of current interbeat in~erval tIn) vs. previous interbeat interval (I~l) to determine first an unstable fixed point. When such fixed point is so determined by program step 42, two following system state points on the delay coordinate plot are examined during program step 44 to see if they are local or close to the fixed point within a radial distance ~, within which distance the local geometry is approximately linear. If such two points are local, the geometry is examined pursuant to program step 46 to ensure that it is a flip saddle. The points are then exa~ined during ; the next program step 48 to re-verify that the beats are not periodic. ~f any of the tests per~formed during the program steps 44, 46 and 48:fails, the Iearning phase is restarted as dia~rammed in FIG. 3. When all such tests are passed, the fixed point is re~alculated during program step 50 to~determine the local eigenvectors and the unst~able ~eigenvalue as components of the local : geometry. The magnitude of the eig nvalue (~u) is then tested during progra~ step 52 to determine if it is , $
WO94/04219 PCT/US93/0~09 2 ~ il 2 rt larger than unity. If not, beating is not chaotic and the learning phase is restarted as denoted in FIG. 3.
If ~u ~ 1, the program continues to the calculation step 54 for determination of the contravariant eigenvectors.
The final step 56 of the learning phase involves system perturbation to observe the resulting change în fixed point location. Such observation enables calculation of the quantities (g) and (C) hereinafter referred to and terminates the learning phase.
The control phase 36 is initiated upon termination of the learning phase 34, as diagrammed in FI~. 3, by program step 58 determining approach to the fixed point on the delay coordinate plot aforementioned. If the approach is close (within radial distance ~), the next calculation step 60 is triggered, whereby a stimulus pulse is inserted and another pulse emitted at the proper time for continued monitoring of interbeat intervals and to await another close approach to the fixed point.
As hereinbefore described, the aperiodic ~ehavior or arrhythmia induced in the tissue lO involved transient high order periodicities, as graphically depicted in FIG. 4 wherein the n~ interbeat interval (I~
has been plotted against the previous interval (I~l) at various stages. A typical sequence of interbeat intervals during induc d aperiodic beating is depicted wherein a shift in the state of the system from point 163 to 164 occurs toward an unstable fixed point 62 lying on the line of identity 64. Thuls point l163 lies - 30 close to stable manifold 66. Points 164 through 167 on the other hand diverge from khe unstable fixed point 62 and hence reveal an unstable ~anifold 68. The local geometry around fixed point 6~ in the plot of F~G. 4 is that of a saddle. In this case the saddle is a *lip saddle as aforementioned in connection with program step 46 in FIG, 3; that is, while the distances of successive state points 163-167 from the fixed point 62 :, `
WOg4~04219 PCT/US93/0~09 ~
- 21 ~ ~ 72 9 ` . ~ `:
monotonically increase in an exponential fashion along - :
.:. :-~ .
the unstable manifold 68 (one of the signs of chaos) the state points alternate on oppo~ite sides of the stable manifold 66. The flip saddle is manif~sted by a short interbeat interval followed by a long interval and vice versa.
In accordance with the present invention, perturbation of the syskem beiny monitored is effected when the state point monotonically approaches the unstable fixed point 62, such perturbation forcing the system state point onto the stable manifold 66 as depicted, for example, in FIG. 4. As a result, th~
system state point will naturally move toward the unstable fixed point 62 rather than away from it, in sharp contrast to prior art methods wherein the stable manifold 66 would instead be moved toward the current system state point. Pursuant to such prior art methods, as well as in the present invention, a linear approximation of the dynamics in the neighboxhood of the desired unstable fixed point 62 is utilized. According to prior art theory however, a system-wide parameter must be varied to move the stable manifold 66 toward the system state point, whereas movement of the system state point toward the stable manifold 66 by proportional perturbation feedback (PPF) is effected pursuant to the present invention without parameter change. Such proportional perturbation feedback (PPF~ method is particularly useful where the cardiac tissue preparation possesses no systemwide parameter tha~ can be;changed with suf~icient rapidity to implement corrective control.
The aforementioned proportional perturbation feedback procedure begins by determining the location ~F
of the unstable fixed point 62 as hereinbefore denoted by step 42 in FIG. 3, as well as its local stable and unstable manifolds 66 and 68. From such determinat~ons, the stable and unstable contra~ariant eigenvectors f5 and ~'' ' ';
W~9~/042~9 PCT~USg3/0~09 fu are derived as denoted by step 50 in FIG. 3~ If ~n iS
the location of the current system state point on the Poincare map of FIG. 4, and p is the prèdicted timing of .
the next natural beat as the system parameter, the -`
5 required advance in timing ~p is proportional` to the ~`
projection of the distance ~n ~ ~F onto the unstable .; .
manifold 68, expressed as~
~p = C(~ F) fu (l), ` ''; :`:'' ~. ' .: ',~,``
where: ~u 1 `- ;
C a l~
~U ~ 1 g o ~
~" ': '`..'`,"
Thus, the constant of proportionality C depends on the :;
unstable eigenvalue ~u~which determines the rate of the ~::
20 exponential divergence of the system from the fixed ::
point 62 along the unstable manifold 6~. The eigenvalue .~
~u is readily determined from the sequence of system `
state points 164 throuqh 167 as denoted in FIG. 4. The .:
ter~ g relates to the sensitivity of points near the fixed point 62 to the advance in timing ~p, and is approximated as~
~: ` g dp ~ ~
The constant C is thus inversely proportional to the : :
. j, . I I . . j ~ ; j I ~, ~
`' projection of g onto the unstable manifold. The system ~;
pertur~ation ~p represents the amount of time to shorten ~.
an anticipated natural beat (by introducting a stimulus) to force the state ~oint onto the stable manifold 6~.
The foreyoing proportional feedback control procedure is `:
performed during the aforeme~tioned learning and interveintion phases 34 and:36.
` During~ the learning phase 34, the interbeat "::
WOg4/04219 PCT/US93/0~09 2 1 '~ ~ 7 2 9 - . ~
interval is monitored until the approximate locations of the unstable fixed point 62 and the stable and unstable manifolds 66 and 68 are determined pursuant to the program diagrammed in FIG. 3. The application of equations ~1) and (2) during the intervention control phase 36 would then be straightforward once the ge~metry of the local plot around the fixed point 62 has bsen determined and the quantity ~ ha~ b~en found~ However the ti~sue 10 lacks an obvious system-wide parameter that could be changed rapidly enough to implement classical control. Accordingly, the interbeat interval, while not a system-wide parameter, is directly manipula~ed by shortening it with an electrically stimulated pulse pursuant to the present invention.
Therefore, the timing of the next interbeat interval is chosen as the analogue of the system parameter pq The sensitivity of the state point to changes in p was determined experimentally by noting the change in the interbeat interval in response to a single stimulus pulse when the state point was near the fixed point.
Thus, pursuant to methods heretofore based on the local geometry about an unstable fixed point, wherein electrically stimulated pulses move the stable manifold toward the state point of the system, the state point itself is moved toward the stable maniford of the system in accordance with the present invention by the interveninq stimuli.
The learning phase 34 typically lasts from 5 to 60 seconds, after which the chaos controllingialgorithm of 3~ comp~ter 16 waits- for the system to make a close approach to the unstable fixed point at a system state point ~ as depicted in FIG. 5A within circle 70 of radius ~. The next point would normally fall further out along the unstable manifold (as well as on the : 35 opposite side of the stable manifold)~ as indicated by point ~. However at this point the computer 16 :intervenes pursuant to its algorithm by injecting the ,-.,~. ' : .-,, ~
. ~,. , W0~4/04219 ~r~ P~T/U~g3/O~n9 electrical stimulus early enough so that the state point actually occurs at ~', lying directly below ~ and by construction near the stable manifold 660 Since the system is now close to the stable manifold, ideally the subsequent spontaneous beat would tend to move closer to the fixed point 62 along the stable manifold. Thus, state point ~ would be confined to the region near the unstable fixed point 6~, thereby regularizing the arrhythmia. However in actual practice this degree of accuracy was not typically obtained. FIG. 5B
illustrates the usual re~ultO When point ~' does not fall precisely on the stable manifold 66, point ~ often is not extremely close to the fixed point 62 (falls outside the circle 70) but still lies fairly close to the stable manifold (since ~' was close to the stable manifold). Nevertheless, point 7 lies closer to the stable manifold than point ~. Thus, the n~xt point falls within the circle 70 in the vicinity of ~ and restarts the cycle (as a new point ~. As the foregving procedural pattern is repeated, a periodic beating results. In this manner, the chaotic (arrhyt~mia) beating is made periodic by only intermittent stimuli.
The foregoing approach did not require any theoretical model and all quantities required were calculated in real time from the input data Using the algorithm hereinbefore set forth, control of the chaotic phase of the induced arrhythmia was successful in most experimental runs perform~d. When the arrhythmia became chaotic`j the c~aos control pro~ram was activated as hereinbefore indicated. The criter a for detecting chaos is the plot of FIG. 4 exhibiting stable and unstable manifolds with a flip saddle roughly along the linear part of the unstable manifold~680` More specifically, chaos detection involves an observed monotonic shift of the system state point towards ~he fixed point 62, thereby directionally determining the ~able manifold 66, followed by monotvnic shift from the ` ~
2 I ~ ~ 7 ~ 9 ` `` ~
fixed point along a clearly different direction corresponding to the unsta~le manifold 68. The chaos control program then chosei and delivPred electrical stimuli as previously described. In order to prove that chaos control was achieved and maintained (defined as a clear conversion of a chaotic sequen~ie to a periodi~
one) thP chaos control program was shut down and a return to chaotic be~avior was consistently observed sometimes preceded by transient complex periodicities.
Several observations were apparent from the pattern of the stimuli delivered by the chaos control program hereinbefore described. First, the stimuli did not simply overdrive the system. Stimuli were delivered sporadically, not on every beat and never more~than once in every three beats on average. The pattern of stimuli was initially erratic and aperiodic, but soon became approximately periodic as the arrhythmia was converted to a nearly periodic rhythm. Thus, the chaos control program rapidly converted the aperiodic behavior of the arrhythmia to a periodic rhythm~ In contrast, periodic pacing by controller 30, as depicted in FIG D 2, through which stimuli was heretofore delivered at a fixed rate was never effective in restoring a periodic rhythm and often made the aperiodicity more marked. Other pacings of an irregular type were heretofore similarly ineffective in converting chaotic to periodic behavior.
It is interesting to note that in sevexal cases chaos control in accoxdance with the present invention had the additional effect of eliminating the shortest islter~eat intervals, hence reducing the average rate Qf tachycardia. Without an understanding of the chaotic nature of the system, it would seem paradoxical that an intervention that could only shorten the i~terbeat intervals would result in a lengthening of thei average interval. However, since very long interbeat intervals tend to be followed by very short interbeat intervals (a consequence of the properties of the ~lip saddle~
WO94/04219 PCT/US93/0~09 elimination of the very long intervals also tend~ to eliminate very short intervals. In cases in which very :~
short intervals predominate during the arrhythmia, their :;
elimination during chaos control will tend to lengthen 5 the average interbeat interval between spontaneous :. .
beats. Thus, where chaos was successfully controlled, the chaotic pattern of the arrhythmia was converted to a low order periodic pattern.
Numerous other modifications and ~ariations of the lO present invention are possible in light of the foxegoing ~ ~
teachings~ Tt is therefore to be understood that within -::
the scope of the appended claims the invention may be practiced otherwise than as specifical1y descrlb-d.
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