Title of Invention	SYSTEM TO CARRY OUT THE METHOD OF DEFIBRILLATION VIA THE ELIMINATION OF SPIRAL TURBULENCE IN A MODEL FOR VENTRICULAR FIBRILLATION
Abstract	We propose a defibrillation method that uses a very-low-amplitude shock (of orderμA/cm2) applied for a brief duration (of order 100 ms) and over a coarse mesh of line electrodes on the ventricles (lower chambers of the heart). Ventricular fibrillation (VF) is turbulent cardiac electrical activity in which rapid, irregular disturbances in the spatiotemporal electrical activation of the heart makes it incapable of any concerted pumping action. VF is the major cause of sudden cardiac death. Present methods of controlling VF include electrical defibrillation as well as injected medication. Both methods yield results that are subject to chance. Electrical defibrillation, though widely used, involves subjecting the whole heart to massive, and often, counterproductive electrical shocks. In contrast, our proposed method uses very low amplitude shocks to provide a safe and efficient treatment of VF. Our proposed method is based on extensive numerical study of several models for ventricular fibrillation.

Title of Invention

SYSTEM TO CARRY OUT THE METHOD OF DEFIBRILLATION VIA THE ELIMINATION OF SPIRAL TURBULENCE IN A MODEL FOR VENTRICULAR FIBRILLATION

Abstract

We propose a defibrillation method that uses a very-low-amplitude shock (of orderμA/cm2) applied for a brief duration (of order 100 ms) and over a coarse mesh of line electrodes on the ventricles (lower chambers of the heart). Ventricular fibrillation (VF) is turbulent cardiac electrical activity in which rapid, irregular disturbances in the spatiotemporal electrical activation of the heart makes it incapable of any concerted pumping action. VF is the major cause of sudden cardiac death. Present methods of controlling VF include electrical defibrillation as well as injected medication. Both methods yield results that are subject to chance. Electrical defibrillation, though widely used, involves subjecting the whole heart to massive, and often, counterproductive electrical shocks. In contrast, our proposed method uses very low amplitude shocks to provide a safe and efficient treatment of VF. Our proposed method is based on extensive numerical study of several models for ventricular fibrillation.

Full Text	FIELD OF INVENTION This invention in general relates to Bio-Medical Engineering. Further this invention relates to Ventricular Fibrillation, a major cause of deaths through cardiac arrest, and more particularly, this invention relates to Elimination of Spiral Turbulence and further this invention relates to Defibrillation via Elimination of Spiral Turbulence in Models for Ventricular Fibrillation. The following description traces the state of the art in the technology in respect of Defibrillation via Elimination of Spiral Turbulence in Models for Ventricular Fibrillation. This invention offers solutions to overcome the limitations inherent in the present state of the art. PRESENT STATE OF THE ART Ventricular fibrillation (VF), the leading cause of sudden cardiac death, is responsible for about one out of every six deaths in the developed world [1]. If no defibrillation is attempted, death occurs in a few minutes. Earlier studies of VF have been carried out in various mammalian hearts [2] and mathematical models [3]. New experiments [4,5] show that VF is turbulent cardiac activity associated with the formation, and subsequent breakup, of electro-physiological spiral waves. Electrical defibrillation applies electrical jolts to the fibrillating heart to make it start beating normally again. It works only about two-thirds of the time and can sometimes damage the heart [6]. In external defibrillation, electrical shocks ( z 5 kV) are applied across the patient's chest; they depolarise all heart cells simultaneously and essentially reset the peacemaking nodes of the heart [7]. Slightly lower voltage ( z 600 V) suffice in open-heart condition in which the shock is applied directly on the heart's surface [8]. LIMITATIONS The main limitation of the elect cal defibrillation schemes in use at the moment is the usage of very high voltages while defibrillating the heart. Further recent mathematical models with low-amplitude defibrillation are not as efficient as this invention. Now the invention will be described in detail with reference to the drawings accompanying this specification. OBJECTS OF THE INVENTION It is the primary object of the invention to invent a novel method, which results in elimination of spiral turbulence leading to ventricular fibrillation. It is further an object of the invention to invent a system, which is efficient in preventing deaths because of ventricular fibrillation. Further objects of the invention will be clear from the description of the invention in the complete specification. PROPOSED SOLUTIONS Now this invention will be described in detail. The description of the invention will refer to the accompanying drawings of the complete specification. The descriptions will extensively deal with the nature of the invention and the manner in which it is to be performed. The statements of the drawings, which accompany this complete specification, are as follows: Fig 1: Shows pseudocolour plots showing the evolution of spatiotempral chaos through spiral breakup in the Panfilov model described in the text. Fig 2: Shows psuedocolour plots of the e field in dimension of = 2 for linear system sizes /. = 128 (top) and L = 512 (bottom) illustrating defibrillation in the Panfilov model by the use of the method of this invention. Fig 3: Shows isosurface (e = 0.6) plots of initial states (left panels) and pseudograyscale plots of the e field on the top square face of a Z. x L x L2 simulation domain, illustrating defibrillation. Fig 4: Shows pseudocolour plots (left panels) of the membrane potential V in the Beeler-Reuter model with L = 200 for times t = 2700 ms (top left), 2720 ms (top right), 2840 ms (bottom left) and 3020 ms (bottom right); pseudocolour plots of V with control (right panels) for the same initial conditions for t = 2700 ms (top left), 2720 ms (top right), 2840 ms (bottom left) and 3020 ms (bottom right). The control is effected by the method described here. Fig 5: Shows pseudocolour plots of the membrane potential V with control in the Luo-Rudy I model with L = 400 for times f = 30 ms (top left), 90 ms (top right), 150 ms (bottom left) and 210 ms (bottom right). The control is effected by the method described here. Before proposing the solution, the models used in the invention are given below: A model proposed by A. V. Panfilov for ventricular fibrillation [9] is used for this invention. For the purpose of illustration this model is used for isotropic cardiac tissues; the equations for the excitability e and recovery g are: Ventricular fibrillation in this model arises because the system evolves to a state In which large spirals break down [9,11]. This state Is a long -lived transient whose lifetime TL increases rapidly with L (e.g., for d = 2, TL ~ 850 ms for L = 100 whereas TL ~ 3200 ms for L = 128), in accord with the experimental finding that the hearts of small mammals are less prone to fibrillation than those of large mammals [12,13]. For time t » TILL, a state with e = g = 0 is obtained. If L > 128, TLIS sufficiently long that a non-equilibrium statistical steady state is established. Here it is shown that this state displays spatiotemporal chaos by calculating Yaupon exponents and showing that several are positive. The number of positive Lyapunov exponents increases with L (and the Kaplan-Yorke dimension DKY [14] increases from 7 to > 35 as L increases). Given that the long transient which leads to VF in model (1) is spatiotemporally chaotic, it may be guessed that the fields e and g have to be controlled globally to achieve defibrillation. In fact, some earlier studies [15] of spiral breakup in models for ventricular fibrillation have used global control. Here it is shown that a judicious choice of control points (on a mesh specified below) leads to an efficient defibrillation scheme for model (1). For d = 2, the simulation domain (of size L X L) is divided into K2 smaller blocks and we choose the mesh size such that it effectively suppresses the formation of spirals. For d = 3, the same control mesh is used but only on one of the square faces of the L x L x Lz simulation box. Now the invention will be described in detail with reference to the drawings, which accompany the Specification below. Pseudocolour plots showing the evolution of spatiotemporal chaos through spiral breakup in model (1) for physical times T between 880 ms and 1430 ms (Fig. 1) wherein the panels on the left show the excitability e and those on the right the recovery g for all points (x,y) on a two-dimensional L x L spatial grid with L = 128. In the defibrillation scheme a pulse is applied to the e field on a mesh composed of lines of width 35x. A network of such lines is used to divide the region of simulation into square blocks whose length in each direction is fixed at a constant value L/K for the duration of control. (The blocks adjacent to the boundaries can turn out to be rectangular.) The essential point here is that, if a pulse is applied to the field at all points along the mesh boundaries for a time Tc, then it effectively simulates Neumann boundary conditions (for the block bounded by the mesh) in so far as it absorbs spirals formed inside this block. Note that Tc is not large at all since the individual blocks into which the mesh divides the system are of a linear size L/K which is so small that it does not sustain long, spatiotemporally chaotic transients. Nor does K, related to the mesh density, have to be very large since the transient lifetime, TL, decreases rapidly with decreasing L. It is found that, for d = 2, L = 128, K =2 and Tc = 44ms. For d = 2, L = 512, K =8 and Tc= 704 ms suffices. Finally it is shown that a slight modification of our defibrillation scheme also works for d = 3 (Fig.3). Pseudocolour plots of the e field in d=2 for L = 128 (top) and L = 512 (bottom) illustrating defibrillation by the control of spiral breakup ( Fig. 2 ) wherein the control mesh divides the domain into four equal squares for L = 128 and , for L= 512, into 49 equal squares, 28 equal rectangles along the edges and 4 small equal squares on the corners. For L =128, 57.3 μ A/cm2 is applied from T = 891 ms to T = 935 ms and by T > 1500 ms spatiotemporal chaos is all but eliminated ((e\|, \g\ <_10 all grid points for l="512," a is applied from t="55" ms to the e field. by spatiotemporal chaos but eliminated at> Isosurface (e = 0.6 ) plots of initial states (left panels) and pseudograyscale plots of the e field on the top square face (right panels ) illustrating defibrillation by the control of spiral breakup as in model (1) (Fig. 3) for d = 3: (top) L = 128 and Lz = 16, with the control mesh dividing the top face into 4 equal squares; and (bottom) L = 256 and Lz = 8, with the control mesh dividing the top face into 64 equal squares. In both cases pulses is applied on the control mesh (top face only) of 57.3 μ A/cm2 with Tip = 22 ms and Tw = 0.11ms. In the former case, with n= 15, spatiotemporal chaos is all but eliminated by T = 1760 ms ( \|e\|, \|sf\| The efficiency of the defibrillation scheme is fairly insensitive to the height of the pulse applied to the e field along the control mesh so long as this height is above a threshold. To obtain the value of e in mV units it is scaled at the peak amplitude of a spike in the e field (which has an amplitude of 0.9 in dimensionless units) to be equal to 110 mV. The latter is a representative average value of the peak voltage of an electrical wave in the heart [12]. With this voltage scaling, dimensioned excitability is computed as 110/0.9 ~ 122.22 mV times dimensionless excitability. It is found, e.g., that, for L = 128, the smallest pulses which yields defibrillation is 57.3 mV/ms for the parameter values are used; however, it was checked that even stronger pulses (e.g.,278.3 mV/ms) also lead to defibrillation. A capacitance density of 1 (jF/cm2 (21) is used, which then yields a current density of 57.3\|jA/cm2. Note that, this threshold is of the order of the smallest potential (z22.18 μ A/cm2) required to trigger an action potential spike in the Panfilov model with g =0. The nullclines for the model, in the absence of the Appalachian, are such that, this smallest potential increases with increasing g. This is physically consistent with the increase in the refractory nature of the heart tissue with increasing g. It has been checked that (a) small, local deformations of the control mesh or (b) the angle of the mesh axes with the boundaries do not affect the efficiency of the defibrillation scheme. Furthermore the application of the control pulse on the control mesh does not lead to an instability of the quiescent state; thus it cannot inadvertently promote VF. It is checked specifically that, with e = 0, g = 0 as the initial condition at all spatial points, a wave of activation travels across the system when the control pulse is initiated. This travels quickly (~ 200 ms for L = 128) to the boundary where it is absorbed and quiescence is restored. The defibrillation method also works if g is stimulated instead of e. This can be implemented by pharmaceutical means in an actual heart. The two-dimensional defibrillation scheme above applies without any change to thin slices of cardiac tissue. However, it is important to investigate whether it can be extended to three dimensions, which is clearly required for real ventricles. A naive extension of the mesh into a cubic array of sheets will, of course, succeed in achieving defibrillation. However, such an array of control sheets cannot be easily implanted in a ventricle. We have tried to see, therefore, if the turbulence in a three-dimensional version of model (1) on a L x L x Lz domain can be controlled with the control mesh present only on one L x L face. For the open faces open boundary conditions are used and for the other faces no-flux Neumann boundary conditions are used. The defibrillation scheme works if Lz 4. A slight modification of this scheme is effective even for Lz > 4: Instead of applying a pulse for a duration Tc, a sequence of n pulses is used separated by a time Tip and each of duration Tw. It is found that, if L=256 and Lz =8, defibrillation occurs in z 2002 ms with Tp = 22ms, Tw = 0.11ms, n = 30 and a control pulse amplitude of 57.3 nA/cm2; if L=128 and Lz =16, defibrillation occurs in ~ 1760ms with Tp = 22 ms, Tw = 0.11 ms, n=15 and a control pulse amplitude of 57.3 \xfiJcm2. It is further found that optimal defibrillation is obtained in the model if Tip is close to the absolute refractory period for model (1) without the Laplacian term. The proposed defibrillation method has also been used for more realistic models of ventricular fibrillation: the Beeler-Reuter model [16] and the Luo-Rudy i model [17]. Representative data from these models are shown in Figs. 4 and 5, respectively. ADVANTAGES OF THE INVENTION Typical electrical defibrillation schemes use much higher voltages than in this study. Recent studies [15,18] have explored low-amplitude defibrillation methods in model systems. They constitute an advance over conventional methods, but lack some of the appealing features of our defibrillation scheme. For example, the scheme of Ref. [15] works only when the slow variable (the analogue of our g) is controlled; though this can be done, in principle, by pharmaceutical means, it is clearly less direct than control via electrical means. Reference [18] uses electrical defibrillation, but has been demonstrated to prevent only one spiral from breaking up, as opposed to the suppression of a spatiotemporally chaotic state with broken spirals by the defibrillation scheme described here. It has been checked explicitly that, for the spatiotemporally chaotic state of model (1), a straightforward implementation of the defibrillation scheme of Ref. [18] is ineffective. [This scheme applies pulses to the fast variable (e in model (1)) on a two-dimensional, discrete lattice of points.] The control current density in Ref. [18] is ~ 57.3 μA/cm2 , which is much lower than 139μA/cm2 , the maximum value of the ionic current during depolarization in the Beeler-Reuter model. It is been checked that the defibrillation scheme described above is not sensitively model dependent. We have shown by explicit calculations that our low-voltage defibrillation scheme which uses a control mesh also works for the biologically realistic Beeler-Reuter and Luo-Rudv I models in d = 2for VF References: [1] American Heart Disease Statistics on WWW (URL: http://sln.fi.edu/biosci/healthy/stats.html). [2] A. T. Winfred, Chaos 8,1 (1998). [3] Computational Biology of the Heart, edited by A V. Panfilov and A V. Holden (Wiley, Chichester, 1997). [4] J. Jalife, R. A Gray, G. E. Morley and J. M. Davidenko, Chaos 8,79 (1998). [5] R. A Gray, A M. Pertsov and J. Jalife, Nature 392,75 (1998); F.X. Witkowski, L.J. Leon, P.A Penkoske, W.R. Giles, M.L, Spano, W.L. Ditto and AT. Winfree, Nature 392,78 (1998). [6] R. Pool, Science 247,1294 (1990). [7] M. S. Eisenberg, L. Bergner, A, P. Hallstrom and R. O. Cummins, Sci. Am. 254,25 (1986). [8] L. W. Piller, Electronic Instrumentation Theory of Cardiac Technology (Staples Press, London, 1970). [9] A V. Panfilov and P. Hogeweg, Phys. Lett. A 176,295 (1993); A V. Panfilov, Chaos 8,57 (1998). [10] W. H. Press, S. A Teukolsky, W. T. Vetterling and B. P. Flannery, Numerical Recipes in C (Cambridge Univ. Press, London, 1995). [II] S. Sinha, A Pande and R. Pandit, Phys. Rev. Lett. 86,3678 (2001). [12] A T. Winfree, When Time Breaks Down (Princeton University Press, Princeton, 1987). [13] Y.-H. Kim, A Garfinkel, T. Ikeda, T.-J. Wu, C. A Athill, J. N. Weiss, H. S. Karagueuzian and P.-S. Chen, J. Clin. Invest. 100,2486 (1997). [14] We calculate the Kaplan-Yorke dimension using the method outlined in [20]. [15] G. V. Osipov and J. J. Collins, Phys. Rev. E 60, 54 (1999). [16] G. W. Beeler and H. Reuter, J. Physiologic. 268, 177 (1977). [17] C. H. Lou and Y. Rudy, Ore. Res. 68,1501 (1991). [18] W-J. Rappel, F. Fenton and A Karma, Phys. Rev. Left. 83,456 (1999). I Claim: 1. An improved system for ventricular defibrillation such as herein described characterized in that means are provided for applying low amplitude pulses on a mesh electrode placed on the surface of the ventricles to eliminate spiral turbulance (if any) occurring in the human body. 2. An improved system for ventricular defibrillation as claimed in claim 1, wherein the said means for applying low amplitude pulses are provided in both two and three-dimensional VF models.

Full Text

FIELD OF INVENTION
This invention in general relates to Bio-Medical Engineering. Further this invention relates to Ventricular Fibrillation, a major cause of deaths through cardiac arrest, and more particularly, this invention relates to Elimination of Spiral Turbulence and further this invention relates to Defibrillation via Elimination of Spiral Turbulence in Models for Ventricular Fibrillation.
The following description traces the state of the art in the technology in respect of Defibrillation via Elimination of Spiral Turbulence in Models for Ventricular Fibrillation. This invention offers solutions to overcome the limitations inherent in the present state of the art.
PRESENT STATE OF THE ART
Ventricular fibrillation (VF), the leading cause of sudden cardiac death, is responsible for about one out of every six deaths in the developed world [1]. If no defibrillation is attempted, death occurs in a few minutes. Earlier studies of VF have been carried out in various mammalian hearts [2] and mathematical models [3]. New experiments [4,5] show that VF is turbulent cardiac activity associated with the formation, and subsequent breakup, of electro-physiological spiral waves. Electrical defibrillation applies electrical jolts to the fibrillating heart to make it start beating normally again. It works only about two-thirds of the time and can sometimes damage the heart [6]. In external defibrillation, electrical shocks ( z 5 kV) are applied across the patient's chest; they depolarise all heart cells simultaneously and essentially reset the peacemaking nodes of the heart [7]. Slightly lower voltage ( z 600 V) suffice in open-heart condition in which the shock is applied directly on the heart's surface [8].
LIMITATIONS

The main limitation of the elect cal defibrillation schemes in use at the moment is the usage of very high voltages while defibrillating the heart. Further recent mathematical models with low-amplitude defibrillation are not as efficient as this invention.
Now the invention will be described in detail with reference to the drawings accompanying this specification.
OBJECTS OF THE INVENTION
It is the primary object of the invention to invent a novel method, which results in elimination of spiral turbulence leading to ventricular fibrillation.
It is further an object of the invention to invent a system, which is efficient in preventing deaths because of ventricular fibrillation.
Further objects of the invention will be clear from the description of the invention in the complete specification.
PROPOSED SOLUTIONS
Now this invention will be described in detail. The description of the invention will refer to the accompanying drawings of the complete specification. The descriptions will extensively deal with the nature of the invention and the manner in which it is to be performed.
The statements of the drawings, which accompany this complete specification, are as follows:

Fig 1: Shows pseudocolour plots showing the evolution of spatiotempral chaos through spiral breakup in the Panfilov model described in the text.
Fig 2: Shows psuedocolour plots of the e field in dimension of = 2 for linear system sizes /. = 128 (top) and L = 512 (bottom) illustrating defibrillation in the Panfilov model by the use of the method of this invention.
Fig 3: Shows isosurface (e = 0.6) plots of initial states (left panels) and pseudograyscale plots of the e field on the top square face of a Z. x L x L2 simulation domain, illustrating defibrillation.
Fig 4: Shows pseudocolour plots (left panels) of the membrane potential V in the Beeler-Reuter model with L = 200 for times t = 2700 ms (top left), 2720 ms (top right), 2840 ms (bottom left) and 3020 ms (bottom right); pseudocolour plots of V with control (right panels) for the same initial conditions for t = 2700 ms (top left), 2720 ms (top right), 2840 ms (bottom left) and 3020 ms (bottom right). The control is effected by the method described here.
Fig 5: Shows pseudocolour plots of the membrane potential V with control in the Luo-Rudy I model with L = 400 for times f = 30 ms (top left), 90 ms (top right), 150 ms (bottom left) and 210 ms (bottom right). The control is effected by the method described here.
Before proposing the solution, the models used in the invention are given below:
A model proposed by A. V. Panfilov for ventricular fibrillation [9] is used for this invention. For the purpose of illustration this model is used for isotropic cardiac tissues; the equations for the excitability e and recovery g are:

Ventricular fibrillation in this model arises because the system evolves to a state In which large spirals break down [9,11]. This state Is a long -lived transient whose lifetime TL increases rapidly with L (e.g., for d = 2, TL ~ 850 ms for L = 100 whereas TL ~ 3200 ms for L = 128), in accord with the experimental finding that the hearts of small mammals are less prone to fibrillation than those of large mammals [12,13]. For time t » TILL, a state with e = g = 0 is obtained. If L > 128, TLIS sufficiently long that a non-equilibrium statistical steady state is established. Here it is shown that this state displays spatiotemporal chaos by calculating Yaupon exponents and showing that several are positive. The number of

positive Lyapunov exponents increases with L (and the Kaplan-Yorke dimension DKY [14] increases from 7 to > 35 as L increases).
Given that the long transient which leads to VF in model (1) is spatiotemporally chaotic, it may be guessed that the fields e and g have to be controlled globally to achieve defibrillation. In fact, some earlier studies [15] of spiral breakup in models for ventricular fibrillation have used global control. Here it is shown that a judicious choice of control points (on a mesh specified below) leads to an efficient defibrillation scheme for model (1). For d = 2, the simulation domain (of size L X L) is divided into K2 smaller blocks and we choose the mesh size such that it effectively suppresses the formation of spirals. For d = 3, the same control mesh is used but only on one of the square faces of the L x L x Lz simulation box.
Now the invention will be described in detail with reference to the drawings, which accompany the Specification below.
Pseudocolour plots showing the evolution of spatiotemporal chaos through spiral breakup in model (1) for physical times T between 880 ms and 1430 ms (Fig. 1) wherein the panels on the left show the excitability e and those on the right the recovery g for all points (x,y) on a two-dimensional L x L spatial grid with L = 128.
In the defibrillation scheme a pulse is applied to the e field on a mesh composed of lines of width 35x. A network of such lines is used to divide the region of simulation into square blocks whose length in each direction is fixed at a constant value L/K for the duration of control. (The blocks adjacent to the boundaries can turn out to be rectangular.) The essential point here is that, if a pulse is applied to the field at all points along the mesh boundaries for a time Tc, then it effectively simulates Neumann boundary conditions (for the block bounded by the mesh) in so far as it absorbs spirals formed inside this block. Note that Tc is not large at all since the individual blocks into which the mesh divides the system are of a linear size L/K which is so small that it does not

sustain long, spatiotemporally chaotic transients. Nor does K, related to the mesh density, have to be very large since the transient lifetime, TL, decreases rapidly with decreasing L. It is found that, for d = 2, L = 128, K =2 and Tc = 44ms. For d = 2, L = 512, K =8 and Tc= 704 ms suffices. Finally it is shown that a slight modification of our defibrillation scheme also works for d = 3 (Fig.3).
Pseudocolour plots of the e field in d=2 for L = 128 (top) and L = 512 (bottom) illustrating defibrillation by the control of spiral breakup ( Fig. 2 ) wherein the control mesh divides the domain into four equal squares for L = 128 and , for L= 512, into 49 equal squares, 28 equal rectangles along the edges and 4 small equal squares on the corners. For L =128, 57.3 μ A/cm2 is applied from T = 891 ms to T = 935 ms and by T > 1500 ms spatiotemporal chaos is all but eliminated ((e|, \g\ <_10 all grid points for l="512," a is applied from t="55" ms to the e field. by spatiotemporal chaos but eliminated at> Isosurface (e = 0.6 ) plots of initial states (left panels) and pseudograyscale plots of the e field on the top square face (right panels ) illustrating defibrillation by the control of spiral breakup as in model (1) (Fig. 3) for d = 3: (top) L = 128 and Lz = 16, with the control mesh dividing the top face into 4 equal squares; and (bottom) L = 256 and Lz = 8, with the control mesh dividing the top face into 64 equal squares. In both cases pulses is applied on the control mesh (top face only) of 57.3 μ A/cm2 with Tip = 22 ms and Tw = 0.11ms. In the former case, with n= 15, spatiotemporal chaos is all but eliminated by T = 1760 ms ( |e|, |sf| The efficiency of the defibrillation scheme is fairly insensitive to the height of the pulse applied to the e field along the control mesh so long as this height is above a threshold. To obtain the value of e in mV units it is scaled at the peak amplitude of a spike in the e field (which has an amplitude of 0.9 in dimensionless units) to be equal to 110 mV. The latter is a representative

average value of the peak voltage of an electrical wave in the heart [12]. With this voltage scaling, dimensioned excitability is computed as 110/0.9 ~ 122.22 mV times dimensionless excitability. It is found, e.g., that, for L = 128, the smallest pulses which yields defibrillation is 57.3 mV/ms for the parameter values are used; however, it was checked that even stronger pulses (e.g.,278.3 mV/ms) also lead to defibrillation. A capacitance density of 1 (jF/cm2 (21) is used, which then yields a current density of 57.3|jA/cm2. Note that, this threshold is of the order of the smallest potential (z22.18 μ A/cm2) required to trigger an action potential spike in the Panfilov model with g =0. The nullclines for the model, in the absence of the Appalachian, are such that, this smallest potential increases with increasing g. This is physically consistent with the increase in the refractory nature of the heart tissue with increasing g.
It has been checked that (a) small, local deformations of the control mesh or (b) the angle of the mesh axes with the boundaries do not affect the efficiency of the defibrillation scheme. Furthermore the application of the control pulse on the control mesh does not lead to an instability of the quiescent state; thus it cannot inadvertently promote VF. It is checked specifically that, with e = 0, g = 0 as the initial condition at all spatial points, a wave of activation travels across the system when the control pulse is initiated. This travels quickly (~ 200 ms for L = 128) to the boundary where it is absorbed and quiescence is restored. The defibrillation method also works if g is stimulated instead of e. This can be implemented by pharmaceutical means in an actual heart.
The two-dimensional defibrillation scheme above applies without any change to thin slices of cardiac tissue. However, it is important to investigate whether it can be extended to three dimensions, which is clearly required for real ventricles. A naive extension of the mesh into a cubic array of sheets will, of course, succeed in achieving defibrillation. However, such an array of control sheets cannot be easily implanted in a ventricle. We have tried to see, therefore, if the turbulence in a three-dimensional version of model (1) on a L x L x Lz domain can be controlled with the control mesh present only on one L x L face. For the open

faces open boundary conditions are used and for the other faces no-flux Neumann boundary conditions are used. The defibrillation scheme works if Lz 4. A slight modification of this scheme is effective even for Lz > 4: Instead of applying a pulse for a duration Tc, a sequence of n pulses is used separated by a time Tip and each of duration Tw. It is found that, if L=256 and Lz =8, defibrillation occurs in z 2002 ms with Tp = 22ms, Tw = 0.11ms, n = 30 and a control pulse amplitude of 57.3 nA/cm2; if L=128 and Lz =16, defibrillation occurs in ~ 1760ms with Tp = 22 ms, Tw = 0.11 ms, n=15 and a control pulse amplitude of 57.3 \xfiJcm2. It is further found that optimal defibrillation is obtained in the model if Tip is close to the absolute refractory period for model (1) without the Laplacian term.
The proposed defibrillation method has also been used for more realistic models of ventricular fibrillation: the Beeler-Reuter model [16] and the Luo-Rudy i model [17]. Representative data from these models are shown in Figs. 4 and 5, respectively.
ADVANTAGES OF THE INVENTION
Typical electrical defibrillation schemes use much higher voltages than in this study. Recent studies [15,18] have explored low-amplitude defibrillation methods in model systems. They constitute an advance over conventional methods, but lack some of the appealing features of our defibrillation scheme. For example, the scheme of Ref. [15] works only when the slow variable (the analogue of our g) is controlled; though this can be done, in principle, by pharmaceutical means, it is clearly less direct than control via electrical means. Reference [18] uses electrical defibrillation, but has been demonstrated to prevent only one spiral from breaking up, as opposed to the suppression of a spatiotemporally chaotic state with broken spirals by the defibrillation scheme described here. It has been checked explicitly that, for the spatiotemporally chaotic state of model (1), a straightforward implementation of the defibrillation scheme of Ref. [18] is

ineffective. [This scheme applies pulses to the fast variable (e in model (1)) on a two-dimensional, discrete lattice of points.] The control current density in Ref. [18] is ~ 57.3 μA/cm2 , which is much lower than 139μA/cm2 , the maximum value of the ionic current during depolarization in the Beeler-Reuter model.
It is been checked that the defibrillation scheme described above is not sensitively model dependent. We have shown by explicit calculations that our low-voltage defibrillation scheme which uses a control mesh also works for the biologically realistic Beeler-Reuter and Luo-Rudv I models in d = 2for VF

References:
[1] American Heart Disease Statistics on WWW (URL:
http://sln.fi.edu/biosci/healthy/stats.html).
[2] A. T. Winfred, Chaos 8,1 (1998).
[3] Computational Biology of the Heart, edited by A V. Panfilov and A V. Holden (Wiley, Chichester, 1997).
[4] J. Jalife, R. A Gray, G. E. Morley and J. M. Davidenko, Chaos 8,79 (1998).
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I Claim:
1. An improved system for ventricular defibrillation such as herein described
characterized in that means are provided for applying low amplitude pulses
on a mesh electrode placed on the surface of the ventricles to eliminate
spiral turbulance (if any) occurring in the human body.
2. An improved system for ventricular defibrillation as claimed in claim 1,
wherein the said means for applying low amplitude pulses are provided in
both two and three-dimensional VF models.

Documents:

0459-mas-2001 abstract duplicate.pdf

0459-mas-2001 abstract.pdf

0459-mas-2001 claims duplicate.pdf

0459-mas-2001 claims.pdf

0459-mas-2001 correspondence others.pdf

0459-mas-2001 correspondence po.pdf

0459-mas-2001 description (complete) duplicate.pdf

0459-mas-2001 description (complete).pdf

0459-mas-2001 drawings duplicate.pdf

0459-mas-2001 drawings.pdf

0459-mas-2001 form-1.pdf

0459-mas-2001 form-13.pdf

0459-mas-2001 form-19.pdf

0459-mas-2001 form-26.pdf

0459-mas-2001 form-4.pdf

0459-mas-2001 form-5.pdf

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Patent Number

199042

Indian Patent Application Number

459/MAS/2001

PG Journal Number

08/2007

Publication Date

23-Feb-2007

Grant Date

01-Mar-2006

Date of Filing

11-Jun-2001

Name of Patentee

PROF. RAHUL PANDIT,

Applicant Address

INDIAN INSTITUTE OF SCIENCE, BANGALORE 560012

Inventors:

#	Inventor's Name	Inventor's Address
1	PROF. RAHUL PANDIT,	INDIAN INSTITUTE OF SCIENCE, BANGALORE 560012

PCT International Classification Number

A61N1/39

PCT International Application Number

N/A

PCT International Filing date

PCT Conventions:

#	PCT Application Number	Date of Convention	Priority Country
1			NA