Abstract:
The present invention discloses a method and device in which an external defibrillator is integrated with an algorithm implemented in a programmable microprocessor which controls and manages the formation of defibrillation waveforms. The waveforms are dynamically adjusted and created to be consistent with a myocardial cell response waveform. Dynamic tilt calculations based on time slices and corresponding fit functions based on best-fit models are used to generate the waveforms. The waveforms include a first and a second phase and are formed with minimal delay therebetween.

Description:
REFERENCE TO RELATED APPLICATION 
     This is a Continuation of Application Ser. No. 08/881,662, filed Jun. 24, 1997 now U.S. Pat. No. 5,991,650, the entire disclosure of which is hereby incorporated by reference. 
     This application is based on U.S. Provisional Application Ser. No. 60/020,525, filed Jul. 1, 1996, and entitled “Continual Waveform Shape Reforming Method and Apparatus for Transchest Resistance Dynamics” the contents of which are herein incorporated by reference and to which priority under 35 U.S.C. §119 is claimed. 
    
    
     FIELD OF THE INVENTION 
     The present invention generally relates to dynamic and autonomous shape-correction of defibrillation waveforms in external defibrillators. More specifically, the present invention relates to a method and apparatus for continual shape-correction of monophasic or biphasic defibrillation waveforms based on parameters which vary during the delivery of the defibrillation pulse to a cardiac patient. 
     BACKGROUND OF THE INVENTION 
     Defibrillation waveforms are typically defined by the energy expended during the delivery of the waveform. The parameters defining the energy are voltage, current and time. Generally, most defibrillator devices use a preset voltage, and assume the impedance of the heart to be about 50Ω. Thus, only the time parameter is a variable. This means that energy delivery is, at best, an approximation based on a range of preset values. The operational specifications for defibrillation waveforms in accordance with the standards of the Association for the Advancement of Medical Instrumentation (AAMI) is indicated to be at a 40% level of accuracy across impedance ranges. 
     Prior art devices use a single measurement of current at the beginning of a waveform to calculate the resistance. The duration or time is then adjusted to construct the correct energy during the delivery of the defibrillation pulse. One of the limitations of this approach is that it assumes the resistance remains constant throughout the defibrillation pulse delivery. Studies regarding capacitative discharge waveforms demonstrate that electrical impedance increases as voltage decreases, and that this relationship is not simply due to the Ohm&#39;s Law. For the stimulation of excitable biological tissues, current decreases at a faster rate than does voltage. This non-linear relationship between impedance and voltage is largely due to the electrode-tissue interface. ( Low Voltage Shocks have a Significantly Higher Tilt of the Internal Electric Field Than Do High Voltage Shocks , by James E. Brewer, et al, Pacing and Clinical Electrophysiology, Volume 18, No. 1, January 1995). 
     The assumption that resistance remains constant is particularly erroneous in light of the transchest/transthoracic application shock delivery involving external defibrillators (EDs). The transchest discharge of shock pulses involves chest resistances which include chest wall resistance, lung series resistance, lung parallel resistance, thoracic cage resistance, in addition to resistance of heart and heart cell membrane. Further, external defibrillators are generally used on random patients under emergency situations. Thus patient variability increases the possible variance of resistance across patients. Realizing this, the assumptions and design parameters of the prior art are inadequate to provide a robust and reliable defibrillation pulse delivery suited for implementation in ED devices. 
     The shape of a defibrillation waveform is a critical element in the successful delivery of a defibrillation waveform. Specifically, prior art defibrillation pulses for monophasic or biphasic waveforms include preset parameters which are used to structure the waveform. For biphasic waveforms, these parameters include an initial voltage of φ 1  and its duration or tilt, and an initial voltage of φ 2  and its duration or tilt. Additionally, the interphase duration between φ 1  and φ 2  is set to account for interphase delay required to switch from one phase to the other. 
     Prior art waveform generation assumptions and calculations contain several limitations. Specifically, the waveforms are not congruent with the myocardial cell response. The theory of myocardial cell response is based on the observation that φ 1  defibrillates the heart and for biphasic waveforms φ 2  performs a stabilizing action that keeps the heart from refibrillating by canceling out (burping) any residual charges in the myocardial cells. For monophasic waveforms, these parameters include the initial voltage and the pulse duration or tilt. Further, the efficacy and advantages of monophasic and biphasic waveform pulses is significantly enhanced if the phases are shaped to simulate the myocardial cell response waveform. For biphasic waveforms, the congruence in simulation between the waveform and the myocardial cell response requires that the residual charges be removed immediately after the delivery of φ 1 . This implies that there should be no interphase delay between the phases. Moreover, the dynamically changing parameters such as the resistance and the myocardial cell response require that the waveform tilt equation and the duration of the phases must take these variables into account. 
     Accordingly, there is a need to provide a method and device to enable an autonomous and accurate delivery of a monophasic or biphasic defibrillation waveform which is compatible with the dynamic myocardial cell response in a variable resistance environment. 
     SUMMARY OF THE INVENTION 
     The present invention provides an autonomous method and device to continually and dynamically reform the shape of a defibrillation waveform consistent with a myocardial cell response profile. Particularly, the invention is focused on continual waveform shape-correction for variable resistances encountered in the transchest delivery of defibrillation pulses to random patients. 
     The present invention divides the defibrillation waveform into discrete time-slices. The time slices may be fixed or variable increments of time slices. For example, a typical time-slice may be 1 millisecond. The voltage and the current are measured at each time slice and the instantaneous resistance is calculated for each measurement at each time-slice. In this manner the value of the variable resistance is monitored based on the selected time-slice. A highly refined and accurate monitoring of the variability of the resistance can be executed by choosing a smaller time-slice. Therefore, if voltage and current or resistance are monitored throughout the waveform, the actual energy can be adjusted even if the resistance is fluctuating from one time-slice to the next. Thus, the present invention enables a dynamic adjustment of the duration of the phase of a monophasic waveform or each phase of a biphasic waveform relative to the change in resistance. A dynamic waveform tilt equation is generated by an algorithm to operate the defibrillation discharge consistent with the variability of resistance and the myocardial cell response. 
     Accordingly, it is an object of the present invention to provide a reliable method and device for delivering dynamically shaped continuous exponential defibrillation pulses to a cardiac patient via electrodes. The electrodes are connected to a voltage source and a control circuit of an external defibrillator device wherein an algorithm implemented in the control circuit imposes a stopping rule to create waveforms which comply with the variability of resistance and the myocardial cell response waveform of the patient. Generally, the method includes continuously measuring a discharge voltage and current based on discrete time slices. The time slices include an initial time slice and a series of other discrete time slices. The resistance is calculated relative to the voltage and current measurements at each time slice. Two waveform tilts are then calculated at each time slice. The first waveform tilt, the actual waveform tilt, is the tilt calculated as the difference between the initial pulse voltage and the voltage measured at each time slice. The second waveform tilt, the cell response waveform tilt, is the tilt calculated according to the myocardial cell response model. The delivery of the pulse is continued and a string of calculations yielding these two waveform tilts and voltages are calculated for each of the time slices. The delivery of the pulse is suspended when the actual waveform tilt becomes greater than or equal to the cell response waveform tilt. 
     It is a further object of the present invention to provide a reliable and adjustable defibrillation pulse energy device for transchest defibrillation shock treatment of a random patient such that a phase independent algorithm, implemented in the device, generates a waveform from a tilt expression. The tilt expression is dynamically set for a monophasic waveform and for each phase of a biphasic waveform and is a function of resistance. The tilt expression is based on resistance measurements at the electrode-tissue boundaries and in compliance with myocardial cell response. 
     With these and other objects, advantages and features of the invention that may become hereinafter apparent, the nature of the invention may be more clearly understood by reference to the following detailed description of the invention, the appended claims and to the drawings herein. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a block diagram of a capacitor charge control circuit associated with the present invention 
     FIG. 2 illustrates one embodiment of the monitoring circuit illustrated in FIG.  1 . 
     FIG. 3 is a block diagram of a capacitor bank selector an isolation subsystem useful in the practice of the present invention. 
     FIG. 4 is a more detailed block diagram of an individual selector, driver and control useful in the practice of the present invention. 
     FIG. 5 is a cell response model useful in setting the theoretical background for the transchest waveform design of the present invention. 
     FIG. 6 is a block diagram of the hardware associated with the pulse delivery algorithm of the present invention. 
     FIG. 7 is a flow chart of the delivery algorithm logic. 
     FIG. 8A is a biphasic shock pulse and the associated myocardial cell response generated in accordance with the present invention using Blair-Walcott theory of maximal cell response for the first phase and 1 st  order charge burping for the second phase. 
     FIG. 8B is a biphasic shock pulse and the associated myocardial cell response generated in accordance with the present invention using Blair-Walcott theory of maximal cell response for the first phase and 2 nd  order charge burping for the second phase. 
     FIG. 8C is a biphasic shock pulse and the associated myocardial cell response generated in accordance with the present invention using Kroll-Irnich theory of effective current for the first phase and 1 st  order charge burping for the second phase. 
     FIG. 8D is a biphasic shock pulse and the associated myocardial cell response generated in accordance with the present invention using Kroll-Irnich theory of effective current for the first phase and 2 nd  order charge burping for the second phase. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The present invention is described hereinbelow. However, in order to fully set the background and distinguish the principal parts of the present invention, a brief discussion of the associated circuitry for the external defibrillator will be presented first. 
     Related Circuitry 
     Referring now to FIG. 1, a charge control circuit  10  may be seen. Circuit  10  includes a pulse generator  12  connected to a pulse transformer  14  which is connected to a passive rectifying and filtering circuit  16 . Circuit  16  is preferably made up of a high speed (fast recovery) diode  18 , which is preferably a UF4007 type, available from General Instruments, and a capacitor  20  which may be in the range of 3-10 microfarads. Circuit common is indicated by an inverted triangle  22 , and an output  23  of the rectifying and filtering circuit  16  is connected to first and second charge switches  24 ,  26 . Charge switches  24 ,  26  are each preferably formed of one or more solid state switching devices such as a silicon controlled rectifier (SCR), a field effect transistor (FET), or an insulated gate bipolar transistor (IGBT). Such devices may be connected in series (to increase voltage capability) or in parallel (to increase current capability) as is well known in the art. Each of the charge switches  24 ,  26  is controlled by a separate one of a pair of charge control circuits  28 ,  30 . 
     The respective outputs  32 ,  34  of the charge switches  24 ,  26  are individually connected to one of a pair of capacitor banks  40 ,  42 . Output  32  is connected to a first capacitor bank  40 , and output  34  is connected to a second capacitor bank  42 . This portion of the circuitry will be described in detail with reference to a pair of capacitor banks but it should be noted that additional capacitor banks may also be included without departing from the spirit or scope of the invention. The output of capacitor bank  40  is connected to an electrode terminal  47  and the output of capacitor bank  42  is connected to an electrode terminal  49 . 
     The circuit is designed to output to electrode terminals  47  and  49  a high voltage defibrillation pulse in the range of approximately 2000-3000 volts in the preferred embodiment. It should be noted however that greater or lesser discharge voltages can also be delivered without departing from the spirit or scope of the invention. In order to generate and deliver the voltage levels desired for defibrillation, a two step process is required. The first step is that of charging the capacitors. The second step is that of discharging the capacitors. To charge low cost, reliable capacitors rapidly to the desired voltage levels, the present invention utilizes charge control circuits  28 ,  30  and charge switch circuits  24 ,  26  to charge the capacitors in parallel. When connected in parallel, the total capacitance of a particular capacitance bank is the sum of all the capacitors connected in parallel, while the voltage across each of the individual capacitors is equal. To discharge the capacitors to electrode terminals  47 ,  49 , charge control circuits  28 ,  30  and charge switch circuits  24 ,  26  configure the capacitors of a capacitor bank in series. This reduces the total capacitance to a fractional value of the individual capacitors and increase the voltage to the sum of the voltages across each individual capacitor. 
     The capacitor banks are preferably of differing capacitive values or differing voltage capacities. For example, in one embodiment, capacitor bank  40  has a total capacitance of 7200 microfarads while capacitor bank  42  has a total capacitance of 440 microfarads when connected in parallel for charging. Therefore, capacitor bank  42  will charge much more rapidly than will capacitor bank  40 . During discharge, capacitor bank  40  has a total capacitance of 200 microfarads while capacitor bank  42  has a total capacitance of 110 microfarads while connected in series. It should be noted that many other capacitor banks could be utilized having many different capacitance values, or all having the same capacitance value without departing from the spirit or scope of the invention. 
     The operation of the charge control circuit  10  is as follows. Pulse generator  12  supplies a series, or train, of preferably square wave pulses, typically at a 50% duty cycle and having an amplitude of approximately 400 volts, at a frequency preferably between 5 KHz and 500 KHz. These pulses have a very rapid rise time. Since the fast rise times and high frequencies of the pulses cause avalanching of most common solid state devices of reasonable cost, the pulses are first passed through passive filter circuit  16 . Diode  18  is a fast recovery diode that provides for charging of capacitor  20  and prevents discharge of the capacitor  20  through secondary  36  of pulse transformer  14 . Capacitor  20  is preferably selected to be able to absorb and store the energy from at least one charge pulse from pulse generator  12 . 
     As stated above, use of a pulse train with a very rapid rise time on individual pulses is desired, but would lead to avalanche breakdown of standard switches if coupled directly thereto. This would cause the switches to lose control of charging, and may lock the switches on, causing the capacitors to be continually charged until they are destroyed. This consequent loss of charging control is unacceptable. Use of rectifying and filtering circuit  16  avoids such avalanche triggering of solid state switches  24 ,  26  by keeping high dV/dt values from reaching switches  24 ,  26 , allowing ordinary solid state devices to be used for switches  24 ,  26 . 
     Circuit  10  also includes voltage monitoring circuits  43 ,  45  for monitoring the voltage on capacitor banks  40  and  42 , respectively. Monitor circuits  43  and  45  are connected to the respective capacitor banks and charge control circuit. Monitoring circuits  43  and  45  are illustrated schematically as block diagrams because there are many different embodiments of monitoring circuits that may be used without departing from the spirit or scope of the invention, such as analog circuitry, digital circuitry and solid state components, for example. 
     FIG. 2 illustrates one preferred embodiment of monitoring circuit  43 . It should be noted that monitoring circuit  45  is the same as monitoring circuit  43 . As can be seen, an operational amplifier  53  is provided as is an analog to digital converter  55  and a microprocessor  57 . Amplifier  60  is connected to capacitor bank  40  via a plurality of resistors  59 . In operation, monitoring circuit  43  has a database of preset values stored in microprocessor  57 . When capacitor bank  40  reaches the preset value selected in processor  57 , charge control circuit  28  is instructed to halt the charging of capacitor bank  40 . In an alternative embodiment, microprocessor  57  has the capability of computing an appropriate predetermined value for charging the respective capacitor bank. 
     When in the charging mode, one or a plurality of capacitor banks may be charged simultaneously. In the embodiment illustrated in FIG. 1 having first and second capacitor banks  40  and  42 , if both capacitor banks  40  and  42  are being simultaneously charged, when capacitor bank  42  is fully charged, charge switch  26  is opened as a result of a command from monitoring circuit  45  and all of the charge available at capacitor  20  is then applied to capacitor bank  40  instead of splitting it between the two capacitor banks. When capacitor bank  40  is completely charged, charge switch  24  is opened as a result of a command from monitoring circuit  43 . Capacitor banks  40  and  42  are now fully charged and the individual capacitors that make up a capacitor bank are ready to be switched into series for discharge. 
     Referring now to FIG. 3, an output circuit  50  suitable for providing biphasic defibrillation pulses may be seen. Output circuit  50  includes a capacitor bank circuit  52 , a selector circuit  54 , and an isolator circuit  56 . The capacitor bank circuit includes first and second capacitor banks  40 ,  42 , each of which have respective phase delivery command lines  44 ,  46 . In the preferred embodiment of the present invention, capacitor bank  40  is configured to discharge a positive first phase of the biphasic output pulse while capacitor bank  42  is configured to discharge a negative second phase. It should be noted that additional capacitor banks can be added without departing from the spirit or scope of the present invention. Selector circuit  54  has a pair of preferably identical selector subsystems. One subsystem  60  is indicated by a chain line. Subsystem  60  includes a solid state phase selector switch  62  connected to a phase selector driver  64  which in turn is connected to a select phase control  66 . It is to be understood that select phase control  66  provides a signal on line  68  to activate and deactivate phase selector driver  64 . 
     When phase selector driver  64  is activated, it drives phase selector switch  62  to a state of conduction (ON) between lines  72  and  74 , connecting capacitor bank  42  to isolator circuit  56  and ultimately to a patient when isolator circuit is itself in a conducting state as will be described infra. When select phase control  66  deactivates phase select driver  64 , phase selector switch  62  is rendered nonconductive (OFF) between lines  72  and  74 , thus stopping any remainder of the portion of a biphasic defibrillation pulse from being delivered from the capacitor bank  42  to a patient  76 . It is to be understood that the phase 1 selector subsystem (connected to capacitor bank  40 ) is formed of the same elements and operates identically to subsystem  60  in the embodiment shown in FIG.  4 . To provide a monophasic defibrillation pulse, only the phase 1 selector subsystem is activated, since capacitor bank  40  is connected to provide a positive polarity output and capacitor bank  42  is connected to provide a negative polarity output. 
     When providing biphasic defibrillation pulse, it has been found preferable to proceed according to the following sequence: 
     1. Turn phase 1 selector switch ON, providing a first, positive polarity, exponentially decaying portion of the pulse. 
     2. Turn phase 1 selector switch OFF, truncating the first portion of the pulse at a desired point. 
     3. After a time delay, turn phase 2 selector switch ON, providing a second, negative polarity, exponentially decaying portion of the pulse. 
     4. Turn phase 2 selector switch OFF, truncating the second portion of the pulse at a desired point. 
     One important aspect of the present invention is the reduction of the transition time between phase 1 and phase 2. In known systems utilizing SCRs as switching mechanisms, any charge in the capacitors must be reduced below the level of the holding current for the SCR before a phase shift can occur. This can take up to 10 seconds due to the large amount of charge typically remaining on the capacitors. This is so even though photoflash capacitors are typically utilized due to their rapid discharge. In these known systems, SCR dump circuits are also required which are complicated circuits which require many components for each capacitor in the capacitor bank and which force the device to throw away all current stored in the bank. 
     In the present invention, the SCR&#39;s have been replaced by IGBT&#39;s and photoflash capacitors are no longer needed, allowing more economical, mass-produced products to be used. The delay of switching between phase 1 and phase 2 depends only on the length of time to shut off phase 1 long enough to allow phase 2 to be energized. This time frame is on the order of microseconds. The discharge of current from either capacitor bank  40 ,  42  may be halted at any time and is able to do so even when voltage levels are in excess of 2000-3000 volts. The discharge of an extremely high voltage phase of opposite polarity is begun within 2-3 microseconds following the truncation of the first phase. 
     Referring now to FIG. 4, details of the phase selector switch  62  may be seen. The preferred embodiment will be described with reference to a pair of IGBT&#39;s, but it should be noted that more may be used as will be described below. To withstand the high voltages and high currents encountered in providing defibrillation pulses (whether monophasic or biphasic) two IGBT&#39;s are connected in series. As stated in the background section, extremely high voltage and current levels are present in external defibrillators. Voltage levels on the order of 2000-3000 volts and currents in excess of 100 amps are common. A first IGBT  80  has a power input  82  and a power output  84  and a signal input or gate  86 . Similarly, a second IGBT  90  also has a power input  92 , a power output  94 , and a signal input, or gate,  96 . Referring now also to FIG. 4, power input  82  is connected to lead  72  carrying the output of capacitor bank  42 . Power output  84  is connected to power input  92  and power output  94  is connected to lead  74 . The connection  70  between phase selector driver  64  and phase selector switch  62  is actually made up of four connections  100 ,  102 ,  104 ,  106 . Connections  100  and  102  couple an isolated driver  110  to IGBT  80 . Similarly connection  68  between the select phase control  66  and the phase selector driver  64  actually includes two leads  112 ,  114 . As is shown, driver  116  for IGBT  90  (and associated connections) is identical to that described in connection with driver  110 . Each of IGBT&#39;s  80 ,  90  is preferably rated to deliver a 360 Joule pulse into a 25 ohm load [at pulse repetition rate of 1 per 5 seconds], and is also preferably rated to withstand 1200 volts in the OFF condition. One such IGBT is type is IXGH25N120A available from IXYS. To prevent unbalanced voltage between IGBT&#39;s  80 ,  90  in the OFF condition, resistors  120 ,  122  are connected in series with each other and in parallel as a voltage divider across the series connection of IGBT&#39;s  80 ,  90 . The resistance of each resistor  120 ,  122  is preferably 3 mega ohms. 
     By adding additional IGBT&#39;s or by using IGBT&#39;s having higher current and voltage limits, the circuit can output each phase successfully at any current or voltage level. Specifically, the present invention allows the switching from phase 1 to phase 2 at voltage levels greater than 1000 volts. For example, by putting four 1200 volt IGBT&#39;s in series for each phase, the circuit can withstand (or hold off) 4800 volts per phase or a total of 9600 volts. 
     The operation of selector subsystem  60  is as follows. When it is desired to turn phase selector switch  62  ON, a low level signal is generated by select phase control  66 , providing a logic ON signal on lead  112  and removing a logic OFF signal on lead  114 . Drivers  110  and  116  may be any type of voltage isolating driver circuits sufficient to meet the speed and voltage requirements of the defibrillator system. Presently, magnetically isolated conventional driver circuits are preferred. When it is time to turn off phase 1, IGBT&#39;s  80  and  90  are closed thus halting the output to the patient without dumping the charge through an auxiliary SCR dumping circuit. The same is done for phase 2. During the time that the current flows through the IGBT&#39;s, peak currents are all within the safe operating areas. 
     Because dumping the charge in capacitor banks  40  and  42  is not needed to change phases, any dumping circuitry desired can be constructed from lower power components because time is not critical. This greatly reduces the size and cost of the components required. 
     Present Invention 
     The disclosure hereinabove generally relates to the circuitry associated with the present invention. However, the elements of the present invention are adaptable to an equivalent or similar circuits and are therefore not limited to the circuit disclosed in supra. 
     The present invention delivers both monophasic and biphasic waveforms as external defibrillation shock pulses. The monophasic waveform and phase one (φ 1 ) of the biphasic waveform of the present invention define the voltage and capacitance parameter values that permit the delivery of an AAMI approved 360 J monophasic waveform. The third parameter that defines a monophasic waveform is duration (d 1 ). For the present invention&#39;s monophasic waveform, the duration of the monophasic pulse is defined as that length of pulse delivery time that optimizes the delivery of current across the myocardium. Two theories provide rationales for choosing an optimal d 1 . These theories are the Kroll-Irnich theory of effective current and the Blair-Walcott theory of maximal cell response. The present invention&#39;s monophasic waveform has a duration based on each of these two theories. The duration also serves as the φ 1  duration of the biphasic waveform. 
     For the present invention&#39;s biphasic waveform, the duration (d 2 ) of phase two (φ 2 ) is defined as that length of pulse delivery time that optimizes the charge burping of current remaining on those cells not captured by φ 1 . The charge burping theory of Kroll-Walcott provides the rationale and method for designing φ 2 . The biphasic waveform has a duration d 2  based on the charge burping theory. The theories and their associated models were augmented for transthoracic defibrillation. The design principles determine the optimal waveform characteristics of external truncated exponential waveforms based on these effective current and myocardial cell response models. These theories and their associate models are extended by incorporating the Lerman-Deale resistive network model of a thorax. The extended model is called the transchest defibrillation model and is illustrated in FIG.  5 . 
     Referring now to FIG. 5, the transchest augmentation of the myocardial cell response model may be seen. The resistance variables include R s  which is the resistance of the defibrillator, the electrode-electrolyte interface, RTC which represents the resistance of the thoracic cage, RCW representing the resistance of the chest wall, RLP the resistance of the lungs in parallel, RH the resistance of the pericardium and myocardium and RM the resistance of the myocardial cell membrane. C 1  represents the capacitor in the defibrillator used to deliver φ 1 , and C 2  the capacitor used to deliver φ 2 . CM represents the cell membrane capacitance and VS represents the forcing function derived from switching C 1  or C 2  into the circuit model at the time φ 1  or φ 2  is delivered to the heart. VM represents the transmembrane potential as seen during the delivery of a shock pulse (VS). A defibrillation waveform is designed by determining a value for its characterizing parameter that produces predetermined responses from a myocardial cell as defined by changes in the cell&#39;s transmembrane potential over time. The predetermined responses produce either cell depolarization or repolarization prolongation. The governing design procedure which may be derived from the model includes finding VS, as a function of time, in order to produce the desired VM response. 
     Each theory is based on predetermined values for resistance and other parameters. Additional parameters are chronaxie and the time constant for a myocardial cell membrane. Effective current theory for the design of φ 1  assumes values for resistance and chronaxie. In addition to these two parameters, maximal cell response theory also assumes a value for the cell time constant. 
     The values for chronaxie and cell time constant are determined experimentally. Studies have estimated the chronaxie for humans in the range of 4 to 6 ms. Using the theory of cell response, a value for the cell time constant can be estimated placing the cell time constant in the range of approximately 4 to 8 ms. The present invention waveforms employ a human chronaxie of 5 ms. A value of 4 was employed for the cell time constant. It should be noted that these ranges are given only as examples and are not limitations. Also, neither the waveforms nor the delivery algorithm are substantially altered by changing these values within the preferred ranges. The present invention is capable of recalculating the tilt relations in the microprocessor whenever the programmable parameters are changed. Set forth below are a number of tables illustrating numerous examples of parameters for the different models. It should be again noted that these tables are set forth as illustrations only. 
     The preferred monophasic waveform and φ 1  of the biphasic waveform have a capacitance of 200 μF. The characterizing parameter values for the monophasic waveform and φ 1  of the biphasic waveform are illustrated in Table IA and IB. 
     
       
         
               
             
               
               
               
               
               
               
             
           
               
                 TABLE IA 
               
             
             
               
                   
               
               
                 Parameters for Blair-Walcott φ 1 . 
               
             
          
           
               
                   
                 φ 1  Time 
                 φ 1   
                 Trailing- 
                 φ 1   
                 Relative 
               
               
                 Resistance 
                 Constant 
                 Duration 
                 Edge Voltage 
                 Tilt 
                 Cell 
               
               
                 (Ω) 
                 (ms) 
                 (d 1 , ms) 
                 Ratio 
                 (%) 
                 Response 
               
               
                   
               
               
                  40 
                  8 
                 6.20 
                 0.461 
                 54% 
                 0.243 
               
               
                  60 
                 12 
                 7.40 
                 0.540 
                 46% 
                 0.286 
               
               
                  80 
                 16 
                 8.35 
                 0.593 
                 41% 
                 0.316 
               
               
                 100 
                 20 
                 9.10 
                 0.634 
                 37% 
                 0.339 
               
               
                 120 
                 24 
                 9.75 
                 0.666 
                 33% 
                 0.356 
               
               
                 140 
                 28 
                 10.30  
                 0.692 
                 31% 
                 0.370 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
               
             
           
               
                 TABLE IB 
               
             
             
               
                   
               
               
                 Parameters for Kroll-Irnich φ 1 . 
               
             
          
           
               
                   
                 φ 1  Time 
                 φ 1   
                 Trailing 
                 φ 1   
                 Relative 
               
               
                 Resistance 
                 Constant 
                 Duration 
                 Edge Voltage 
                 Tilt 
                 Cell 
               
               
                 (Ω) 
                 (ms) 
                 (d 1  ms) 
                 Ratio 
                 (%) 
                 Response 
               
               
                   
               
               
                  40 
                  8 
                  7.60 
                 0.387 
                 61% 
                 0.237 
               
               
                  60 
                 12 
                  9.55 
                 0.451 
                 55% 
                 0.277 
               
               
                  80 
                 16 
                 11.25 
                 0.495 
                 51% 
                 0.302 
               
               
                 100 
                 20 
                 12.70 
                 0.530 
                 47% 
                 0.321 
               
               
                 120 
                 24 
                 14.05 
                 0.557 
                 44% 
                 0.335 
               
               
                 140 
                 28 
                 15.25 
                 0.580 
                 42% 
                 0.347 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE IIA 
               
             
             
               
                   
               
               
                 The parameter values for Blair-Walcott φ 2  with 110 μF 
               
               
                 capacitance and 1 st -order charge burping. 
               
             
          
           
               
                   
                   
                 φ 2   
                 Trailing 
                 φ 2   
               
               
                 Resistance 
                 φ 2  Time 
                 Duration 
                 Edge Voltage 
                 Tilt 
               
               
                 (Ω) 
                 Constant (ms) 
                 (d 2 ) 
                 Ratio 
                 (%) 
               
               
                   
               
               
                  40 
                  4.4 
                 3.65 
                 0.436 
                 56% 
               
               
                  60 
                  6.6 
                 3.70 
                 0.571 
                 43% 
               
               
                  80 
                  8.8 
                 3.75 
                 0.653 
                 35% 
               
               
                 100 
                 11.0 
                 3.80 
                 0.708 
                 29% 
               
               
                 120 
                 13.2 
                 3.85 
                 0.747 
                 25% 
               
               
                 140 
                 15.4 
                 3.90 
                 0.776 
                 22% 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE IIB 
               
             
             
               
                   
               
               
                 Parameters for Blair-Walcott φ 2  with 30 μF capacitance 
               
               
                 and 2 nd -order charge burping. 
               
             
          
           
               
                   
                   
                 φ 2   
                 Trailing- 
                 φ 2   
               
               
                 Resistance 
                 φ 2  Time 
                 Duration 
                 Edge Voltage 
                 Tilt 
               
               
                 (Ω) 
                 Constant (ms) 
                 (d 2)   
                 Ratio 
                 (%) 
               
               
                   
               
               
                  40 
                 1.2 
                 11.95  
                 0.000 
                 100%  
               
               
                  60 
                 1.8 
                 9.95 
                 0.004 
                 100%  
               
               
                  80 
                 2.4 
                 7.65 
                 0.041 
                 96% 
               
               
                 100 
                 3.0 
                 6.35 
                 0.120 
                 88% 
               
               
                 120 
                 3.6 
                 5.75 
                 0.203 
                 80% 
               
               
                 140 
                 4.2 
                 5.40 
                 0.277 
                 72% 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE IIC 
               
             
             
               
                   
               
               
                 The parameter values for Kroll-Irnich φ 2  with 110 μF 
               
               
                 capacitance and 1 st -order charge burping. 
               
             
          
           
               
                   
                 φ 2  Time 
                 φ 2   
                 Trailing- 
                 φ 2   
               
               
                 Resistance 
                 Constant 
                 Duration 
                 Edge Voltage 
                 Tilt 
               
               
                 (Ω) 
                 (ms) 
                 (d 2 ) 
                 Ratio 
                 (%) 
               
               
                   
               
               
                  40 
                  4.4 
                 3.55 
                 0.446 
                 55% 
               
               
                  60 
                  6.6 
                 3.60 
                 0.580 
                 42% 
               
               
                  80 
                  8.8 
                 3.65 
                 0.661 
                 34% 
               
               
                 100 
                 11.0 
                 3.65 
                 0.718 
                 28% 
               
               
                 120 
                 13.2 
                 3.70 
                 0.756 
                 24% 
               
               
                 140 
                 15.4 
                 3.75 
                 0.784 
                 22% 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE IID 
               
             
             
               
                   
               
               
                 The parameter values for Kroll-Irnich φ 2  with 30 μF 
               
               
                 capacitance and 2 nd -order charge burping. 
               
             
          
           
               
                   
                 φ 2  Time 
                 φ 2   
                 Trailing- 
                 φ 2   
               
               
                 Resistance 
                 Constant 
                 Duration 
                 Edge Voltage 
                 Tilt 
               
               
                 (Ω) 
                 (ms) 
                 (d 2 ) 
                 Ratio 
                 (%) 
               
               
                   
               
               
                  40 
                 1.2 
                 11.85  
                 0.000 
                 100%  
               
               
                  60 
                 1.8 
                 9.70 
                 0.005 
                 100%  
               
               
                  80 
                 2.4 
                 7.25 
                 0.049 
                 95% 
               
               
                 100 
                 3.0 
                 6.00 
                 0.135 
                 87% 
               
               
                 120 
                 3.6 
                 5.40 
                 0.223 
                 78% 
               
               
                 140 
                 4.2 
                 5.10 
                 0.297 
                 70% 
               
               
                   
               
             
          
         
       
     
     FIGS. 8A,  8 B,  8 C and  8 D illustrate the preferred biphasic waveforms, based on a total system resistance of 80 Ω (with transchest resistance ≧79 Ω). As can be seen, the waveform design theories are not sensitive to absolute voltage values for the leading edges of φ 1  and φ 2 . 
     Referring now to FIG. 6, an embodiment of the pulse delivery algorithm hardware and its integration with the external defibrillator circuit is shown. Microprocessor  200  is a programmable unit that controls the defibrillator charge and discharge controls via selector switches  201 . Capacitor banks  202  and  204  are discharged to produce the biphasic shock pulses as required. The voltage of the shock is measured by voltmeters  206  and  208  and the amperage is registered by amp meter  210 . Multiplexor  212  accepts the analog electrical quantities, voltage from voltmeters  206  and/or  208  and current from amp meter  210 , and multiplexes them into a sequence. The multiplexed sequence is transmitted into A/D converter  214  as input. Subsequently, the sequence is digitized and introduced into microprocessor  200 . Based on the digitized measurements of voltage and current and an implementation of the stopping rule, micro-processor  200  performs the necessary calculations and starts, continues or stops the discharge of a shock pulse. Isolators  216  and  218  isolate current and voltage sources from patient  220 , respectively. 
     FIG. 7 shows a flow chart of the logic of the waveform delivery. The logic is initiated under block  230  when a pulse is discharged from the external defibrillator. The initial voltage and current values are read under block  232 . The logic proceeds to block  234  where the next voltage and current values are read. Resistance values are computed under block  236  for the parameters read under block  234 . These computed resistance values are used to compute an index into a tilt lookup table under block  238 . Thereafter the algorithm proceeds to extract a next tilt stopping value from the look-up table under block  240 . The next tilt stopping value is determined at each time slice. The tilt stopping value is one of the significant parameters of the present invention. The algorithm proceeds to calculate a tilt value under block  242  between the initial discharge voltage and the voltage measured based on the time slice. Under decision block  244 , the values of the tilts obtained under block  240  and  242  are compared. If the value of the computed tilt under block  242  is less than the tilt stopping value of block  240 , the logic proceeds to block  246  where the pulse discharge is continued. In the alternate, if the value of the computed tilt is equal to or greater than the tilt stopping value of block  240 , the pulse discharge is terminated. 
     Accordingly, the algorithm of the present invention enables a continuous measurement of voltage and current during the waveform delivery. The transthoracic resistance is calculated as a function of the voltage and current each time slice these parameters are measured. Thus, the algorithm continually adjusts the duration of the pulse discharge. The algorithm properly adjusts the amount of time needed to discharge the defibrillator capacitors  202  and  204  to compensate for changes in resistance due to the changes in voltage during delivery. 
     Recent medical research in defibrillation has demonstrated that resistance is a function of voltage (JACC 1989; 13: 207-214) and that this relationship is hyperbolic (PACE 1995; 18 [PtII]: 214-220). Tang (JACC) reported an increase in mean resistance from the first phase of a biphasic waveform to the second using an animal model. He suggested that the resistance changes were primarily at the electrode-tissue interface and his hypothesis was confirmed by Brewer (PACE). Brewer (PACE) went further to determine that the myocardial tissue itself acts as a linear conductor but that a hyperbolic relationship between voltage and resistance does exist at the electrode-tissue interface. Realizing this, the delivery algorithm of the present invention measures resistance as a function of voltage to correct for changes in resistance at the electrode-tissue boundaries. The capability of continually adjusting the discharge duration not only provides a defibrillation shock pulse that automatically compensates for patient to patient differences, but additionally automatically compensates for the effects on the duration of a pulse discharge from voltage-dependent changes in resistance. The delivery algorithm thereby achieves the appropriate duration of a shock pulse in accordance with the implemented calculations for waveform design. 
     The waveform delivery algorithm is phase independent and operates in the same way for each phase of a waveform being discharged. The algorithm uses the tilt expression appropriate for each phase of a waveform. The present invention also generates a waveform to be congruent with the myocardial cell response waveform. Referring now to FIGS. 8A and 8B, first and second order charge burping shock pulses and the corresponding myocardial cell response waveforms may be seen. The waveforms are generated using the Blair-Walcott design model for phase one. In these figures relative shock-cell voltage and time are the design parameters. As can be observed, the biphasic shock pulse simulates the myocardial cell response and there is no interphase duration between φ 1  and φ 2 . Similarly, referring now to FIGS. 8C and 8D, first and second order charge burping shock pulses and the myocardial cell response corresponding thereto are shown. The waveforms are generated using the Kroll-Inrich design model for phase one. A monophasic waveform is generated in the same manner as the first phase of the biphasic waveform. 
     The waveform tilt is adapted to each phase of a waveform. The waveform tilt values are determined from a combination of the Blair-Walcott or Kroll-Inrich theory with first or second order charge burping as previously described in Tables I and II. The waveform tilt data have been fit to analytical expression so that the expression yields a tilt value as a function of resistance. For Ω=(V/I), the best fit expressions are: 
     Blair-Walcott φ 1 : 
     
       
         Tilt=122.0−[42.6*Log 10 (Ω)]; 
       
     
     Kroll-Irnich φ 1 : 
     
       
         Tilt=117.8−[35.4* Log 10 (Ω)]; 
       
     
     First-order φ 2 : 
     
       
         Tilt=286.6−[206.3* Log 10 (Ω)]+[38.6* Log 10 (Ω) 2 ]; 
       
     
     Second-order φ 2 : 
     
       
         Tilt=−345.8+[527.3* Log 10 (Ω)]−[155.5* Log 10 (Ω) 2 ]. 
       
     
     It should be noted that these analytical expressions depend upon the values chosen for chronaxie and cell membrane time constant. As previously stated, the values chosen for these are merely exemplary values and changes may be made without departing from the spirit or scope of the present invention. These formulas are implemented in the algorithm of the present invention to calculate the waveform tilt of the discharge pulses and shape them accordingly. In the preferred embodiment, the waveforms induce the myocardial profile. 
     Studies in cardiac tissue stimulation have shown that changing from one phase to another induces propagation from a cathode, and termination (break) from an anode. Thus, in a device such as the external defibrillator of the present invention where a cathode and an anode terminal (electrodes) are used to defibrillate the heart, inducing the second phase φ 2  immediately after the first phase φ 1  provides significant advantages. In other words, the attenuation and preferably the elimination of an interphase duration between phase φ 1  and φ 2  is most desirable. Several studies support the hypothesis that anode and cathode break stimulation occur in cardiac tissue and assist the diffusion of depolarization into a previously hyperpolarized region (See, for example  Mechanisms for Electrical Stimulation of Excitable Tissue, by Roth BJ, Critical Reviews In Biomedical Engineering  1994, 22 (3-4) p253-305 ISSN 0278-940X). According to this paper, two mechanisms for defibrillation have been hypothesized: (1) the relatively high junctional resistance between cardiac cells causes each cell to be depolarized on one side and hyperpolarized on the other; and (2) the fiber tracts Within the heart behave like individual fibers, with fiber curvature providing a mechanism for polarization. Similarly, other studies confirm simultaneous depolarization and hyperpolarization during stimulation of refractory and excitable tissue that act as virtual anodes and cathodes (See, for example; Virtual Electrodes in Cardiac Tissue; A Common Mechanism for Anodal and Cathodal Stimulation; by Wikswo JP Jr.; Lin SF; Abbas RA,  Biophysics Journal Dec . 1995, 69(6) p32195-210, ISSN 0006-3495). Further, yet another study conducted to numerically simulate electrical stimulation of cardiac tissue was based on four types of excitations which comprise: cathode make (CM), anode make (AM), cathode break (CB) and anode break (AB). The mechanisms of excitation were: for CM, tissue under the cathode was depolarized to threshold; for AM, tissue at a virtual cathode was depolarized to threshold; for CB, a long cathodal pulse produced a steady-state depolarization under the cathode and hyperpolarization at virtual a virtual anode. At the end (break) of the pulse, the depolarization diffused into the hyperpolarized tissue resulting in excitation. For AB, a long anodal pulse produced a steady-state hyperpolarization under the anode and depolarization at a virtual cathode. It was found that at the end (break) of the pulse, the depolarization diffused into the hyperpolarized tissue, resulting in excitation. Strength duration curves for CM and AM were compared. They were found to be similar except when the duration was shorter than 0.2 ms, in which case the AM threshold rose more quickly with decreasing duration than did the CM threshold. Accordingly, it is advantageous to eliminate or at least limit to below 0.2 ms the interphase duration between φ 1  and φ 2  (See , for example, A Mathematical Model of Make and Break Electrical Stimulation of Cardiac Tissue by a Unipolar Anode or Cathode; by Roth BJ;  IEEE Trans Biomed Eng Dec  1995, 42 (12) p1174-84). Yet another study shows interaction between adjacent depolarization and hyperpolarization tissue cause anode-break and cathode-break stimulation (See, for example; The Effect of Externally Applied Electrical Fields on Myocardinal Tissue; by Roth BJ and Wikswo JP Jr.;  Proceedings of the IEEE,  1996,V84,N3 (MAR), P379-391). 
     The time-intensity relations of tissue stimulation by electric currents and the associated break phenomenon is well established in the art. In one of the earliest publications, stimulation by breaking constant currents is disclosed. The publication indirectly indicates depolarization and hyperpolarization and the resultant anode-break and cathode-break stimulation (See, for example; On the Intensity-time Relations for Stimulation by Electric Currents; by H. A. Blair,  J. Gen. Physiol . 1932; 15: 731-755). 
     Accordingly, the advantages of eliminating at best, and/or significantly reducing, the interphase duration between φ 1  and φ 2  is clearly implied in most of the teachings of the references cited in supra. The present invention advantageously utilizes those teachings and provides a continual waveform shape reforming method and device. Specifically, myocardial cell response as well as transchest resistance dynamics are considered to enable the continual waveform shape reforming based on the electrical impedance which varies in the course of a defibrillation pulse delivery. 
     The invention is not to be taken as limited to all of the details thereof as modifications and variations thereof may be made without departing from the spirit or scope of the invention.