722 Strength-Interval Curves for Cardiac Tissue Predicted Using the Bidomain Model BRADLEY J. ROTH, PH.D. From the Department of Physics & Astronomy, Vandcrbill University, Nashville, Tennessee Cardiac Strength-Interval Curves. Introduction: Strengtb-interval curves are predicted for unipolar anodal and catbodal stimulation of cardiac muscle. Methods and Results: Cardiac tissue is represented by tbe bidoniain model, and tbe active properties of tbe membrane are described by tbe Beeler-Reuter model. Two successive stimuli (S| and S,) are delivered througb a single extracellular electrode. Tbe S, tbresbold is deter- mined as a function of tbe S,-Sj interval, for anodal and cathodal S^ stimuli witb 2-. 5-, 10-, and 20-msec durations. Eacb of tbe resulting cathodal and anodal strength-interval curves is di- vided into two parts: one section corresponding to make stinuilaticm (long intervals) and tbe otber section corresponding to break stimulation (.short intervals). Generally, tlic catbodal strengtb-interval curves are decreasing functions of interval, except for an anomalous section ofthe 20-msec duration catbodal curve In tbe interval range from 310 to 318 msec. At sbort in- tervals, tbe anodal strengtb-interval curve contains a deep dip, wbicb is more prominent for longer S^ durations. Tbe catbodal tbresbold is less tban tbe anodal threshold for all intervals except those corresponding to the end of tbe refractory period. Conclusion: Tbe bidomain model predicts complex anodal and cathodal strength-interval curves, witb the anodal curve containing a dip (supernormal stimulation). These results resem- ble tbe experimental observations of Dekker. (J Cardiovasc Electrophysiol. Vol. 7. pp. 722-737. August 1996) cathode make, cathode break, anode make, anode break, bidomain. anisotropy, electrical stimulation, .supernormal Introduction Tbe response of cardiac muscle to premature electrical stimulation depends on the delay, or in- terval, between the last normal stimulu.s and the premature stimulus. We can quantify this response by plotting the minimtim stimulus strength tiequired to excite cardiac tissue as a function of the inter- val (i.e., tbe strength-interval curve). Tbe experi- mentally observed strength-interval curve depends on the polarity of the stimulu.s. For stimulation fix)m a utiipolar cathode, the strength-interval curve usually decreases monotonically. When the stim- ulus is from a unipolar anode, however, the strength-interval curve often contains a dip (Fig. 1). Part of the curve (the anomalous section) has a positive slope, indicating that the excitation thresh- old becomes larger for longer intervals.' '" Address for correspondence: Bradley J. Roth, Ph.D., Depi. of Physics & Astronomy, Vanderbili Universily. Box 1807. Station B, Nashville, TN 37235. Fax: 615-343-7263. Manuscript received 26 June 1995; Accepted tor publication 18 April 1996. Dekker* measured the anodal and catbodal strength-intei-va 1 curves in dogs and demonstrated that the curves were generated by two distinct phe- nomena: make excitation and break excitation. "Make" excitation occurs at the start of a stimu- lus pulse, and "breiik" excitation occurs at the end of a stimulus pulse (Fig. 2 inset). Dekker there- fore observed four mechanisms of stimulation: cathode make, anode make, cathode break, and anode breiik. He measured a strength-interval curve for each mechanism (Fig. 2). His mitke curves de- creased monotonically with the interval, while his break curves contained dips. At long intervals (di- astolic stimulation), cathtxle-make stimulation had the lowest stimulus threshold, followed by antxle make, cathode break, and Hnally antxlc break. In a previous publication, we predicted mech- anisms for these different mtxles of stimulation." Catbode-niake .stimulation is straightforwaid: Tlie stimulus dept>larizes the tissue under tbe cathode to threshold, resulting in excitation of an action potential wavefront that propagates outward from tbe electrode (Fig. 3a). Mathematical studies us-