This ebook is the first authorized digital version of Kernighan and Ritchie's 1988 classic, The C Programming Language (2nd Ed.). One of the best-selling programming books published in the last fifty years, "K&R" has been called everything from the "bible" to "a landmark in computer science" and it has influenced generations of programmers. Available now for all leading ebook platforms, this concise and beautifully written text is a "must-have" reference for every serious programmers digital library.

As modestly described by the authors in the Preface to the First Edition, this "is not an introductory programming manual; it assumes some familiarity with basic programming concepts like variables, assignment statements, loops, and functions. Nonetheless, a novice programmer should be able to read along and pick up the language, although access to a more knowledgeable colleague will help."

The C programming language

Applied Numerical Analysis. By C.F. Gerald. Pp. xii, 340. £3·60. 1970. (Addison-Wesley.)

Propagation of excitation in the heart involves action potential (AP) generation by cardiac cells and its propagation in the multicellular tissue. AP conduction is the outcome of complex interactions between cellular electrical activity, electrical cell-to-cell communication, and the cardiac tissue structure. As shown in this review, strong interactions occur among these determinants of electrical impulse propagation. A special form of conduction that underlies many cardiac arrhythmias involves circulating excitation. In this situation, the curvature of the propagating excitation wavefront and the interaction of the wavefront with the repolarization tail of the preceding wave are additional important determinants of impulse propagation. This review attempts to synthesize results from computer simulations and experimental preparations to define mechanisms and biophysical principles that govern normal and abnormal conduction in the heart.

Basic Mechanisms of Cardiac Impulse Propagation and Associated Arrhythmias

Elucidation of the mechanisms of cardiac conduction disturbances leading to reentry will require resolution of the details of multidimensional propagation at a microscopic size scale (less than 200 micron). In practice, this will necessitate the combined analysis of extracellular and transmembrane action potentials. The purpose of this paper is to demonstrate the relationships between the time derivatives of the extracellular waveforms and the underlying action potentials in the experimental analysis of anisotropic propagation at this small size scale, and apply these relationships to human atrial muscle at different ages. The extracellular waveforms and their derivatives changed from a smooth contour during transverse propagation in young preparations to complex polyphasic waveforms in the older preparations. The major problem was to estimate the size and location of small groups of fibers that generated the complex waveforms in the older preparations. We found dissimilarities in the derivatives that distinguished source (bundle) size from the distance of the source to the measurement site. The differences in the extracellular waveforms and their derivatives indicated that there was electrical uncoupling of the side-to-side connections between small groups of fibers with aging. These changes produced a prominent zigzag course of transverse propagation at a microscopic level which, in turn, accounted for the increased complexity of the waveforms. The waveform differences also correlated with the development of extensive collagenous septa that separated small groups of fibers. The electrophysiological consequence was an age-related decrease in the "effective" transverse conduction velocities to the range of the very slow conduction (less than 0.08 m/sec) which makes it possible for reentry to occur in small regions of cardiac muscle with normal cellular electrophysiological properties.

Relating extracellular potentials and their derivatives to anisotropic propagation at a microscopic level in human cardiac muscle. Evidence for electrical uncoupling of side-to-side fiber connections with increasing age.

The discontinuous nature of propagation in normal canine cardiac muscle. Evidence for recurrent discontinuities of intracellular resistance that affect the membrane currents.

Simultaneous extracellular and intracellular recordings of normal action potentials, action potentials initiated at a time when the membrane was partially depolarized (by premature beats or elevated extracellular potassium), and action potentials at reduced temperature were made for Purkinje strands from the left ventricle of the dog with a 50µ tungsten extracellur electrode and a special guarded intracellular microelectrode. The peak-to-peak amplitude of the extracellular wave form was proportional to the maximum rate of rise of the intracellular action potential, and the duration of the extracellular wave form was proportional of the duration of the upstroke of the intracellular potential. Wave forms of extracellular potentials were computed from the recorded intracellular potentials with an equation which included the effects of membrane currents away from the point of observation. The computed wave forms accurately reproduced the recorded extracellular wave forms in all cases, and the wave forms were not directly porportional to the second spatial derivative or the second temporal derivative of the intracellular potential. Extracellular potentials are shown to be directly related to the spatial distribution of the intracellular potential and as such are a sensitive index of propagation and a source of information of the kind previously thought to be obtainable only with an intracllular electrode.

Extracellular Potentials Related to Intracellular Action Potentials in the Dog Purkinje System

The purpose of this paper is to describe how the transmembrane and extracellular potential waveforms, and their derivatives, are related to each other and to the sodium current and conductance in propagating cardiac action potentials. The results show that the shape of the transmembrane potential and the kinetics of the sodium current and conductance are highly determined by boundary effects at sites where impulse conduction begins and where it ends at a collision or an anatomical end. These propagation nonuniformities produced a relationship between Vmax and the internal membrane variables gNa and INa that is just the opposite of the classical relation between Vmax and the magnitude of the sodium current. For example, in these cases, both peak INa and the area under the gNa curve decreased when Vmax increased. In addition, Vmax, was shown to coincide in time with the maximum rate of increase of gNa and INa. The maximum negative slope of the extracellular waveform coincided in time with Vmax of the transmembrane potential for all shapes of the waveforms. Therefore, either the maximum negative slope of the extracellular waveform or Vmax of the action potential provides a time marker for the same underlying depolarizing event, i.e., the maximum rate of increase of the depolarizing current and its conductance.

Relating the Sodium Current and Conductance to the Shape of Transmembrane and Extracellular Potentials by Simulation: Effects of Propagation Boundaries

The spread of excitation wave fronts over the atrial septum of puppies, adult dogs, and rabbits was studied in vitro by extracellular measurements with a 50µ-diameter electrode Wave front spread through the AV node of puppies and rabbits was determined, and the functional location of the junctional region between atrial muscle and the AV node was evaluated during antegrade atrial and retrograde His bundle pacing For dogs of all ages, the pattern of spread over the septum was greatly affected by the location of the pacemaker site simulating a high or low sinus node position For all sinus pacing positions, wave fronts spread over the crista terminalis to form a posterior input to the AV node, while the anterior septal wave fronts formed another input No functional evidence could be found for narrow, specialized inteniodal tracts of fixed location Rather, wave fronts spread over broad areas creating patterns of simultaneous, multiple wave fronts which corresponded in extent to the gross anatomical landmarks of the septum Only in this fashion were the findings consistent with the idea of three general routes of intemodal conduction in the dog and two general routes in the rabbit The position of the functional boundary between atrium and AV node could be accounted for only by overlapping of the two tissues of this region; the boundary shifted between antegrade and retrograde conduction Antegrade wave fronts within the AV node accelerated from the superior border of the node to the exit at the His bundle; retrograde excitation wave fronts from the His bundle decelerated through the AV node The amplitude of the atrial wave forms as well as the status of die inputs from the posterior and anterior regions of the atrial septum were found to be important factors in AV node conduction

Excitation Sequences of the Atrial Septum and the AV Node in Isolated Hearts of the Dog and Rabbit

Extracellular recordings of normal action potentials, action potentials at reduced temperature, and action potentials initiated when the membrane was partially depolarized due to elevated extracellular potassium were made at varying distances from the surface of Purkinje strands of the dog left ventricle. As the electrode was withdrawn from the surface, the time between the positive and negative peaks increased; the amplitude of the simple biphasic wave form decreased markedly at first, and, thereafter, it decreased more gradually. The extracellular wave forms could be described by a single equation for all distances right up to the membrane surface even in the presence of interventions which drastically changed the intracellular potential and the conduction velocity. Wave forms of extracellular potentials at varying distances from the strand were computed from intracellular potentials and showed good agreement with the measured wave forms. Most major bundles in the dog conduction system have polyphasic extracellular wave forms rather than the relatively simple kind characteristic of the single strand. By using the equation that describes how the extracellular potential about a single strand varies as a function of distance, it was shown that the recorded polyphasic wave forms of the bundle studied resulted from the superposition of potentials from a number of asynchronously excited strands situated at varying distances from the recording electrode instead of from an underlying complex intracellular action potential. Extracellular recordings were chosen over intracellular recordings for this study, because they can indicate the presence of more than one excitation wave in a single record, thus permitting the resolution of the sequence of activation of the conduction system to its most elementary level.

J. Mailen Kootsey

Papers

Extracellular Potentials Related to Intracellular Action Potentials in the Dog Purkinje System

Relating the Sodium Current and Conductance to the Shape of Transmembrane and Extracellular Potentials by Simulation: Effects of Propagation Boundaries

Excitation Sequences of the Atrial Septum and the AV Node in Isolated Hearts of the Dog and Rabbit

Cardiac extracellular potentials. Analysis of complex wave forms about the Purkinje networks in dogs.

Slow Conduction in Cardiac Muscle: A Biophysical Model