Charles R. Katholi

Mathematical relationship between automaticity of the sinus node and the AV junction

Abstract Stable sinus and AV junctional rates (each in the same animal) were obtained in 50 open-chest dogs anesthetized with pentobarbital. After cannulation of both the sinus node and the AV node arteries, the control sinus rate was 135 ± beats per minute (mean ± 1 SD), the range being 84 to 192. Following selective eserinization of the sinus node (10 or 100 μg per milliliter, 2 ml.), which progressively slows the sinus node until a stable AV junctional rhythm emerges, the mean AV junctional rate was 88 ± 19 beats per minute, ranging between 48 and 126. The plot of AV junctional rates (AVJR) versus corresponding sinus rates (SR) from each dog demonstrates a 2:3 ratio between these two variables. On mathematical analysis of these data there is a consistent correlation (r = 0.942; p

A mathematical model of automaticity in the sinus node and AV junction based on weakly coupled relaxation oscillators

Abstract A general mathematical model is proposed for the study of the effects of changes in two interacting pacemaker rates on the nature of cardiac rhythms. The model is based on the weak interaction of two systems of differential equations each of which is capable of self-perpetuating oscillations. Some results of computer experimentation with the model are presented for one simple system of coupling the oscillators. The mathematical model reproduces satisfactorily the physiological results of experiments previously performed on dogs in this laboratory. The model is useful in both the design and analysis of biologic experiments to define most known determinants of either normal or abnormal cardiac rhythm.

The Predictive Value of Creatine Phosphokinase and Alkaline Phosphatase in Identification of Heterotopic Ossification in Patients After Spinal Cord Injury

OBJECTIVE To determine the predictive value of serum levels of creatine phosphokinase (CPK) and alkaline phosphatase (ALP) in identifying patients with spinal cord injury (SCI) who are at risk to develop heterotopic ossification (HO) at the hips. DESIGN Prospective cohort study. SETTING Tertiary-care level I trauma center. PARTICIPANTS Consecutive sample of 18 adults with acute traumatic SCI. Patients were excluded if they had medical or surgical conditions that are known to cause elevated enzyme levels. INTERVENTIONS Not applicable. MAIN OUTCOME MEASURES Conventional hip radiographs were taken approximately 3 weeks after injury and again from between 3 to 6 months after injury. Serum ALP and CPK were measured approximately 3 weeks after SCI. Patients were later separated into 2 groups: group 1 was comprised of those who developed HO and group 2 was comprised of those who did not. RESULTS The initial radiographs showed no evidence of HO in either group. The radiographs taken at 3 to 6 months showed HO in 7 of 18 patients. The levels of CPK at the initial evaluation were significantly higher (R=.947, P<.0024) in group 1 than in group 2 and correlated with the severity of HO. There was no correlation between serum ALP levels and subsequent development of HO between the 2 groups (P=.07). CONCLUSION Elevated serum levels of CPK have value in predicting the HO.

Total Curve Analysis of Regional Cerebral Blood Flow with 133Xe Inhalation: Description of Method and Values Obtained with Normal Volunteers

Regional cerebral blood flow (rCBF) is studied by the 133Xe inhalation method. A mathematical function related to radiation originating from air passages, which contaminates the desired signal, is proposed. Its incorporation into the theoretical model permits use of the entire recorded head curve in subsequent least-squares analyses. Results from this total curve analysis are compared with results from the standard model of Obrist et al. [2] for four normal rest studies performed on each of nine healthy volunteers.

The Arrhythomogenic Effect of Gossypol in the Rat Heart

Gossypol has been used as a male contraceptive for more than 10 years in China [1, 2]. It is considered to be highly effective, reversible, and inexpensive, but it has some reported side effects, one of which is cardiac arrhythmias. Gossypol has been at least circumstantially associated with sinus bradycardia, bundle branch block, premature beats, and ventricular fibrillation in some patients and experimental animals [3, 4, 5, 6, 7, 8]. However, the direct cardiac electrophysiologic effects of gossypol are virtually unknown. We report here on our investigation of the effects of gossypol on the transmembrane action potentials and impulse conduction velocities in atrial and ventricular muscle cells of isolated rat hearts.