Modeling Fibrillation Potentials—a New Analytical Description for the Muscle Intracellular Action Potential

Abstract

The single-fiber action potential (SFAP) can be modeled as a convolution of a biolectrical source (the excitation) and a transfer function, representing the electrical volume conduction. In the Dimitrov-Dimitrova (D-D) convolutional model, the first temporal derivative of the intracellular action potential (IAP) is used as the source. In this model, the ratio between the amplitudes of the second and first phases of the SFAP (which we call the PPR, after peak-to-peak ratio) increases invariably with radial distance. This is not the case of real recorded fibrillation potentials (FPs). Moreover, FPs show a wider PPR range than that which the D-D model can provide. These discrepancies suggest that the D-D model should be revised. Since the volume conduction parameters seem to have no apparent effects on the PPR, we assume that the origin of this difference lies in the excitation source. This paper presents a new analytical description of the IAP based on that expressed in the D-D model. The new approximation is shown to model FPs with a range of PPRs comparable to that observed in a set of real FPs which we used as our test signals.

The peak-to-peak ratio of single-fibre potentials is little influenced by changes in the electrode positions close to the muscle fibre

“…Second, in both diagrams most lines lie within an area limited by a lower-PPR limit of 0.5 and an upper-PPR limit of 1.5. This result is in good agreement with previous reports for potentials recorded using a single fibre electrode (Rodriguez et al, 2006(Rodriguez et al, , 2009. Finally, note that most lines with a steep gradient (over 0.4 or under À0.4) include PPR values either greater than 1.5 or lower than 0.5.…”

“…1(b)) (Dimitrov and Dimitrova, 1974;Miller-Larsson, 1985). The concept of the peak-to-peak ratio (PPR) of a SFAP, defined as the absolute value of the quotient of V 2 over V 1 , was introduced by the current authors in 2006 (Rodriguez et al, 2006) but at that time was only studied in a small collection of fibrillation potentials. Our preliminary studies were extended in a recent work (Rodriguez et al, 2009) in which we recorded a large number of SFAPs from the right tibialis anterior muscle of four normal subjects.…”

Analysis of the relationship between the rise-time and the amplitude of single-fibre potentials in human muscles

“…The results of the present work suggest that we should admit some variability in the duration of the IAP depolarization portion in order to be able to generate the range of risetimes observed experimentally. This proposal is in agreement with several other studies that have demonstrated that to explain the changes of certain SFAP parameters it is necessary to consider the excitation source as a variable function (Rodriguez et al, 2006(Rodriguez et al, , 2007(Rodriguez et al, , 2009(Rodriguez et al, , 2010.…”

“…The second, third and fourth IAP phases model the repolarization process occurring at the membrane of the cell after the depolarization. The duration of this repolarization portion is controlled by parameter T spl (Dimitrov and Dimitrova, 1998;Rodriguez et al, 2006). We shall refer to A 1 , A 2 , A 3 and T spl as excitation parameters.…”

“…Since the introduction of the D-D and N-S convolutional models, few studies have addressed the accuracy of the underlying SFAP approximations (Albers et al, 1989;Van Veen et al, 1993;Rodriguez et al, 2006). The accuracy of SFAP models is predominantly related to their ability to generate potentials as similar as possible to experimental recordings.…”