Journal of Neuroscience Methods 97 (2000) 45 – 50 Chronaxie calculated from current – duration and voltage – duration data Jan Holsheimer a, *, Emiel A. Dijkstra a , Hilde Demeulemeester b , Bart Nuttin b a Department of Electrical Engineering, Institute for Biomedical Technology, Uniersity of Twente, PO Box 217, NL-7500 AE Enschede, The Netherlands b Department of Neurological Surgery, Uniersity Hospital Gasthuisberg, 3000 Leuen, Belgium Received 5 July 1999; received in revised form 21 December 1999; accepted 27 December 1999 Abstract To determine the rheobase and the chronaxie of excitable cells from strength – duration curves both constant-current pulses and constant-voltage pulses are applied. Since the complex impedance of the electrode-tissue interface varies with both the pulsewidth and the stimulation voltage, chronaxie values estimated from voltage – duration measurements will differ from the proper values as determined from current – duration measurements. To allow a comparison of chronaxie values obtained by the two stimulation methods, voltage – duration curves were measured in human subjects with a deep brain stimulation electrode implanted, while the current and the load impedance of the stimulation circuit were determined in vitro as a function of both stimulation voltage and pulsewidth. Chronaxie values calculated from voltage – duration data were shown to be 30 – 40% below those estimated from current–duration data. It was also shown that in the normal range of stimulation amplitudes (up to 7 V) the load impedance increases almost linearly with the pulsewidth. This result led us to present a simple method to convert voltage – duration data into current – duration data, thereby reducing the error in the calculated chronaxie values to 6%. For this purpose voltage – duration data have to be measured for pulses up to 10–20 times the expected chronaxie. © 2000 Elsevier Science B.V. All rights reserved. Keywords: Current – duration measurements; Voltage – duration measurements; Chronaxie; Rheobase; Deep brain stimulation www.elsevier.com/locate/jneumeth 1. Introduction The strength – duration curve of an excitable cell rep- resents the relation between the pulsewidth and the threshold stimulus current (I th ), or voltage (V th ). The curve is characterized by a reduction of the stimulus amplitude when the pulsewidth is increased. An exam- ple is shown in Fig. 1a. The curve is generally described by two parameters, the rheobase and the chronaxie. The rheobase (I rh or V rh ) is defined as the lowest stimulus amplitude, or threshold, needed for activation and relates to a large pulswidth. The chronaxie (C ) is defined as the pulsewidth corresponding to twice the rheobase. Weiss (1901) proposed the following empiri- cal equation, known as Weiss’s law, to describe the (linear) relation between the pulsewidth (PW) and the threshold charge (I th · PW) I th · PW =I rh · PW +I rh · C (1a) When constant-voltage pulses instead of constant- current pulses are applied, this equation is replaced by V th · PW =V rh · PW +V rh · C (1b) I th · PW (charge per pulse) and V th · PW are linearly related to PW and the rheobase is the slope of this line. Fig. 1b shows the strength–duration curve of Fig. 1a converted according to Eq. (1b). The non linear relations between PW and I th and between PW and V th follow from Eqs. (1a) and (1b), respectively. I th =I rh (1 +C /PW) (2a) V th =V rh (1 +C /PW) (2b) According to the definition of chronaxie given above C =PW when I th =2I rh (or V th =2V rh ). Whereas the rheobase and the chronaxie are primar- ily related to passive membrane properties of the ex- * Corresponding author. Tel.: +31-53-4892762; fax: +31-53- 4892287. E-mail address: j.holsheimer@el.utwente.nl (J. Holsheimer) 0165-0270/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. PII:S0165-0270(00)00163-1