Dielectric elastomer membranes are one of the most promising transducers for developing soft large strain sensors. In this article, we describe the sensor response for a potential biomedical application. It is widely accepted that diseased arteries at various stages have a unique constitutive response. This means that ideally the output of an in situ artery sensor would have distinct profiles corresponding to various stages of unhealthiness. An in situ sensor can potentially allow access to information about the mechanical state of the artery that is not currently available. Furthermore, the potential to combine the functions of providing structural support (stent) and monitoring the mechanical state (sensor) is appealing. Traditional sensors such as strain gages and piezoelectric sensors are stiff and fail at low strains (<1%), whereas some dielectric elastomers are viable at strains up to and even surpassing 100%. Investigating the electromechanical response of a deformable tube sensor sandwiched between a pulsating pressure source and a nonlinear elastic distensible thick wall has not been attempted before now. The successful development of a multiphysics model that correlates the electrical output of a pulsatile membrane sensor to its state of strain would be a significant breakthrough in medical diagnostics. The artery is described using a structural model for a tubular membrane reinforced with two families of initially crimped fibers subjected to a pulsating pressure profile. In this article, the fundamental mechanics associated with electromechanical coupling during dynamic finite deformations of dielectric elastomers is derived. A continuum model for the dynamic response of tubular dielectric elastomer membranes configured for sensing is presented. The pressure profile leads to a nonlinear response of the artery sensor due to the nonlinear deformation behavior of the arterial wall. At pressures above 13 kPa, the artery undergoes infinitesimal deformation, which leads to very small changes in the sensor signal. In this range, fabricating thinner sensors and synthesizing hybrid polymers with higher dielectric constants can enhance the sensitivity.