Clinical Facts Along With a Feedback Control Perspective Suggest That Increased Response Time Might Be the Cause of Parkinsonian Rest Tremor

Vrutangkumar V. Shah SysIDEA Lab, Mechanical Engineering, Indian Institute of Technology Gandhinagar, Gandhinagar 382355, India e-mail: shah_vrutangkumar@iitgn.ac. in Sachin Goyal 1 Assistant Professor Department of Mechanical Engineering, University of California, Merced, CA 95343 e-mail: sachin.goyal@ucmerced.edu Harish J. Palanthandalam- Madapusi Assistant Professor SysIDEA Lab, Mechanical Engineering, Indian Institute of Technology Gandhinagar, Gandhinagar 382355, India e-mail: harish@iitgn.ac. in Clinical Facts Along With a Feedback Control Perspective Suggest That Increased Response Time Might Be the Cause of Parkinsonian Rest Tremor Parkinson’s disease (PD) is a neurodegenerative disorder characterized by increased response times leading to a variety of biomechanical symptoms, such as tremors, stoop- ing, and gait instability. Although the deterioration in biomechanical control can intui- tively be related to sluggish response times, how the delay leads to such biomechanical symptoms as tremor is not yet understood. Only recently has it been explained from the perspective of feedback control theory that delay beyond a threshold can be the cause of Parkinsonian tremor (Palanthandalam-Madapusi and Goyal, 2011, “Is Parkinsonian Tremor a Limit Cycle? ” J. Mech. Med. Biol., 11(5), pp. 1017–1023). The present paper correlates several observations from this perspective to clinical facts and reinforces them with simple numerical and experimental examples. Thus, the present work provides a framework toward developing a deeper conceptual understanding of the mechanism behind PD symptoms. Furthermore, it lays a foundation for developing tools for diagno- sis and progress tracking of the disease by identifying some key trends. [DOI: 10.1115/1.4034050] Introduction Patients suffering from PD experience a variety of biomechani- cal symptoms including tremors, stooping, rigidity, and gait insta- bility [1]. Since the discovery of this disease in 1817 [2], the connections between these apparently unrelated biomechanical symptoms have puzzled researchers and have led to a range of hypotheses and conjectures about the source of these symptoms [3,4], and it is not clear whether there is a single underlying expla- nation for these symptoms [5,6]. PD is a neurodegenerative disor- der and is also characterized by a permanent increase in response time in both voluntary and involuntary motor responses. The impairment of response time in PD was first noted in Ref. [7], stat- ing, “recent measurements with special apparatus for muscular response to a single visual stimulus have given the figures of 0.24 s for normal individuals and 0.36 s for the subjects with paralysis agitans. ” Several detailed studies since then have come up with similar conclusions [8–11]. This has added another dimension to the mystery surrounding the symptoms. Although the deterioration in biomechanical control can intui- tively be related to sluggish response times, how the increase in response time leads to such biomechanical symptoms as tremors is not yet understood [12]. In fact, it is argued that Parkinsonian tremor may have a pathophysiology different from most other symptoms of the disease [3,4]. Neuroprosthetic therapies such as deep brain stimulation [13] suppress Parkinsonian tremor, how- ever, the fundamental mechanism behind these therapies is also unresolved [14]. On another front, empirical mathematical models are proposed, which can simulate Parkinsonian tremor, for instance, a limit- Corresponding author. Contributed by the Design Engineering Division of ASME for publication in the J OURNAL OF C OMPUTATIONAL AND N ONLINEAR D YNAMICS . Manuscript received November 25, 2015; final manuscript received June 24, 2016; published online September 1, 2016. Assoc. Editor: Sotirios Natsiavas. cycle-exhibiting system such as the Van Der Pol oscillator can be fit to experimentally measured data [15]. But such an approach lacks physical underpinnings and does not provide any insights into some of the other key features of Parkinsonian tremor. For example, why a PD patient trying to keep still would exhibit trem- ors (referred to as rest tremors) [1], whereas these tremors would often disappear during voluntary motion [3], is not explained by such models. Recently, arguments based on a control-system anal- ogy were used to support the hypothesis that Parkinsonian tremor may indeed be a limit-cycle oscillation [16] and established a direct logical connection between increased response time and limit-cycle behavior of Parkinsonian tremor. Since then, similar connections between increased time delays and limit-cycle oscil- lations in human biomechanics (although not necessarily in the context of PD) have also been drawn [17–19]. In this paper, we exploit this link between increased time delays (observed as an increase in response times) and Parkinsonian tremors to address two specific objectives (see Fig. 1). First, we wish to draw qualitative observations based on this hypothesis that are supported by clinical facts, explained using feedback con- trol theory, and reproduced by simple numerical and experimental Fig. 1 The contributions of this work Journal of Computational and Nonlinear Dynamics C 2017 by ASME Copyright V JANUARY 2017, Vol. 12 / 011007-1 Downloaded From: https://computationalnonlinear.asmedigitalcollection. asme.org/ on 09/10/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use