Sachin Goyal

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

Modeling Thermal Fluctuations of Bio-Filaments With Elastic Rod Theory

Bio-filaments at sub-micron scales such as DNA perform their biological functions via well-regulated structural deformations that involve large twisting and bending. The strain energies associated with these deformations are of the order of the thermal kinetic energies of surrounding solvent molecules. Therefore, the bio-filaments at such small length scales also exhibit large fluctuations in their shape due to the random collisions of the solvent molecules with them. These thermal fluctuations may, on one hand, help the bio-filaments explore functionally desirable configuration space, while, on the other hand, hinder the regulation of their deformations by motor proteins. Nevertheless, it seems indispensable to model the thermal fluctuations to accurately study the dynamics of deformation of bio-filaments. This paper presents the first elastic rod formulation that incorporates the thermal fluctuations by modeling the impacts of solvent molecules as distributed stochastic force. For quasi-static fluctuations, this formulation leverages the simplicity of a rod formulation noted by Anker et al. [1] that allows solving it as an initial value problem (IVP) in single iteration, and yet capturing arbitrarily large (nonlinear) deformations with rigorous description of constitutive laws.Copyright

Computational Rod Model With User-Defined Nonlinear Constitutive Laws

Author(s): Fatehiboroujeni, Soheil; Palanthandalam-Madapusi, Harish J; Goyal, Sachin | Abstract: Computational rod models have emerged as efficient tools to simulate the bending and twisting deformations of a variety of slender structures in engineering and biological applications. The dynamics of such deformations, however, strongly depends on the constitutive law in bending and torsion that, in general, may be nonlinear, and vary from material to material. Jacobian-based computational rod models require users to change the Jacobian if the functional form of the constitutive law is changed, and hence are not user-friendly. This paper presents a scheme that automatically modifies the Jacobian based on any user-defined constitutive law without requiring symbolic differentiation. The scheme is then used to simulate force-extension behavior of a coiled spring with a softening constitutive law.

NONLINEAR OSCILLATIONS INDUCED BY FOLLOWER FORCES IN PRE-STRESSED CLAMPED RODS SUBJECTED TO DRAG

Author(s): Fatehiboroujeni, Soheil; Gopinath, Arvind; Goyal, Sachin | Abstract: Elastic-driven slender filaments subjected to compressive follower forces provide a synthetic way to mimic the oscillatory beating of biological flagella and cilia. Here, we use a continuum model to study the dynamical, nonlinear buckling instabilities that arise due to the action of nonconservative follower forces on a prestressed slender rod clamped at both ends and allowed to move in a fluid. Stable oscillatory responses are observed as a result of the interplay between the structural elastic instability of the inextensible slender rod, geometric constraints that control the onset of instability, energy pumped into the system by the active follower forces, and motion-driven fluid dissipation. Initial buckling instabilities are initiated by the effect of the follower forces and inertia; fluid drag subsequently allows for the active energy pumped into the system to be dissipated away and results in self-limiting amplitudes. By integrating the equations of equilibrium and compatibility conditions with linear constitutive laws, we compute the critical follower forces for the onset of oscillations, emergent frequencies of these solutions, and the postcritical nonlinear rod shapes for two forms of the drag force, namely linear Stokes drag and quadratic Morrison drag. For a rod with fixed inertia and drag parameters, the minimum (critical) force required to initiate stable oscillations depends on the initial slack and weakly on the nature of the drag force. Emergent frequencies and the amplitudes postonset are determined by the extent of prestress as well as the nature of the fluid drag. Far from onset, for large follower forces, the frequency of the oscillations can be predicted by evoking a power balance between the energy input by the active forces and the dissipation due to fluid drag.

Towards Adjoint-Based Inversion of the Lamé Parameter Field for Slender Structures With Cantilever Loading

Continuum models of slender structures are effective in simulating the mechanics of nano-scale filaments. However, the accuracy of these simulations strictly depends on the knowledge of the constitutive laws that may in general be non-homogeneous. It necessitates an inverse problem framework that can leverage the data provided by physical experiments and molecular dynamics simulations to estimate the unknown parameters in the constitutive law. In this paper, we formulate a simple but representative inverse problem as a nonlinear least-squares optimization problem whose cost functional is the misfit between synthetic observations of a cantilever displacement field and model predictions. A Tikhonov regularization term is added to the cost functional to render the problem well-posed and account for observational error. We solve this optimization problem with an adjoint-based inexact Newton-conjugate gradient method. We show that the reconstruction of the Lame parameter field converges to the exact coefficient as the observation error decreases.Copyright

Robustness Analysis of Algorithms to Estimate Constitutive Laws of Biological Filaments

The structure-function relationship of biological filaments is greatly impacted by their mesoscale mechanics that involves twisting and bending deformations. For example, the mechanics of DNA looping is a key driver in gene regulation. The continuum-rod models have emerged as efficient tools for simulating the nonlinear dynamics of such deformations. However, there is no direct way to derive or measure the constitutive law of biological filaments for their continuum modeling. Therefore, it is an active area of research to develop inverse algorithms based on a continuum rod model that can estimate the constitutive law from the atomistic configurations of the filament. This paper presents a set of such algorithms that can use data from the dynamic states of deformation obtained from atomistic simulations or other sources. Depending on the kinematic quantities that are computed from the configuration data, the inverse algorithms differ in their steps to estimate the internal restoring moments and forces. The paper investigates and compares the robustness of these inverse algorithms accounting for the effect of noise in the data.Copyright

Estimating Constitutive Law of a Filament From its Deformed Shapes Using Input Reconstruction

Twisting and bending dynamics of biological filaments such as DNA play a central role in their biological activity including gene expression. The elastic rod model is an efficient tool to simulate such deformations. However, the accuracy of elastic rod predictions depend strongly on the constitutive law, which follows from the atomistic structure of the DNA molecule and is known to be nonlinear and to vary along the length according to the base pair sequence of the DNA. Unfortunately, it is impractical to derive the constitutive law analytically from the atomistic structure. Identification of the nonlinear sequence-dependent constitutive law from experimental data and feasible molecular dynamics simulations remains a significant challenge. In this paper, we extend earlier work by employing techniques based on input reconstruction and state estimation filters to estimate the constitutive law using molecular dynamics data of deformations in bio-filaments.Copyright

A Method for Identification of the Constitutive Law of Biological Filaments From Their Dynamic Equilibria

There are several biological filaments that play vital role in cellular processes via twisting and bending deformations. From the double-stranded DNA molecule containing genetic information to the cytoskeletal fibers that provide shape to the cell, biological filaments undergo conformational changes as they perform their biological tasks. Therefore the ability of a filament to deform, which depends on their atomistic structure, is a characteristic property that governs its biological functions. Since there is no direct analytic method to derive the deformability or constitutive law of such filaments from their atomistic structure, the constitutive law has to be identified from their actual deformations. An inverse approach based on a continuum rod model was developed recently that uses deformations in static equilibrium to estimate the constitutive law in bending and torsion. We extend the inverse method to use dynamic states of deformations, and consequently expand its scope to leverage a wide variety of choices in molecular dynamics simulations for identifying the constitutive law. This paper presents and validates the technique applying it to filaments with artificial atomistic structure.Copyright

A Biomechanical Approach to Diagnosis and Monitoring of Parkinson’s Disease

Parkinson’s disease is an idiopathic and degenerative disorder of the central nervous system. Among the symptoms, the tremor at rest is one of the prominent symptoms. The challenge however is that there are no definitive diagnostic test that can confirm the presence or severity of Parkinson’s disease. This is a serious handicap especially since the drugs usually prescribed to control these symptoms have serious side effects and their dosages have to be tuned extensively. Also, the exact origin of tremor is unknown. There have been recent efforts [19] to understand the mechanism behind the Parkinsonian tremor, from a control-system perspectives. From these efforts, it appears that increased sensorimotor loop delay may be a cause for Parkinsonian tremor and thus serve as a key distinguishing feature. In the current work, we adopted this hypothesis and with the help of a relatively straightforward analysis of the motor control loop along with the help of some simulation and experimental examples, we first attempt to explain several qualitative observations relating to Parkinson’s Disease. Further, we explore the possibilities of for progress tracking, diagnosis, and early diagnosis before onset of tremor using biomechanical means.Copyright

Beaded elastic rods to simulate the diffusive dynamics of biofilament deformations

The twisting and bending dynamics of bio-filaments such as DNA are crucial to their biological functions. The nature and time-scales of these deformations are not only influenced by the structural elasticity of the bio-filament but also by their diffusion mechanics. While the elastic rod theory is still evolving to model the structural elasticity with rigorous descriptions of contituive laws, beaded chain models have been very successful to simulate the diffusion mechanics. This paper presents a framework that merges the strengths of beaded chain models with an elastic rod model to simulate the diffusive deformations (twisting and bending) of stiff bio-filemants.