**3. Pathophysiological mechanisms of lead-pipe rigidity**

This session will begin with an overview of the basic principles of muscle mechanics. When an active muscle is stretched, the muscle force output increases proportionally with the increasing muscle length. The dependence of muscle force on muscle length gives rise to a "spring-like" behavior (Gordon et al., 1966; Matthews, 1959; Rack & Westbury, 1969). This spring-like property of skeletal muscle has been shown to play a key role in the maintenance of posture and control of movement. A limb's posture is maintained when the forces exerted by agonist and antagonist muscle groups are equal and opposite.

Rotational movements about human joints are promoted by a resultant torque which is a summation of the individual contributions of agonist muscles minus contributions of antagonist muscles, where a single torque is mathematically defined as the product of force times the moment arm for each muscle. The corresponding measure of rotational position is the joint angle, which determines the length of each muscle acting on the joint. Ultimately, it

Physiological and Biomechanical Analyses of Rigidity in Parkinson's Disease 491

physiological underpinnings of this common symptom in patients with Parkinson's disease. The use of this approach may offer a means of assessing the efficacy of rehabilitation programs and therapeutic interventions. Efficacy of anti-Parkinson medication on the biomechanical and physiological characteristics associated with parkinsonian rigidity will

Fig. 2. Schematics of the net (solid line) torque-angle relationship showing four possible types of interactions between stretched and shortening muscles during extension of a right wrist. **A**: torque-angle relationship characterizing spring-like property of the stretched flexor and shortening extensor muscles in healthy subjects; **B**: the potential impact of a shortening reaction in the extensor muscles (contributing to extensor torque), inducing a flattened net torque-angle relation and promoting the perception of the constant rigidity; **C**: the effect of a stretch-induced inhibition in flexor muscles, causing spring-like force generated by a muscle stretch to decline as the muscle length increases. **D:** The combined effect of shortening reaction and stretch-induced inhibition on the net torque. The units and torque curves are

be discussed in later section of this Chapter.

arbitrary.

is the torque-angle relationship that serves to characterize the musculature of the joint as a whole (Feldman, 1966). Given the phenomenon that individual muscles are characterized by the length-tension relationship or spring-like property, thus the net torque-angle relation, arising from the summation of the stretched muscles and shortening muscles in normal subjects, manifests a steep curve. Fig. 2A shows that the net torque-angle characteristics of the joint arising from the summation of the spring-like properties of the stretched flexor muscle and shortening extensor muscle display spring-like behavior in healthy subjects, which is characterized by a steep torque-angle curve.

However, the natural spring-like property can be altered, generating a relatively flat torque-angle relationship that is equivalent to a plastic sensation perceived in parkinsonian rigidity. Such a flattened torque-angle relationship can be resulted from either the impact of a shortening reaction or a stretch-induced inhibition or a combination of the two. In the case of parkinsonian rigidity (Figs. 2B-2D), the torque produced by the stretched muscles (i.e., wrist flexors in this example) is increased due to the exaggerated long-latency stretch reflexes (Lee & Tatton, 1975) and enhanced tonic muscle responses (Dietrichson, 1971). There are two ways in which a joint could generate relatively constant torque with the changing joint position. Firstly, if there is an inappropriate shortening reaction in parkinsonian rigidity, the increasing force generated by the stretched flexor is offset by increasing activation of the shortening extensor. This muscle interaction could lead to a flat net torque-angle relationship, and promote the perception of the constant rigidity. Fig. 2B shows the potential interactions between stretched and activated shortening muscle in the presence of a shortening reaction. Another possibility, shown in Fig. 2C, is that a reduction in activation of stretched muscle at an elongated muscle length counteracts the otherwise gradual increase in muscle force (i.e., spring-like or elastic-like muscle force) as the muscle length of the stretched flexors is elongated throughout the stretch. Due to this counteracting effect, the net torque is relatively constant throughout the rotation of the limb. During the passive flexion or extension movement, one group of muscles is shortened whereas the other group is stretched. Both shortening reaction and stretch-induced inhibition have counteracting effects within a specified movement, generating the promotion of constant rigidity (uniformity) as defined in rigidity. Fig. 2D schematically illustrates the net torque resulting from a combined effect of the two mechanisms.

During passive movements, one group of muscles is shortened whereas the other group of muscles is stretched. Thus, the two mechanisms are potentially generating counteracting effects on the net torque resistance simultaneously. However, a dissociation of the two mechanisms is not readily available and technically challenging. Application of a biomechanical model (Holzbaur et al., 2005) implemented through the Software for Interactive Musculoskeletal Modeling (Delp & Loan, 1995) made it possible to quantify the torque generated by shortening muscles and by stretched muscles, separately, and to identify which mechanism predominates. Our findings obtained through the biomechanical modeling approach indicate that both shortening reaction and stretch-induced inhibition contribute significantly to the lead-pipe nature of parkinsonian rigidity (Xia et al., 2011). During the passive flexion movement, shortening reaction plays a predominant role in the genesis of lead-pipe rigidity, whereas stretch-induced inhibition is a primary contributor to the manifestation of lead-pipe rigidity during the passive extension movement. The knowledge gained from these studies provides new insights into the biomechanical and

is the torque-angle relationship that serves to characterize the musculature of the joint as a whole (Feldman, 1966). Given the phenomenon that individual muscles are characterized by the length-tension relationship or spring-like property, thus the net torque-angle relation, arising from the summation of the stretched muscles and shortening muscles in normal subjects, manifests a steep curve. Fig. 2A shows that the net torque-angle characteristics of the joint arising from the summation of the spring-like properties of the stretched flexor muscle and shortening extensor muscle display spring-like behavior in healthy subjects,

However, the natural spring-like property can be altered, generating a relatively flat torque-angle relationship that is equivalent to a plastic sensation perceived in parkinsonian rigidity. Such a flattened torque-angle relationship can be resulted from either the impact of a shortening reaction or a stretch-induced inhibition or a combination of the two. In the case of parkinsonian rigidity (Figs. 2B-2D), the torque produced by the stretched muscles (i.e., wrist flexors in this example) is increased due to the exaggerated long-latency stretch reflexes (Lee & Tatton, 1975) and enhanced tonic muscle responses (Dietrichson, 1971). There are two ways in which a joint could generate relatively constant torque with the changing joint position. Firstly, if there is an inappropriate shortening reaction in parkinsonian rigidity, the increasing force generated by the stretched flexor is offset by increasing activation of the shortening extensor. This muscle interaction could lead to a flat net torque-angle relationship, and promote the perception of the constant rigidity. Fig. 2B shows the potential interactions between stretched and activated shortening muscle in the presence of a shortening reaction. Another possibility, shown in Fig. 2C, is that a reduction in activation of stretched muscle at an elongated muscle length counteracts the otherwise gradual increase in muscle force (i.e., spring-like or elastic-like muscle force) as the muscle length of the stretched flexors is elongated throughout the stretch. Due to this counteracting effect, the net torque is relatively constant throughout the rotation of the limb. During the passive flexion or extension movement, one group of muscles is shortened whereas the other group is stretched. Both shortening reaction and stretch-induced inhibition have counteracting effects within a specified movement, generating the promotion of constant rigidity (uniformity) as defined in rigidity. Fig. 2D schematically illustrates the net torque resulting from a combined effect of the two

During passive movements, one group of muscles is shortened whereas the other group of muscles is stretched. Thus, the two mechanisms are potentially generating counteracting effects on the net torque resistance simultaneously. However, a dissociation of the two mechanisms is not readily available and technically challenging. Application of a biomechanical model (Holzbaur et al., 2005) implemented through the Software for Interactive Musculoskeletal Modeling (Delp & Loan, 1995) made it possible to quantify the torque generated by shortening muscles and by stretched muscles, separately, and to identify which mechanism predominates. Our findings obtained through the biomechanical modeling approach indicate that both shortening reaction and stretch-induced inhibition contribute significantly to the lead-pipe nature of parkinsonian rigidity (Xia et al., 2011). During the passive flexion movement, shortening reaction plays a predominant role in the genesis of lead-pipe rigidity, whereas stretch-induced inhibition is a primary contributor to the manifestation of lead-pipe rigidity during the passive extension movement. The knowledge gained from these studies provides new insights into the biomechanical and

which is characterized by a steep torque-angle curve.

mechanisms.

physiological underpinnings of this common symptom in patients with Parkinson's disease. The use of this approach may offer a means of assessing the efficacy of rehabilitation programs and therapeutic interventions. Efficacy of anti-Parkinson medication on the biomechanical and physiological characteristics associated with parkinsonian rigidity will be discussed in later section of this Chapter.

Fig. 2. Schematics of the net (solid line) torque-angle relationship showing four possible types of interactions between stretched and shortening muscles during extension of a right wrist. **A**: torque-angle relationship characterizing spring-like property of the stretched flexor and shortening extensor muscles in healthy subjects; **B**: the potential impact of a shortening reaction in the extensor muscles (contributing to extensor torque), inducing a flattened net torque-angle relation and promoting the perception of the constant rigidity; **C**: the effect of a stretch-induced inhibition in flexor muscles, causing spring-like force generated by a muscle stretch to decline as the muscle length increases. **D:** The combined effect of shortening reaction and stretch-induced inhibition on the net torque. The units and torque curves are arbitrary.

Physiological and Biomechanical Analyses of Rigidity in Parkinson's Disease 493

decrease the non-neural mechanical torque. This observation appears to be attributed to the

In clinic, parkinsonian rigidity is examined and assessed using a numerical rating scale which is known as the Unified Parkinson Disease Rating Scale (Fahn & Elton, 1987; Goetz et al., 2008). However, the nature of this assessment tool is highly qualitative and subjective because it is largely dependent on examiners' individual interpretation and experience (Patrick et al., 2001; Prochazka et al., 1997). When the actual change in rigidity resulting from treatment is small, it may be challenging for the examiners to detect. This can limit ability for evaluation of treatment effectiveness especially in large multi-center clinical drug trials in which a large number of investigators are involved, because differences can exist between different examiners (i.e., inter-rater) and between assessments performed on different visits by a given examiner (i.e., intra-rater) with respect to the efficacy of treatment. Reliability studies have demonstrated varying degrees of inter-rater reliability with respect to rigidity component of clinical rating tools, ranging from low, moderate, very good to excellent (Martinez-Martin, 1993; Rabey et al., 1997; Richards et al., 1994; Van Dillen & Roach, 1988). A need for more accurate evaluations has been expressed to improve the management of symptoms in patients with Parkinson's disease (Obeso et al., 1996; Ondo et

During the past several decades, considerable efforts have been made aiming to quantify assessment of parkinsonian rigidity by means of biomechanical measures. A variety of quantitative methods have been developed to measure the dynamics of joint stiffness associated with rigidity (Lee et al., 2002; Prochazka et al., 1997; Teräväinen et al., 1989; Watts et al., 1986; Wiegner & Watts, 1986). The underlying approach is to measure the amount of imposed force resistance to externally generated passive movement about the examined joint. The passive movements applied in earlier studies were induced either by a torque motor (Fung et al., 2000; Mak et al., 2007; Shapiro et al., 2007; Watts et al., 1986; Xia et al., 2006) or generated by an examiner to closely resemble a clinical setting (Caligiuri, 1994; Endo et al., 2009; Patrick et al., 2001; Prochazka et al., 1997; Sepehri et al., 2007). Variables described in these previous studies included peak torque (Mak et al., 2007), impulse (i.e., an integral of torque with respect to time; Fung et al., 2000), work score which is calculated as a torque integral with respect to joint angular position (see Fig. 3; Fung et al., 2000; Mak et al., 2007; Shapiro et al., 2007; Teräväinen et al., 1989; Xia et al., 2006, 2009), elastic coefficient (Endo et al., 2009), and mechanical impedance calculated based on the force imposed and

There are a few advantages of quantification by force or torque measures over quantification by EMG. Torque-based assessment of rigidity is more objective and reliable than EMGderived evaluation. However, there are limitations in estimation of using surface EMGs as its measures are susceptible to the placement of electrodes, condition of soft tissues and concerns of cross-talk. Biomechanical measures using torque can avoid the limitations inherent in EMG measures. In addition, non-neural contribution to parkinsonian rigidity is also included in torque measures but is not reflected in EMG recordings. Previous studies have shown that correlation is relatively weak between clinical degree of rigidity and EMG quantification of rigidity while correlation is found to be much stronger between clinical degree of rigidity and torque quantification of rigidity (Endo et al., 2009; Levin et al., 2009;

displacement of the movement (Patrick et al., 2001; Prochazka et al., 1997).

mechanism of anti-Parkinson medication therapy.

al., 1998; Ward et al., 1983).

**5. Biomechanical quantification of parkinsonian rigidity** 
