*2.1.1. Tissues and joints*

Any biomedical device, either implantable or external, should take into account the peculiar characteristics of living tissues. Focusing on the musculoskeletal system, a great variety of tissues can be described: cortical bone, cancellous bone, muscular fibres, tendon, ligament, cartilage, synovial fluid, fibrous tissues… All these tissues show non-linear, viscoelastic and hysteretic properties. Some of them, such as the muscular tissues, also display active mechanical behaviour. Moreover, tissue characteristics may vary significantly with age, sex, ethnicity, fitness, pathology or malformation. The properties of biological tissues work together to produce the observed features of joints and limbs, which therefore also display non-linear, viscoelastic and patient-dependent behaviour.

Human joints may differ significantly from one another in terms of dimensions, degrees of freedom, neutral position, range of motion, associated muscular power and weight of the adjacent limb segments, neighbouring structures, etc. A "general purpose" actuator is hard to imagine, but dedicated devices can be tailored to target specific joints and pathologies. Furthermore, once the application has been selected, a statistical analysis of the target population could be carried out and possibly *ad-hoc* assessment of joint characteristics, biometric parameters, classic associated malformations or impairments and comorbidities, so that an appropriate average set of biomechanical parameters is acquired for a "typical user".

Modelling of the joint behaviour is often an essential step in the design process. The desired application can direct modelling choices as to whether a detailed or simplified description of the joint should be included. For example, it may be a purpose of the new device to activate only one degree of freedom (d.o.f.) of a di- or tri-axial joint; in this case, the extra d.o.f's can be excluded from the joint model, but it must be realised that the neglected mobility can produce unwanted stresses or sliding, or pain when the actuator is in use, and it is up to the designer to decide if not controlling those events is acceptable, or else they ought to be controlled by some other means (e.g by fixing and preventing movements along the extra d.o.f.'s). Joint characteristics cannot be considered as unchangeable data, but have to be connected to the current design case: for instance, in judging what a suitable range of motion (ROM) for the actuator should be, the designer must consider the joint type, but also the application (what is the required movement for the rehabilitation exercise?), the pathology (is it likely to change the ROM? Does the actuator have to work to restore the physiological ROM?), the relationships with posture (e.g. certain positions of adjacent joints can affect the available ROM of the target one), the influence of other d.o.f.'s, etc. In relation to this, it can also be decided if joint mechanical properties can be linearised within the ROM of interest.

#### *2.1.2. Expected loads*

92 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges

**2. Uses of SMA actuators in medical rehabilitation** 

properties, special requirements must be fulfilled in order for these devices to be able to be used in electromagnetically shielded environments. In particular, if the Joule's Effect is chosen as a means to heat SMA elements and produce phase transformation, care will have to be taken in controlling any unwanted stray magnetic fields generated by the current flow.

This section will provide guidelines for designing SMA actuators aiming at moving human joints. General statements and suggestions will be accompanied by the discussion of a case study taken from the authors' experience, i.e. an ankle mobiliser conceived as a lightweight and portable tool for providing neurologic patients (stroke, traumatic brain injury, paresis) with motor support and sensorial stimulation not only during the very early phase of rehabilitation when they are still unable to exercise, but also during the subsequent phase of

The initial step of a biomechanical design is identifying the anatomical compartment, the pathology of interest and aim of the medical device. This is however just the basic set of information to tackle the problem and provides a very rough description of the actual boundary conditions affecting the following steps. Further human-related design constraints that ought to be considered in developing rehabilitation devices span from the mechanical properties of the joint, to the typical characteristics of target patients, and as far as

Any biomedical device, either implantable or external, should take into account the peculiar characteristics of living tissues. Focusing on the musculoskeletal system, a great variety of tissues can be described: cortical bone, cancellous bone, muscular fibres, tendon, ligament, cartilage, synovial fluid, fibrous tissues… All these tissues show non-linear, viscoelastic and hysteretic properties. Some of them, such as the muscular tissues, also display active mechanical behaviour. Moreover, tissue characteristics may vary significantly with age, sex, ethnicity, fitness, pathology or malformation. The properties of biological tissues work together to produce the observed features of joints and limbs, which therefore also display

Human joints may differ significantly from one another in terms of dimensions, degrees of freedom, neutral position, range of motion, associated muscular power and weight of the adjacent limb segments, neighbouring structures, etc. A "general purpose" actuator is hard to imagine, but dedicated devices can be tailored to target specific joints and pathologies. Furthermore, once the application has been selected, a statistical analysis of the target population could be carried out and possibly *ad-hoc* assessment of joint characteristics, biometric parameters, classic associated malformations or impairments and comorbidities, so that an appropriate average set of biomechanical parameters is acquired for a "typical user".

motor relearning, thanks to a specially-designed biofeedback-based control system.

**2.1. Biomechanical, bioengineering and clinical specifications** 

considering the psychological impact.

non-linear, viscoelastic and patient-dependent behaviour.

*2.1.1. Tissues and joints* 

Considering the force or torque generated by the actuator, it is important to keep in mind that joints have passive and active torque-angle characteristics that can be activated by the patient voluntarily or unconsciously.

A passive response is elicited from the muscles and periarticular structures when the joint is moved from its neutral angle, i.e. a resting position where forces producing joint flexion are balanced by those producing joint extension (including or not including gravity, according to limb position in space). As mentioned above, this response is generally nonlinear, viscoelastic and hysteretic, even in physiologic conditions. It can be evaluated by means of a motor-dynamometer-encoder system, in such a manner that the joint can be mobilised passively at controlled speed across a set range of motion, and resisting torque and position can be acquired simultaneously throughout the movement. By changing movement speed the viscoelastic characteristics can be evidenced, while conducting tests both in the flexion and extension direction (or inversion and eversion; or adduction and abduction; etc.) can reveal the hysteresis. The obtained torque-angle curves can be used as load curves in the design of the actuator. The absolute values of passive joint torques strongly depend not only on pathology (viz. contracture, retraction, fibrosis, etc.), but also on age, sex and muscular trophism, and of course change from joint to joint in the body. For this reason we can only give here some examples to clarify the order of magnitude of these torques. Maximum physiological passive torques can be as low as 50-60Ncm for finger joints [52], 100-300Ncm for the elbow [53] and up to 500-1000Ncm for the ankle joint [53-54], also depending on the angle of the knee. In healthy conditions, joint passive stiffness is not prevalently affected by movement speed. The same may not be true in some pathological cases. Muscle contracture and joint retraction can cause the reported values of joint passive stiffness to increase several times and can even make joints completely rigid to any practical purpose.

Apart from a passive response, joints can resist imposed movement also through the activation of the associated muscle groups. Muscular power can be delivered voluntarily (active motion) or by reflex activation. Involuntary active motion can also be produced by neurological conditions such as cloni, dystonia, chorea, etc. During limb and joint passive mobilisation muscle stretching can occur: a dedicated physiologic reflex produces instantaneous muscular contraction when the muscle fibres are elongated over a certain limit. This so called *stretch reflex* is much exasperated in spastic syndromes and may produce an involuntary, uncontrolled increase of resisting loads. Spasticity strongly depends on the speed of stretching; preconditioning the limb by a few cycles of slow manual stretching can help reduce momentarily the intensity of stretch reflex. Very severe spasticity, however, may correspond to the absolute impossibility of mobilising a joint.

Furthermore it must be remembered that the limbs adjacent to a joint possess a mass, and are therefore subjected to gravity and inertial forces connected to accelerations produced even in different parts of the body. One important case is gait. Where and when any or all of these components of the resisting or facilitating loads for the actuation must be taken into account has to be decided for each new application separately, in particular considering the typical position held by the target patient while the actuator is functioning, whether the patient will be prone to uncontrollable movements (jerks, dystonia, convulsions, etc.), or, on the contrary, whether some physiological movements will be typically impeded or suppressed (paresis, coma, castings, etc).
