The use of cantilever based accelerometers for assessing human body movement was first proposed in the 1950s, although the devices in the early stage were somewhat unreliable, large and expensive [37]. Thanks to the revolutionary advancement of microfabrication technologies, state-of-the-art micro-accelerometers have become more accurate, reliable, smaller and cost effective [38–42]. Their applications in biomedical areas have been extensively explored, significantly changing this field of body motion measurement [43–45].

A typical cantilever based accelerometer structure can be represented by a mass-spring-damper system, as illustrated in Figure 4. The key component is a proof mass suspended by a compliant beam (cantilever) anchored to a supporting frame. The inertial force generates a relative movement between the proof mass and the supporting frame, and induces mechanical stress within the cantilever. Both of the relative movement and the mechanical stress can indicate the external acceleration.

Equation (1) is the second-order mathematical model that describes the movement of the proof mass as a function of the applied external acceleration [46]: (1) m d 2 x dt 2 + b dx dt + kx − m × a   sin   ω t = 0where m is the proof mass, x is the displacement of the proof mass, t is the time variable, b is the damping coefficient, k is the spring constant of the cantilever, a is the external acceleration to be determined, and ω is the angular frequency of the external acceleration. In a cantilever based microaccelerometer, the displacement of the proof mass is often on the order of a few μm or less. Such a small displacement needs to be converted to a measurable physical signal to determine the external acceleration. Many sensing mechanisms have been utilized to determine the cantilever displacement and hereby the acceleration, through capacitive, piezoresistive, piezoelectric or tunneling current measurement.

Gyroscopes refer to the sensors that measure the rotary rate of an object. A micromachined gyroscope utilizes the Coriolis effect to convert the rotary motion of the subject into a measurable linear motion. The rotary rate can therefore be determined using the above described sensing mechanisms of measuring linear accelerations.

As known, Coriolis effect refers to the generation of an imaginary force (Coriolis force) perpendicular to the moving direction of the subject within a rotating coordinate system [61]. This is illustrated in Figure 6(a) and briefed described as below. Imagine that an observer sitting on the x-axis of a rotating coordinate system around z-axis observes a moving particle traveling at the velocity V in the space. Because of the rotating coordinate system, the particle has a trajectory toward the x-axis with an acceleration 2V × Ω from the view of the observer. This apparent acceleration observed in a rotating coordinate system is called Coriolis acceleration, proportional to the rotation rate of the coordinate system (Ω) and the traveling velocity of the object (V). According to this phenomenon, a micromachined gyroscope without any rotary parts can be designed, which consists of two sets of mass-spring-damper systems positioned in the perpendicular directions [Figure 6(b)]. One set is in the driving mode and the other is in the sensing mode. Each of the mass-spring-damper sets is basically a linear accelerometer. During the operation, the proof mass in the driving set is actuated at a certain frequency. Upon a rotary movement of the frame, the Coriolis acceleration generated in the orthogonal direction provides inputs to the sensing set, which is measured by the sensing mode accelerometer.

The governing equations of the system in Figure 6(b) can be described by two mass-spring-damper systems coupled in two orthogonal directions [61]: (2) m x ¨ + c x x ˙ + k x x = τ x m y ¨ + c y y ˙ + k y y = τ y − 2 m Ω z x ˙where x and y are the displacements of the proof mass in x and y directions respectively, c_x and c_y are the damping coefficients in the two directions, k_x and k_y are the spring constants in the two directions, τ_x and τ_y are the external force in the driving and sensing modes, and Ω_z is the angular rate of the coordinate system to be determined. It should be pointed out that the above configuration only presents one typical form of linear vibratory micromachined gyroscope. Many other configurations, including but not limited to linear vibratory gyroscopes [62] and torsional gyroscopes [63], are also available.

Packaging and integration are essential for solid-state micromachined inertial sensors. Packaging not only provides a mechanical housing to avoid the damping, manage the thermal transfer, isolate the mechanical shock and protect the sensors from a harsh chemical environment, but also electrically connects the sensor to the outside environment and isolates it from external electromagnetic interference. The packaging also reduces the variation of damping conditions among devices designed and fabricated through the same process [64]. The packaging techniques should be considered at the design phase since different packaging methods may require different fabrication processes and configurations. In practice, anodic bonding, eutectic bonding, thermal fusion bonding or glass frit bonding techniques are regularly used [46].

The mechanical sensing components in solid-state inertial sensors need to be integrated with the controlling and measuring circuitry. Two types of integration methods, namely hybrid integration and monolithic integration, are usually used [55]. Hybrid integration employs wire bonding to electrically connect the sensing component with its controlling IC, where the electrical interconnects are exposed outside the packaging. Monolithic integration, on the other hand, fabricates the sensor and its controlling IC simultaneously within a single step. It thus minimizes the contact issues and parasitic effects, which is good for many CMOS-compatible fabrication processes [46]. Detailed discussion of packaging and integration is beyond the scope of this review, and can be found in literatures [46,51–55,64].

As above mentioned, the human vestibular system measures body motion based on the bending of hair cell bundles. Inspired by this, an artificial hair cell sensor using polymeric and metallic materials was developed [65]. The utility of such a sensor in motion measurement is also demonstrated [66]. Figure 7(a) shows the schematic of the artificial hair cell, where a cantilever with a piezoresistive strain-gauge is suspended in the atmosphere and an SU-8 pillar is attached on the distal end of the cantilever. An on-axis force towards the SU-8 pillar induces a mechanical strain at the cantilever base and is measured by a piezoresistor. The artificial hair cell sensor is integrated within a fluidic system to mimic the natural vestibular system [Figure 7(b)]. By placing the artificial hair cell sensor inside a channel filled with water, the device possesses the geometry similar to that of a semicircular canal in the vestibular system. When an external acceleration is applied, the fluid inside the channel has a relative movement with the sensor and bends the hair cell to a certain extent corresponding to the acceleration magnitude. Different from a cantilever based accelerometer, the system uses the liquid fluid as the proof mass, while the cantilever sensor is a measuring apparatus rather than a sensing component. The sensor shows a good linearity and a sensitivity of 16.9 mV/g with a water-filled channel system under accelerations at 225 Hz.

Another instance of motion sensor utilizing the liquid as the proof mass is the liquid droplet based motion sensor, which uses a liquid droplet as the proof mass. The basic structure and configuration of such a sensor can be found in [67] and is seen in Figure 8.

It consists of a hydrophobic substrate patterned with an array of microelectrodes and a 20 μL saline droplet resides on top of the substrate. When an external acceleration is applied, the ionic droplet moves relatively with the substrate surface due to the inertial effect. This relative motion is captured by the electrode array as the conductive ionic droplet changes the electrical impedance between every two adjacent microelectrodes. In the droplet based motion sensor, the wettability of the substrate surface determines the dynamic contact angle hysteresis and surface friction of the droplet movement. A superhydrophobic surface is desired to obtain a sensor with low measuring threshold, high sensitivity and good linearity. The governing equation of a liquid droplet based sensor can be expressed as [67]: (3) m d 2 x dt 2 + b dx dt − ( m × a − F threshold ) = 0where m is droplet mass, x is the relative displacement, t is the time variable, b is the damping coefficient, a is the magnitude of the external acceleration, and F_threshold denotes the capillary force due to the dynamic contact angle hysteresis.

It is noted that comparing to the governing equation of a solid-state accelerometer, Equation (3) lacks a term representing the spring. As the result, the liquid droplet does not return to the original point, which makes it incapable of continuous measurement. An improved design is presented by utilizing a curved channel instead of a planar substrate to hold the liquid droplet [68], shown in Figure 9. As the liquid droplet displaces, the tangential component of the gravity along the channel surface provides the restoring force and moves the droplet back to the origin. The governing equation in this situation can be expressed as [68]: (4) R 2 θ ¨ + ξ R θ ˙ + g   sin ( θ ) = a 0   sin ( 2 π ⋅ f ⋅ t )   cos ( θ )where: R is the radius of the circular channel,

ξ = b m is the dimensionless damping coefficient and

A non-linear spring is involved that allows continuous measurement. The relationship between the droplet displacement and the frequency and magnitude of external acceleration shows the sensor has the greatest response around 8.7 Hz (Figure 10), which is within the frequency range of human body motion (<10 Hz). It is therefore feasible to apply liquid droplet based motion sensor for low frequency body motion sensing.

A similar approach is to measure the external acceleration based on the motion of a microscale liquid-metal (LM) droplet [69]. The concept is shown in Figure 11(a). The LM droplet initially stays in the center of the glass channel, connecting the electrodes across the middle of the channel. When an external acceleration is applied, the droplet will move towards one end of the channel and be deformed by the channel. As the droplet moves, it covers the corresponding electrodes. The position of the LM droplet, and hereby the external acceleration, can thus be indicated by the light-emitting diodes (LED) connected to the electrodes [Figure 11(b)]. Linear accelerations as large as 40 g can be measured.

Thermal convection based accelerometer uses air as the inertial component [70]. A suspending electrical microheater is used to heat the surrounding air [Figure 12(a)]. Once a thermal equilibrium is developed, the temperature field has a radial pattern where the air close to the heater is at a higher temperature, and the air at a distance is at a lower temperature. At a steady state, the temperature distribution is symmetric. When an external acceleration is applied, the temperature field around the heater changes due to the inertial effect of the air, resulting in an asymmetric temperature field, which can be predicted using finite element analysis [Figure 12(b)] [71]. Such an asymmetric temperature field around the heater is measured by the temperature transducers patterned around the heaters, which can be either thermocouples or thermistors.

Since the suspending heating element increases the fabrication complexity and is less robust to vibration shocks, an improved design is to pattern the heaters on a surface with low thermal conductivity. For example, porous silicon has been used as the thermal isolation material between the microheater and the substrate [71].

Like sensors using liquid materials as the proof mass, thermal convection-based accelerometers also have good sensing performance within the frequency range below 100 Hz, which covers the frequency range of body motion. Representative characteristics of solid-state accelerometers and non solid-state motion sensors are compared in Table 1.

It is seen that although all the systems are based on inertial effects, they possess vastly different characteristics. The unique characteristic of each sensing type renders it more suitable for some applications over others. For biomedical applications, sensors with biocompatible materials, suitable measurement ranges and relatively low resonant frequencies are particularly desirable.

As mentioned at the beginning of this review, one of the most straightforward applications of motion sensors is to evaluate balance disorders. A common occurrence in the aging population is unexpected falls. Based on the clinical survey, one out of every three 65-year and elder falls each year. This often causes severe problems such as hip fractures and even deaths. In the clinical practice, Berg Balance Scale (BBS) and the Timed Up and Go test (TUG) are the standard methods for evaluation of balance capacity. In these behavioral tests, the patient is asked to perform a series of motion tasks, e.g., sitting unsupported, reaching forwards while standing, and turning around while carrying a full cup of water. The time used for accomplishing such tasks is the measure of the patient’s balance capability [74,75]. These methods require a doctor’s input and tend to be subjective. A quantitative alternative solution of balance assessment is proposed using a commercial tri-axial accelerometer (ActivPal⁻ Trio) [76], where the torso acceleration of both healthy and balance disordered patients under different clinical conditions are measured. The comparison with BBS and TUG testings shows that the accelerometry data inversely correlates with BBS scores and positively correlates with TUG values with statistical significance. The difference of the accelerometry data between the fallers and the non-fallers can clearly sort different balance conditions, which shows the feasibility of using solid-state accelerometers for quantitative balance evaluation. Many research groups and industrial partners are developing algorithms that judge the existence of an emergency fall [77,78], where the characteristics of the acceleration change during the fall are investigated to give an early warning to the subject for gestural adjustment. The development of the algorithms and the design of the sensor network are beyond the scope of this review, and can be found in the literature [79–81].

The balance prosthesis system usually involves a vibrotactile feedback system that contains a motion sensing system and a tactor actuation system. The sensing system uses solid-state accelerometers and gyroscopes to detect the body orientation and provides this information to the patient through the mechanical actuators. As a result, the patient can adjust his motor system for controlling body posture. A representative vibrotactile feedback system with three capacitive accelerometers can be found in [82], which effectively reduces the sway in patients with bilateral vestibular loss. A motion sensor with six DOFs sensing capacity applied in a vibrotactile system can lead to the improvement of dynamic gait index (DGI, a fall risk factor) in community older adults by observing significant improvement of mediolateral sway control in the subjects [83]. With the current development of solid-state motion sensors, a sensor with six DOFs sensing capacity can be implemented within a chip whose planar area is as small as 5 mm × 5 mm, similar to that of human vestibular organ, which make the implantable balance prosthesis possible. However, despite of the extensive studies about implantable artificial vestibular system [84,85], clinical demonstration of vestibular prosthesis has not been available. This is largely due to the lack of understanding of the interface between the vestibular system and the neural system. In addition, the biocompatibility and long-term reliability of the solid-state sensors, and the signal processing for appropriate data interpretation still need investigation.

In sports medicine, motion sensors can be used to measure the intensity of the physical activities, and hereby the energy expenditure during the exercise. For example, the acceleration and the oxygen consumption during treadmill walking and stair walking are successfully correlated in a recent study [86]. The exercise activities of patients with chronic heart failure are monitored using pedometers, a conventional scale inertial sensor with the similar working principle as the solid-state accelerometer but only counts the steps that a subject has walked [87]. Moreover, utilizing a network of solid-state sensors, different activity types, posture and gaits can be recognized, which could provide a comprehensive measure of energy expenditure [88]. When combined with other types of sensors, e.g., thermal sensors for body temperature monitoring and pressure sensor for blood pressure monitoring, these sensors are expected to provide a better estimate of energy expenditure and metabolic work, which contribute greatly to rehabilitation.

Personalized healthcare service, especially monitoring of daily activities is passionately advocated by U.S. healthcare practitioners. Giant healthcare and electronic companies including Intel, Qualcomm, Philips, General Electric, etc. are working aggressively in this emerging area [89]. People with suddenly reduced physical activities need special and/or immediate attention, even if the reduction is not recognized by the subjects themselves. For example, deterioration of chronic diseases such as chronic heart failure, diabetes, and Alzheimer’s disease usually correlates with decreased activities [90]. Wearable motion sensors carried by the patient can transfer information about the reduced physical activities in a timely fashion through a wireless sensor network to help the clinician in charge reach a treatment decision. Remote patient surveillance is also critical for the hospitals, where miniaturized motion sensors can be integrated on the hospital beds as well as on the patient body. Combining the measurement obtained from other types of sensors (e.g., pressure sensors), these motion sensors give the physical activities of the patient to decide whether he needs critical and emergent care [e.g., the patients in Intensive Care Unit (ICU)]. This practice is expected to reduce considerably the cost of critical care.

Position monitoring of tumors during radiation therapy is particularly essential for an effective cancer treatment. Even a nearly imperceptible movement may have a substantial negative impact on a patient’s outcome [91]. The position change of a solid tumor can be caused by two events, the mobility of the tumor organ itself and the movement of the patient’s body, e.g., breathing. In order to properly deliver the radiation dose to a defined region, vigilant and active monitoring of the tumor position is required. Solid-state accelerometers are extensively used for this purpose. Depending on the two sources of movement, both tumor position monitoring (organ-level) and body motion monitoring (body-level) can be implemented. Bandala reported a tumor motion tracking method using wireless inertial sensors [25], which contains a three-axis accelerometer, a single-axis gyroscope, a dual-axis gyroscope, a Bluetooth module for wireless data transmission and a microcontroller equipped with the tracking algorithm. The miniaturized navigation system tracks the tumor motion comprehensively with six DOFs. The system has shown satisfactory functionality when tested ex vivo. Researchers also monitored body motion to indirectly measure the tumor position, which does not require implanting the sensor into the tumor organ and simplifies the medical implementation. For example, a low-cost wireless accelerometer is placed on patient’s skin to detect the head motion, which predicts the brain tumor position during the radiation. These studies demonstrate the feasibility of improving radiation oncology efficacy using miniaturized motion sensors [92].