Patent Application
20090012579
1. Field of the Invention
The present invention relates to using functional electrical stimulation to artificially activate muscle movement, More specifically, the present invention relates to a method and apparatus for activating a muscle to produce a non-isometric functional movement in a body part through functional electrical stimulation.
2. Related Art
Functional electrical stimulation (FES) of skeletal muscles can restore functional movements, such as standing or walking in patients with upper motor neuron lesions. This is achieved by applying the FES to paralyzed or weak muscles in the patients to artificially activate the functional movements.
Unfortunately, despite many technical advances, the FES has not had desirable impact on rehabilitation. This lack of effectiveness in practice is caused by several factors. Firstly, the physiological and biomechanical processes involved in the generation of FES-elicited movements are highly non-linear and time varying. Hence, numerous tests would be required to find the desired stimulation patterns necessary to produce the desired muscle force and limb motion for each patient and for each functional movement. Secondly, commercially available FES systems are typically open-loop systems which make controlling the movements of paralyzed limbs in patients extremely difficult. Finally, other factors that occur during a FES-elicited movement, such as muscle fatigue, spasticity, and the influence of voluntary upper-body forces further complicate the control task.
One solution that can partially overcome the above-described shortcomings is the use of mathematical muscle models in conjunction with FES systems that monitor muscle performance. Mathematical models that are accurate and predictive enable FES stimulators to deliver patterns customized for each person to perform a desired functional movement while continuously adapting the stimulation protocols to the actual needs of the patient.
Previously, phenomenological Hill-type, Huxley-type cross-bridge, or analytical approaches have been developed to model the behavior of muscle contraction under both isometric and non-isometric conditions. Unfortunately, all of the above mathematical models that have been developed to date have one or all of the following drawbacks: (1) they are applicable only to isometric conditions—it is desirable to extend the models to predict non-isometric contractions when the limbs are allowed to move freely in response to the FES; (2) they are only able to predict muscle forces and associated movements in response to a narrow range of stimulation frequencies—it is desirable to develop models that are able to predict muscle forces and movements to a wide range of stimulation patterns and physiological conditions; and (3) too many model parameters need to be identified, which makes the real-time implementation of the FES-based system impossible—it is desirable to minimize the number of model parameters and still be able to capture the behavior of the muscle in response to the FES.
Hence, what is needed is a method and an apparatus that uses a mathematical model which is capable of predicting a desired FES to activate a muscle to produce a desired non-isometric movement without the above-described problems.
One embodiment of the present invention provides a system that activates a muscle to produce a functional movement in a subject through electrical stimulation. During operation, the system first obtains a non-isometric model which defines a functional movement associated with the muscle in response to electrical stimulation of the muscle. Next, the system uses the non-isometric model to compute an electrical stimulation which produces a desired functional movement in the subject. The system then applies the computed electrical stimulation to the muscle to produce the desired functional movement in the subject.
In a variation on this embodiment, the system obtains the non-isometric model by determining parameters for the non-isometric model empirically for the subject.
In a further variation on this embodiment, the system determines parameters for the non-isometric model by: (1) determining a first set of parameters under isometric conditions; (2) determining a second set of parameters under isovelocity conditions; and (3) determining a third set of parameters under non-isometric conditions.
In a variation on this embodiment, the non-isometric model defines the relationship between force behaviors in response to an electrical stimulation and movements in response to the electrical stimulation.
In a further variation on this embodiment, the force behaviors include: the force generated by non-isometric contraction of the muscle; and the time derivative of the force generated by non-isometric contraction of the muscle.
In a further variation on this embodiment, the movements can include: (1) an angular displacement; (2) an angular velocity; and (3) an angular acceleration.
In a variation on this embodiment, an electrical stimulation is a train of pulses, wherein the train of pulses is characterized by: (1) interpulse interval (IPI); (2) duration of the pulses; and (3) amplitude of the pulses.
In a further variation on this embodiment, the electrical stimulation can comprise: a constant IPI within the train of pulses; or a variable IPI within the train of pulses.
In a further variation on this embodiment, after applying the computed electrical stimulation to the muscle, the system next measures a functional movement in the subject in response to the computed electrical stimulation. Next, the system computes a difference between the measured functional movement and the desired functional movement. The system then uses the computed difference as feedback to adjust the electrical stimulation to facilitate obtaining the desired functional movement in the subject. Finally, the system applies the adjusted electrical stimulation to the muscle.
In a further variation on this embodiment, the system adjusts the electrical stimulation by changing one of the following: (1) the IPI; (2) the duration of the pulses; or (3) the amplitude of the pulses.
In a variation on this embodiment, the system computes the electrical stimulation by computing an electrical stimulation that substantially minimizes fatigue in the muscle while producing the desired functional movement in the subject.
Table 1 presents a list of detailed definitions of the symbols used in the mathematical model for the non-isometric movement.
The following description is presented to enable any person skilled in the art to make and use the invention, and is provided in the context of a particular application and its requirements. Various modifications to the disclosed embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be applied to other embodiments and applications without departing from the spirit and scope of the present invention. Thus, the present invention is not limited to the embodiments shown, but is to be accorded the widest scope consistent with the claims.
The data structures and code described in this detailed description are typically stored on a computer-readable storage medium, which may be any device or medium that can store code and/or data for use by a computer system. This includes, but is not limited to, magnetic and optical storage devices such as disk drives, magnetic tape, CDs (compact discs), DVDs (digital versatile discs or digital video discs), or any device capable of storing data usable by a computer system.
The model that describes a functional movement associated with the muscle in response to an electrical stimulation is summarized by a set of differential equations.
Before describing each of the differential equations in details, we first introduce “Ca2+-troponin complex”. The Ca2+-troponin complex forms within the muscle when the muscle is stimulated by the FES, which causes the muscle to contract. In a preferred embodiment of the present invention, the FES is a train of pulses. During the initial phase of the FES, as the number of Ca2+-troponin complexes increases in the muscle, the contraction force increases as well. We use a variable CN to represent the normalized concentration of Ca2+-troponin complex in the stimulated muscle, and our first equation defines the dynamics of the rate-limiting step leading to the formation of the Ca2+-troponin complex:
wherein ĊN is a shorthand for the time derivative of CN. Note that Eq. (1) is a response to the train of pulses, wherein the summation is performed over n pulses delivered at time ti within the train of pulses until time t.
Some of the parameters of Eq. (1) are defined below and again summarized in Table 1, which presents a list of detailed definitions of the symbols used in the mathematical model:
t: Time since the beginning of the electrical stimulation;
ti: Time when the ith pulse is delivered;
τc: Time constant controlling the rise and decay of CN;
Ri: Scaling term that accounts for the differences in the degree of activation produced by each pulse relative to the first pulse of the train.
Note that Ri=1 for i=1, and Ri=1+(R0−1) exp[−(ti−ti−1)/τc] for i>1, wherein R0 is a mathematical term characterizing the magnitude of enhancement in CN due to the following stimulations. Note that when the stimulation stops, CN will begin an exponential decay governed by the term −CN/τc.
The second and the core equation is the force equation:
Eq. (2) represents the rate of change of the muscle force F due to the FES, wherein {dot over (F)} is used as a shorthand for the time derivative of the muscle force F. The equation is derived from modeling the muscle as a linear spring, damper, and motor in series (see Wexler, A. S., Ding, J., Binder-Macleod, S. A., “A mathematical model that predicts skeletal muscle force,” IEEE Transactions on Bio-Medical Engineering 44: 337-348, 1997). Note that the equation contains two terms: term I and II.
Term I represents force increase with time due to the FES. This increase in force F is driven by CN/(KM+CN) and is scaled by A(θ) and G(θ){dot over (θ)}. Note that CN/(KM+CN) follows “Michaelis-Menton Kinetics” so that its value increases with the number of Ca2+-troponin complex CN. As a result, force F increases initially with increasing CN. However, the force increase slows down and eventually saturates when CN>>KM. KM is called the sensitivity of strongly bound cross-bridges to CN, and is alternatively defined as the value of CN that achieves the half maximum of the force increase rate.
A(θ) is a variable that measures the strength of the muscle and a function of movement θ due to the force F. In one embodiment of the present invention, the movement is generated by the FES to quadriceps femoris muscle, which causes flexion of the knee which is measured by knee flexion angle θ. In one embodiment of the present invention, A(θ) can be represented by:
A(θ)—a(40−θ)2+b(40−θ)+A40, (2a)
where a, b and A40 are all scaling factors that are defined in Table 1. Note that the movement due to the stimulated muscle force is not limited to angular movement of a joint. For example, the movement can also include the movement generated by linear contraction of the muscle.
{dot over (θ)} represents the angular velocity of a joint or linear velocity of the muscle while G(θ) is a factor that measures the strength decrease with increased velocity, and is a function of the movement θ. In one embodiment of the present invention, G(θ) can be expressed as:
G(θ)=V1θ exp ([3.0523/τ2−0.0574]θ), (2b)
wherein V1 is an empirically determined scaling factor, and τ2 represents a time constant of the force decay due to the extra friction between actin and myosin resulting from the presence of strongly bound cross-bridges in the muscle.
Term II in Eq. (2) represents the force decay due to two friction mechanisms in the muscle. The two friction mechanisms are characterized by τ1 and τ2 respectively, wherein τ1 is the time constant of force decay due to friction in the absence of CN, i.e., no strongly bound cross-bridges in the muscle, and τ2 is the time constant of force decay due to friction in the presence of strongly bound cross-bridges in the muscle.
Note that in comparison to Hill-type models (see Perumal, R., Wexler, A. S., Ding, J., and Binder-Macleod, S. A., “Modeling the length dependence of isometric force in human quadriceps muscles,” Journal of Biomechanics 35, 919-930, 2002), the force model of Eq. (2) has made the following improvements: (a) it takes into account the viscous resistance of the contractile and connective tissue in addition to the contractile and elastic component of the standard Hill model; (b) it models the rate of change of force with time rather than the force alone; and (c) the force-velocity relationship (modeled through the term G(θ){dot over (θ)}) arises as a consequence of the model. In contrast, for Hill-type models the force-velocity relationship is introduced as part of the contractile element.
In the third and the last of the set of differential equations, we represents the general non-isometric movements for the lower leg in response to the electrical stimulation as:
wherein the parameters L, I, FLOAD, FM, and λ are defined in Table 1. Note that Eq. (3) is specific to an angular movement due to knee flexion where L is the effective moment arm from the knee joint center of rotation to a point on the shank where all the forces are assumed to act. λ is the resting angle that accounts for the difference between the knee flexion angle, θ, when the leg is in a resting position at the beginning of the stimulation and the vertical angle of 90°. Hence, at the resting position, λ+θ will have a value of 90° which ensures that (Fload+FM) cos (θ+λ) will be zero at the beginning of the stimulation. We will discuss all the terms Eq. (3) in more detail below.
The model represented by Eqs. (1)-(3) is governed by 13 parameters: R0, τc, a, b, A40, τ1, τ2, KM, V1, FM-Isovel, L/I, FM, and λ, wherein R0 and τc are constants and the remaining parameters need to be determined for each subject individually. Note that parameter FM-Isovel is the value of parameter FM when the stimulated movement has a constant velocity, which is referred to as an “isovelocity condition.”
In one embodiment of the present invention, trains of pulses (or pulse trains) are used as standard FES to activate the muscle force and movement.
In a preferred embodiment, the pulses are narrow square pulses, for example, pulses generated with transistor-transistor logic (TTL), and subsequently amplified to a specified voltage suitable for stimulating a subject's muscle. Each pulse train is identified by three variables: (1) interpulse intervals (IPIs): the time separation between adjacent pulses; (2) duration (i.e., width) of the pulses; and (3) amplitude of the pulses (in Volts).
Traditionally, muscles are activated with constant frequency trains (CFTs), wherein the pulses within each train are separated by a constant IPI.
Studies have shown that varying the stimulation frequency and pattern within a pulse train can significantly affect the force generation from the muscle, as well as other factors associated with muscle performance, such as fatigue and spasticity. Hence, stimulation patterns for optimally maintaining a desired force or motion profile repetitively during the FES is more complex than CFTs. In one embodiment of the present invention, we use “variable frequency trains” (VFTs).
Another form of preferred pulse trains is referred to as “doublet frequency trains” (DFTs) wherein each DFT comprises pulse doublets throughout the train.
Note that the types of pulse trains that may activate a desired functional movement are not limited to the three types mentioned above.
Determining Parameters in the Model through Experiments
In one embodiment of the present invention, isometric force data, isovelocity force data, and general non-isometric force data are measured from the human quadriceps femoris muscle in response to the FES, which produces knee flexion movements in the lower leg.
In
In
For each subject, all data are measured in a single testing session. Each testing session includes three parts. First, subjects are tested under isometric conditions at knee flexion angles of 15°, 40°, 65°, and 90°. The testing order for each angle is randomly determined and a rest period of five minutes is provided between the angles. Next, subjects are tested at an isovelocity speed of −200°/s, wherein the negative sign is due to a constant “shortening velocity”. Finally, non-isometric tests are performed with ankle weights of 0, 4.54 kg, and 9.08 kg. Again, the testing order for the non-isometric loads is randomly determined for each subject and a rest period of five minute is provided between testing each load. After testing is completed, the data from isometric, isovelocity, and general non-isometric testing are used to determine the parameters of the model. Furthermore, additional data are measured during the general non-isometric testing which are used to evaluate the predictive ability of the model.
The parameters in the model are determined empirically using the above-described experimental setup for each subject under text. Specifically, the parameters are determined under one of the three conditions: (1) parameters a, b, A40, τ1, τ2 and KM are determined under isometric conditions; (2) parameters V1 and FM-Isovel are determined under isovelocity conditions; and (3) parameters L/I, FM, and λ are determined under general non-isometric conditions.
The process starts with determining a stimulator voltage (step 300). Specifically, the stimulator voltage is determined by gradually increasing the FES voltage applied to the muscle until a maximal voluntary contraction (MVC) force is obtained through measurement. The stimulator voltage is then set to a predetermined percentage of the obtained MVC voltage and kept unchanged throughout the reminder of the testing session.
Next, the process determines parameters under isometric conditions (step 302). Note that under the isometric conditions the angular velocity, {dot over (θ)}, becomes zero. Hence, Eq. (2) becomes:
Fixed values τc=20 ms and R0=2 are used because previously it has been demonstrated that these values are sufficient for human quadriceps muscles under non-fatigue condition. The values A40, τ1, τ2, KM are determined first at 40° of knee flexion by fitting Eqs. (1) and (4) to the measured forces produced by stimulating the muscle with a combination of VFT20 and VFT80 trains. While these parameter values are kept fixed, the values of a and b are determined at knee flexion angles of 15°, 65°, and 90° by fitting the measured force responses to the VFT20-VFT80 train combination. The values of a and b are obtained by first determining the value of A from fitting the VFT20-VFT80 force responses at angles of 15°, 65°, and 90°, and then fitting the values of A at the above four angles to the parabolic equation given by a(40−θ)2+b(40−θ)+A40.
The process next determines parameters under isovelocity conditions (step 304). Specifically, when the lower leg moves at a constant velocity, the angular acceleration, {umlaut over (θ)}, becomes zero and Eq. (3) can be written as
F=F
KC
+F
M-Isovel cos θ. (5)
Eq. (5) represents the relationship between the muscle force due to stimulation, F, and the force measured by the KinCom dynamometer, FKC. Note that FM in Eq. (3) is replaced by FM
More specifically, the process first obtains the value of FM
Finally, the process determines parameters under general non-isometric conditions (step 306). Specifically, the process first determines λ for each subject by subtracting the resting value of θ from the vertical angle of 90°. Next, the process determines the values of the ratio L/I and FM at each of the three loads (0, 4.54 kg, and 9.08 kg) by fitting the model (Eqs. (1)-(3)) to the shortening velocity response to the VFT20 train.
The system first obtains a non-isometric model which defines a functional movement associated with the muscle in response to electrical stimulation of the muscle (step 400). In one embodiment of the present invention, the non-isometric model is defined by the above-described Eqs. (1)-(4). Note that the non-isometric model contains multiple parameters that are specific to each of the subject.
Next, the system determines parameters for the non-isometric model empirically for the subject (step 402).
The system then uses the non-isometric model to compute an electrical stimulation which produces a desired functional movement in the subject (step 404). Note that this step can be performed through simulation on a computing device, such as a personal computer.
The system next applies the computed electrical stimulation to the muscle of the subject to produce a functional movement in the subject (step 406).
Next, the system measures the functional movement in the subject in response to the computed electrical stimulation (step 408).
The system then computes a difference between the measured functional movement and the desired functional movement (step 410).
Next, the system uses the computed difference as feedback to adjust the electrical stimulation to facilitate obtaining the desired functional movement in the subject (step 412). If pulse trains are used as the electrical stimulation, adjusting the electrical stimulation then involves changing one of the following in the pulse trains: (1) the IPI; (2) the duration of the pulses; or (3) the amplitude of the pulses. More specifically, adjusting the IPI can involve: (1) adjusting the IPI in a CFT; (2) adjusting multiple IPIs in a VFTs; and (3) adjusting IPIs in a DFTs both within doublets and in-between adjacent doublets.
The system then applies the adjusted electrical stimulation to the muscle (step 414). Note that the system can repeat step 408 to step 414 in a feedback loop until the difference between the measured functional movement and the desired functional movement is sufficiently small, thereby achieving the desired functional movement.
Furthermore, the above-described process, in combination with the non-isometric model which can accurately predict the relationship between frequency and pattern of the electrical stimulation on the functional movements, facilitates choosing an optimal electrical stimulation that both substantially minimizes fatigue in the muscle and produces the desired functional movement in the subject.
The foregoing descriptions of embodiments of the present invention have been presented only for purposes of illustration and description. They are not intended to be exhaustive or to limit the present invention to the forms disclosed. Accordingly, many modifications and variations will be apparent to practitioners skilled in the art. Additionally, the above disclosure is not intended to limit the present invention. The scope of the present invention is defined by the appended claims.
| Filing Document | Filing Date | Country | Kind | 371c Date |
|---|---|---|---|---|
| PCT/US2006/004969 | 2/10/2006 | WO | 00 | 8/4/2008 |
| Number | Date | Country | |
|---|---|---|---|
| 60652369 | Feb 2005 | US |
