Fiber optic micro sensor for the measurement of tendon forces
A fiber optic sensor developed for the measurement of tendon forces was designed, numerically modeled, fabricated, and experimentally evaluated. The sensor incorporated fiber Bragg gratings and micro-fabricated stainless steel housings. A fiber Bragg grating is an optical device that is spectrally sensitive to axial strain. Stainless steel housings were designed to convert radial forces applied to the housing into axial forces that could be sensed by the fiber Bragg grating. The metal housings were fabricated by several methods including laser micromachining, swaging, and hydroforming. Designs are presented that allow for simultaneous temperature and force measurements as well as for simultaneous resolution of multi-axis forces.
The sensor was experimentally evaluated by hydrostatic loading and in vitro testing. A commercial hydraulic burst tester was used to provide uniform pressures on the sensor in order to establish the linearity, repeatability, and accuracy characteristics of the sensor. The in vitro experiments were performed in excised tendon and in a dynamic gait simulator to simulate biological conditions. In both experimental conditions, the sensor was found to be a sensitive and reliable method for acquiring minimally invasive measurements of soft tissue forces. Our results suggest that this sensor will prove useful in a variety of biomechanical measurements.
KeywordsFiber Bragg grating sensor Tendon forces
Fiber Bragg Grating
Dynamic Gate Simulator
Our understanding of the neuromuscular control system in healthy people and in those with disabilities would be significantly enhanced by using in vivo tendon force measurement methods. By measuring bone-soft tissue interface forces, we could enhance the control algorithms for prosthetic devices. Additionally, such data would significantly extend our knowledge of tissue mechanics, biomechanics and orthopedics.
Currently, most soft tissue force measurements are estimated indirectly using biomechanical models that approximate the actual system. If the forces could be measured accurately and in natural settings, and then combined with imaging devices such as MRI, we could completely characterize tissue properties such as stress–strain relationships .
The aim of this study was to investigate the design, fabrication and characterization of a novel fiber optic sensor whose primary application is the measurement of tendon forces. The sensor incorporates fiber Bragg gratings and micro-fabricated stainless steel housings. A fiber Bragg grating is an optical device that is spectrally sensitive to axial strain. Stainless steel housings are designed to convert radial forces that are applied to the housing into axial forces that can be sensed by the fiber Bragg grating. This sensor offers several advantageous properties. First, it is smaller and less invasive than traditional tendon force sensors. Second, by measuring spectral response, it is insensitive to transmission losses caused the optical fiber bending away from the measurement area of interest. Third, the housing design allows us to incorporate a temperature sensing reference. Finally, the use of multiple wavelengths or housings with a preferential orientation, allows us to resolve or isolate multi-directional forces.A major portion of this effort involves the design, modeling, and fabrication of stainless steel housings that are capable of converting radial forces into axial forces that can be exerted on a fiber Bragg grating. Three fabrication methods are investigated for their suitability in providing the desired housing shape. These methods are laser micromachining, swaging, and hydroforming. An assembly method is developed as well as a calibration method. Finally in vitro testing is performed on excised tendon.
In vivo force measurements
Indirect Estimation Techniques of In Vivo Tendon Forces
Currently, the primary means of estimating forces transmitted through tendons are indirect, mathematical techniques . In most experimental preparations, single or multi-degrees of freedom load cells are used to measure joint torques, where the measured torque results from all the muscles and soft tissues that span the joint. Estimates of moment arms from cadavers coupled with measurements of the muscle’s physiological cross-sectional area are used to perform static and dynamic optimization procedures in order to distribute the forces across each of the muscles at the joint of interest. Combining this information with imaging techniques that approximate the muscle insertion points on the different tendons gives estimates of the tendon forces.
These estimation techniques are severely limited by a number of factors. The torque generated by each individual muscle is highly dependent on the magnitude of its moment arm , so attempts to scale generalized moment arm relationships derived from cadaver studies to different sized subjects creates a great deal of numerical error. Furthermore, under dynamic conditions such as during gait, muscle behavior is highly non-linear and time-varying, characteristics not reliably captured by current muscle models. Finally, the mathematical complexity involved in attempting to model every muscle spanning a joint and the indeterminacy of redundant actuators require simplifications to be made regarding the number of muscles represented in the optimization procedure. This lumping of muscles into clusters usually leads to muscle forces being overestimated, and consequently the magnitude and concentration of forces acting on and through the tendon being biased.
Direct estimation of tendon forces
In 1969, Salmons introduced a technique for quantifying tendon forces directly using a buckle transducer. This buckle transducer, also used later by others [3, 4, 5, 6, 7] to measure tendon forces, was nothing more than a small mechanical buckle instrumented with strain gauges that responded to tension in the tendon. Due to the size of the buckle transducer, this technique has only been used to study the Achilles tendon due to this tendon’s accessibility and size. Results from these studies have offered some of the most compelling insights into tendon behavior under natural conditions, including information on the loads that are generated during walking, running, and other dynamic conditions.
The primary limitation of this technique is the invasiveness of introducing and removing the sensor. The transducer is implanted under local anesthesia with an incision approximately 50 mm long made on the lateral side of the Achilles tendon. Wires from the strain gauges are brought outside the skin and covered with a sterile dressing. Normal activity cannot be resumed for 2–3 weeks so the wound can heal completely. Clearly such an invasive procedure would be impossible to introduce into single session experiments. Furthermore, complications with these buckle transducers, such as infections and pain, have limited the use of these sensors to a small and restricted research population.
A number of studies have looked into utilizing fiber optics as a means of sensing in vivo tendon forces [8, 9, 10, 11, 12, 13]. The primary advantage of this technique is that the fibers are very small (approximately 200μm), reducing the invasiveness caused by introducing the sensor into the tendon. Furthermore, optical sensors can be readily incorporated into imaging devices such as MRI and CT, allowing experimenters to monitor both kinetic and kinematic variables simultaneously . In  Komi et. al. demonstrated that in reduced rabbit preparations, the fiber optic sensor output was very/highly linear with increasing tendon loads (r = 0.999). They further demonstrated that the fiber was able to track dynamic loading conditions and that the fiber measurements were repeatable. Erdemir et. al. [11, 12, 13] further tested the application of optical sensors for measuring tendon forces, and addressed the effect of skin on the transducer output and force predictions. Using human cadaver feet as the test preparation and the same fiber configuration as in , they found that skin movement, loading rate, and cable migration all influenced the accuracy of the optical sensor. These early experiments indicate that fiber optical sensing of tendon forces may be a viable option for in vivo human testing if artifacts such as “skin effects”, sensor placement, and proper calibration can be addressed.
Background on optical force transducers
The basic idea behind a fiber optical force sensor is that an external pressure exerted on the surface of the fiber will cause a deformation that can be measured by the resulting change or modulation of the light signal that passes through the fiber. There are two methods that have chiefly been used to produce this effect: intensity based and spectral based optical force sensors.
Intensity based optical force sensing
The main advantages of this approach lie in the ease of inserting the sensor and the low cost. However, heavy, static loading has led to permanent bending of the plastic fiber [12, 13]. More importantly, in full in vivo measurements, optical losses due to tendon forces and losses due to bending of skin surrounding the tendon have been difficult to differentiate [12, 13, 14].
Spectral based optical force sensing
All optical fibers have wavelength dependent or spectral properties called dispersion. Thus, another approach for constructing a fiber optic force sensor is altering the fiber’s spectral properties as a result of mechanical deformation. This approach offers the advantage of being resistant to errors that are induced by intensity variations such as cable bends and connector losses. In this study we investigated a special spectral based sensor called a fiber Bragg grating (FBG) . FBGs are very mature products that have been used in civil engineering applications for over a decade to accurately measure forces in bridges, robotic actuators [16, 17] and other structures.
Strain Sensitivity of FBG Sensor
where p 12 and p 11 are components of the strain-optic tensor and v is Poisson’s ratio.
The FBG sensor is extremely sensitive to axial strain. Small changes in the length of the fiber Bragg grating cause measurable changes in the reflected light spectrum. However, since a sensor that is implanted within a tendon will undergo a significant amount of compression loading due to the structure of the tendon and the plane of force exertion, this compressive load must be converted to axial loading on the fiber. To accomplish this, we integrated a bowed housing or a flexure mount onto the FBG. In the next section we describe the methods for designing, fabricating and testing this modified FBG sensor.
Notably, by monitoring the reflection from the grating, the sensor terminates at the end of the housing. This makes insertion easier than with other fiber optic methods that measure light transmission. Transmission measurements require that the fiber be inserted completely through the tendon and that each end of the fiber be polished to optical quality.
Moreover, it is possible to adjust the compliance of the sensor by including a fill material within the housing. This is illustrated in Figure 3b. The fill material increases the stiffness of the sensor and thus helps prevent permanent deformation or buckling of the struts. A rigid fill material like hard epoxy would be suitable for higher loads, while a flexible material like silicone would be useful for lighter forces.
The sensors shown in Figures 3a and b primarily consist of a bare fiber Bragg grating integrated with a custom made flexure mount. A variety of fiber Bragg gratings were obtained from a commercial vendor, Corvis Corporation, with center wavelengths varying from 1545nm to 1560nm. The length of the grating regions were all 5 mm. The largest challenge was fabricating the small flexure mounts. We investigated a number of different fabrication methods, however, the following two methods showed the most promise for producing reliable parts with consistent sizes and shapes: (1) hydroforming combined with laser micromachining, (2) swaging combined with laser welding and micromachining.
Swaging is a forming technique in which the diameter of a rod, bar, or tube is reduced over a portion of its length in a tapered fashion . Specifically, a work piece is rotated and fed into tapered dies that open and shut rapidly at rates that can exceed 1000 Hz. As the tubing is fed through, the die is inserted into a spindle and outer rollers on the spindle force the two halves together. These two halves are then laser welded together to form the part. As in hydroforming, once the surface profile is formed, the struts are fabricated by laser machining. The process and fixture are illustrated in Figure 4b.
Fiber bragg grating subjected to axial displacement
In order to better understand the behavior of the sensor, it is useful to test its performance under controlled conditions. We decided that a useful environment for the initial characterization of sensor performance would be uniform hydrostatic pressure.
In Vitro testing
In vitro tests were completed to evaluate the sensor in representative tendon material.
Characterization using excised deer tendon
Characterization within a dynamic gait simulator
In this paper we describe a fiber optic sensor that has been developed for the measurement of tendon forces. The sensor incorporates fiber Bragg gratings and micro-fabricated stainless steel housings. Stainless steel housings convert radial forces that are applied to the housing into axial forces that can be sensed by the fiber Bragg grating. This sensor offers a number of advantages over competing technologies including small size, high sensitivity, fast response time, large dynamic range and insensitivity to EMI.
Metal housings were fabricated using several methods including laser micromachining, swaging, and hydroforming. Swaging and hydroforming offered the best possibility of manufacturing large quantities of housing that have uniform dimensions and thus require less sensor-specific calibration.
A testing process was developed that allows for the study of sensors under controlled hydrostatic loading. Testing results indicate that these sensors can be produced with resolutions below 0.5 psi. These sensors were also successfully demonstrated in realistic in vitro testing conditions.
In the future, successful implementation of this sensor will require future study in several important areas. First, improved assembly methods will need to be developed. In particular these methods should be suitable for small housing dimensions and should result in more robust sensors. Along these lines, we are currently exploring the use of 3D printing as a means of fabricating consistent flexure mounts. Second, we are currently expanding our design to allow for distributed pressure sensing. In this design, multiple FBGs that are designed with different center wavelengths are distributed along the same optical fiber. This will allow sensing to take place at multiple locations with only a single optical feed. Third, we are investigating an introducer method that will make insertion of the sensor minimally invasive.
The authors wish to sincerely thank Drs. Neil Sharkey and Stephen Piazza of the Penn State Universities CELOS laboratory for use of their Dynamic Gait Simulator (DGS). This work was supported by the National Institutes of Health (NIH).
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