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Zhu C, Gerald RE, Huang J. Micromachined Optical Fiber Sensors for Biomedical Applications. Methods Mol Biol 2022; 2393:367-414. [PMID: 34837190 DOI: 10.1007/978-1-0716-1803-5_20] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Optical fibers revolutionized the rate of information reception and transmission in telecommunications. The revolution has now extended to the field of physicochemical sensing. Optical fiber sensors (OFSs) have found a multitude of applications, spanning from structural health monitoring to biomedical and clinical measurements due to their unique physical and functional advantages, such as small dimensions, light weight, immunity to electromagnetic interference, high sensitivity and resolution, multiplexing, and remote operation. OFSs generally rely on the detection of measurand-induced changes in the optical properties of the light propagating in the fiber, where the OFS essentially functions as the conduit and physical link between the probing light waves and the physicochemical parameters under investigation. Several advanced micromachining techniques have been developed to optimize the structure of OFSs, thus improving their sensing performance. These techniques include fusion splicing, tapering, polishing, and more complicated femtosecond laser micromachining methods. This chapter discusses and reviews the most recent developments in micromachined OFSs specifically for biomedical applications. Step-by-step procedures for several optical fiber micromachining techniques are detailed.
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Affiliation(s)
- Chen Zhu
- Department of Electrical and Computer Engineering, Missouri University of Science and Technology, Rolla, MO, USA
| | - Rex E Gerald
- Department of Electrical and Computer Engineering, Missouri University of Science and Technology, Rolla, MO, USA
| | - Jie Huang
- Department of Electrical and Computer Engineering, Missouri University of Science and Technology, Rolla, MO, USA.
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O'Connor SM, Kaufman KR, Ward SR, Lieber RL. Sensor Anchoring Improves the Correlation Between Intramuscular Pressure and Muscle Tension in a Rabbit Model. Ann Biomed Eng 2021; 49:912-921. [PMID: 33001290 PMCID: PMC8083084 DOI: 10.1007/s10439-020-02633-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2020] [Accepted: 09/18/2020] [Indexed: 10/23/2022]
Abstract
Intramuscular pressure (IMP) shows promise for estimating individual muscle tension in vivo. However, previous pressure measurements show high variability during isometric contraction and poor correlation with tension during dynamic contraction. We hypothesized that enhanced sensor anchoring/orientation would improve tension estimation and thus developed a novel pressure sensor with a barbed housing. Sensors were inserted into the tibialis anterior (TA) of New Zealand White rabbits (N = 8) both parallel and perpendicular to the fiber orientation. We measured muscle stress and IMP during both isometric and dynamic contractions. Passive stress showed good agreement for both insertion directions across muscle lengths (ICC > 0.8). Active stress and IMP agreement were good (ICC = 0.87 ± 0.04) for perpendicular insertions but poor (ICC = 0.21 ± 0.22) for parallel insertions across both dynamic contractions and isometric contractions within the muscle's range of motion. These findings support use of IMP measurements to estimate muscle tension across a range of contraction conditions.
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Affiliation(s)
- Shawn M O'Connor
- School of Exercise and Nutritional Sciences, San Diego State University, San Diego, CA, USA
| | - Kenton R Kaufman
- Department of Orthopedic Surgery, Mayo Clinic, Rochester, MN, USA
| | - Samuel R Ward
- Department of Orthopaedic Surgery, University of California San Diego, La Jolla, CA, USA
- Department of Bioengineering, University of California San Diego, La Jolla, CA, USA
- Department of Radiology, University of California San Diego, La Jolla, CA, USA
| | - Richard L Lieber
- Department of Orthopaedic Surgery, University of California San Diego, La Jolla, CA, USA.
- Department of Bioengineering, University of California San Diego, La Jolla, CA, USA.
- Veteran's Administration San Diego Healthcare System, San Diego, CA, USA.
- Shirley Ryan AbilityLab and Northwestern University, 355 E. Erie Street, Chicago, IL, 60611, USA.
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Coote JM, Alles EJ, Noimark S, Mosse CA, Little CD, Loder CD, David AL, Rakhit RD, Finlay MC, Desjardins AE. Dynamic physiological temperature and pressure sensing with phase-resolved low-coherence interferometry. OPTICS EXPRESS 2019; 27:5641-5654. [PMID: 30876162 PMCID: PMC6410922 DOI: 10.1364/oe.27.005641] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/08/2023]
Abstract
We report the development and characterisation of highly miniaturised fibre-optic sensors for simultaneous pressure and temperature measurement, and a compact interrogation system with a high sampling rate. The sensors, which have a maximum diameter of 250 µm, are based on multiple low-finesse optical cavities formed from polydimethylsiloxane (PDMS), positioned at the distal ends of optical fibres, and interrogated using phase-resolved low-coherence interferometry. At acquisition rates of 250 Hz, temperature and pressure changes of 0.0021 °C and 0.22 mmHg are detectable. An in vivo experiment demonstrated that the sensors had sufficient speed and sensitivity for monitoring dynamic physiological pressure waveforms. These sensors are ideally suited to various applications in minimally invasive surgery, where diminutive lateral dimensions, high sensitivity and low manufacturing complexities are particularly valuable.
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Affiliation(s)
- J. M. Coote
- Department of Medical Physics and Biomedical Engineering, University College London, Gower Street, London WC1E 6BT, United Kingdom
- Wellcome/EPSRC Centre for Interventional and Surgical Sciences, University College London, Charles Bell House, 43-45 Foley Street, London W1W 7TS, United Kingdom
| | - E. J. Alles
- Department of Medical Physics and Biomedical Engineering, University College London, Gower Street, London WC1E 6BT, United Kingdom
- Wellcome/EPSRC Centre for Interventional and Surgical Sciences, University College London, Charles Bell House, 43-45 Foley Street, London W1W 7TS, United Kingdom
| | - S. Noimark
- Department of Medical Physics and Biomedical Engineering, University College London, Gower Street, London WC1E 6BT, United Kingdom
- Wellcome/EPSRC Centre for Interventional and Surgical Sciences, University College London, Charles Bell House, 43-45 Foley Street, London W1W 7TS, United Kingdom
- Materials Chemistry Research Centre, Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, United Kingdom
| | - C. A. Mosse
- Department of Medical Physics and Biomedical Engineering, University College London, Gower Street, London WC1E 6BT, United Kingdom
- Wellcome/EPSRC Centre for Interventional and Surgical Sciences, University College London, Charles Bell House, 43-45 Foley Street, London W1W 7TS, United Kingdom
| | - C. D. Little
- Department of Medical Physics and Biomedical Engineering, University College London, Gower Street, London WC1E 6BT, United Kingdom
- Wellcome/EPSRC Centre for Interventional and Surgical Sciences, University College London, Charles Bell House, 43-45 Foley Street, London W1W 7TS, United Kingdom
- The Royal Free Hospital, Pond Street, London NW3 2QG, United Kingdom
| | - C. D. Loder
- The Royal Free Hospital, Pond Street, London NW3 2QG, United Kingdom
| | - A. L. David
- Wellcome/EPSRC Centre for Interventional and Surgical Sciences, University College London, Charles Bell House, 43-45 Foley Street, London W1W 7TS, United Kingdom
- Institute for Women’s Health, University College London, 86-96 Chenies Mews, London WC1E 6HX, United Kingdom
| | - R. D. Rakhit
- Wellcome/EPSRC Centre for Interventional and Surgical Sciences, University College London, Charles Bell House, 43-45 Foley Street, London W1W 7TS, United Kingdom
- The Royal Free Hospital, Pond Street, London NW3 2QG, United Kingdom
| | - M. C. Finlay
- Department of Medical Physics and Biomedical Engineering, University College London, Gower Street, London WC1E 6BT, United Kingdom
- Wellcome/EPSRC Centre for Interventional and Surgical Sciences, University College London, Charles Bell House, 43-45 Foley Street, London W1W 7TS, United Kingdom
- Barts Heart Centre, St Bartholomew’s Hospital and Queen Mary University of London, Charterhouse Square, London EC1M 6BQ, United Kingdom
| | - A. E. Desjardins
- Department of Medical Physics and Biomedical Engineering, University College London, Gower Street, London WC1E 6BT, United Kingdom
- Wellcome/EPSRC Centre for Interventional and Surgical Sciences, University College London, Charles Bell House, 43-45 Foley Street, London W1W 7TS, United Kingdom
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Go SA, Litchy WJ, Evertz LQ, Kaufman KR. Evaluating skeletal muscle electromechanical delay with intramuscular pressure. J Biomech 2018; 76:181-188. [PMID: 29908653 DOI: 10.1016/j.jbiomech.2018.05.029] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2017] [Revised: 03/13/2018] [Accepted: 05/30/2018] [Indexed: 11/28/2022]
Abstract
INTRODUCTION Intramuscular pressure (IMP) is the fluid pressure generated within skeletal muscle and directly reflects individual muscle tension. The purpose of this study was to assess the development of force, IMP, and electromyography (EMG) in the tibialis anterior (TA) muscle during ramped isometric contractions and evaluate electromechanical delay (EMD). METHODS Force, EMG, and IMP were simultaneously measured during ramped isometric contractions in eight young, healthy human subjects. The EMD between the onset of force and EMG activity (Δt-EMG force) and the onset of IMP and EMG activity (Δt EMG-IMP) were calculated. RESULTS A statistically significant difference (p < 0.05) was found between the mean force-EMG EMD (36 ± 31 ms) and the mean IMP-EMG EMD (3 ± 21 ms). CONCLUSIONS IMP reflects changes in muscle tension due to the contractile muscle elements.
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Affiliation(s)
- Shanette A Go
- Department of Orthopedic Surgery, Mayo Clinic Rochester, 200 1st Street SW, Rochester, MN 55905, USA; Mayo Clinic School of Medicine, Mayo Clinic Rochester, 200 1st Street SW, Rochester, MN 55905, USA
| | - William J Litchy
- Department of Neurology, Mayo Clinic Rochester, 200 1st Street SW, Rochester, MN 55905, USA
| | - Loribeth Q Evertz
- Department of Orthopedic Surgery, Mayo Clinic Rochester, 200 1st Street SW, Rochester, MN 55905, USA; Mayo Clinic School of Medicine, Mayo Clinic Rochester, 200 1st Street SW, Rochester, MN 55905, USA
| | - Kenton R Kaufman
- Department of Orthopedic Surgery, Mayo Clinic Rochester, 200 1st Street SW, Rochester, MN 55905, USA.
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Characterization of three dimensional volumetric strain distribution during passive tension of the human tibialis anterior using Cine Phase Contrast MRI. J Biomech 2016; 49:3430-3436. [PMID: 27665350 DOI: 10.1016/j.jbiomech.2016.09.002] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2015] [Revised: 08/25/2016] [Accepted: 09/07/2016] [Indexed: 11/23/2022]
Abstract
Intramuscular pressure correlates strongly with muscle tension and is a promising tool for quantifying individual muscle force. However, clinical application is impeded by measurement variability that is not fully understood. Previous studies point to regional differences in IMP, specifically increasing pressure with muscle depth. Based on conservation of mass, intramuscular pressure and volumetric strain distributions may be inversely related. Therefore, we hypothesized volumetric strain would decrease with muscle depth. To test this we quantified 3D volumetric strain in the tibialis anterior of 12 healthy subjects using Cine Phase Contrast Magnetic Resonance Imaging. Cine Phase Contrast data were collected while a custom apparatus rotated the subjects' ankle continuously between neutral and plantarflexion. A T2-weighted image stack was used to define the resting tibials anterior position. Custom and commercial post-processing software were used to quantify the volumetric strain distribution. To characterize regional strain changes, the muscle was divided into superior-inferior sections and either medial-lateral or anterior-posterior slices. Mean volumetric strain was compared across the sections and slices. As hypothesized, volumetric strain demonstrated regional differences with a decreasing trend from the anterior (superficial) to the posterior (deep) muscle regions. Statistical tests showed significant main effects and interactions of superior-inferior and anterior-posterior position as well as superior-inferior and medial-lateral position on regional strain. These data support our hypothesis and imply a potential relationship between regional volumetric strain and intramuscular pressure. This finding may advance our understanding of intramuscular pressure variability sources and lead to more reliable measurement solutions in the future.
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Design Considerations of a Fiber Optic Pressure Sensor Protective Housing for Intramuscular Pressure Measurements. Ann Biomed Eng 2016; 45:739-746. [PMID: 27495350 DOI: 10.1007/s10439-016-1703-6] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2016] [Accepted: 07/30/2016] [Indexed: 10/21/2022]
Abstract
Intramuscular pressure (IMP), defined as skeletal muscle interstitial fluid pressure, reflects changes in individual muscle tension and may provide crucial insight into musculoskeletal biomechanics and pathologies. IMP may be measured using fiber-optic fluid pressure sensors, provided the sensor is adequately anchored to and shielded from surrounding muscle tissue. Ineffective anchoring enables sensor motion and inadequate shielding facilitates direct sensor-tissue interaction, which result in measurement artifacts and force-IMP dissociation. The purpose of this study was to compare the effectiveness of polyimide and nitinol protective housing designs to anchor pressure sensors to muscle tissue, prevent IMP measurement artifacts, and optimize the force-IMP correlation. Anchoring capacity was quantified as force required to dislodge sensors from muscle tissue. Force-IMP correlations and non-physiological measurement artifacts were quantified during isometric muscle activations of the rabbit tibialis anterior. Housing structural integrity was assessed after both anchoring and activation testing. Although there was no statistically significant difference in anchoring capacity, nitinol housings demonstrated greater structural integrity and superior force-IMP correlations. Further design improvements are needed to prevent tissue accumulation in the housing recess associated with artificially high IMP measurements. These findings emphasize fundamental protective housing design elements crucial for achieving reliable IMP measurements.
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Reinhardt L, Siebert T, Leichsenring K, Blickhan R, Böl M. Intermuscular pressure between synergistic muscles correlates with muscle force. J Exp Biol 2016; 219:2311-9. [DOI: 10.1242/jeb.135566] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/27/2015] [Accepted: 05/16/2016] [Indexed: 11/20/2022]
Abstract
ABSTRACT
The purpose of the study was to examine the relationship between muscle force generated during isometric contractions (i.e. at a constant muscle–tendon unit length) and the intermuscular (between adjacent muscles) pressure in synergistic muscles. Therefore, the pressure at the contact area of the gastrocnemius and plantaris muscle was measured synchronously to the force of the whole calf musculature in the rabbit species Oryctolagus cuniculus. Similar results were obtained when using a conductive pressure sensor, or a fibre-optic pressure transducer connected to a water-filled balloon. Both methods revealed a strong linear relationship between force and pressure in the ascending limb of the force-length relationship. The shape of the measured force–time and pressure–time traces was almost identical for each contraction (r=0.97). Intermuscular pressure ranged between 100 and 700 mbar (70,000 Pa) for forces up to 287 N. These pressures are similar to previous (intramuscular) recordings within skeletal muscles of different vertebrate species. Furthermore, our results suggest that the rise in intermuscular pressure during contraction may reduce the force production in muscle packages (compartments).
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Affiliation(s)
- Lars Reinhardt
- Science of Motion, Friedrich-Schiller-University Jena, Seidelstr. 20, Jena D-07749, Germany
| | - Tobias Siebert
- Institute of Sport and Motion Science, University of Stuttgart, Allmandring 28, Stuttgart D-70569, Germany
| | - Kay Leichsenring
- Institute of Solid Mechanics, Technical University Braunschweig, Schleinitzstr. 20, Braunschweig D-38106, Germany
| | - Reinhard Blickhan
- Science of Motion, Friedrich-Schiller-University Jena, Seidelstr. 20, Jena D-07749, Germany
| | - Markus Böl
- Institute of Solid Mechanics, Technical University Braunschweig, Schleinitzstr. 20, Braunschweig D-38106, Germany
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Evaluation of a fiber-optic technique for recording intramuscular pressure in the human leg. J Clin Monit Comput 2015; 30:699-705. [PMID: 26271511 DOI: 10.1007/s10877-015-9750-3] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2014] [Accepted: 08/10/2015] [Indexed: 10/23/2022]
Abstract
To evaluate a forward-sensing fiber-optic pressure technique for recording of intramuscular pressure (IMP) in the human leg and investigate factors that may influence IMP measurements used in diagnosing compartment syndromes. IMP in the tibialis anterior muscle was recorded simultaneously by a fiber-optic technique and needle-injection technique in 12 legs of 7 healthy subjects. Both measurement catheters were placed in parallel with the muscle fibers to the same depth, as verified by sonography. IMP recordings were performed at rest before, during and after applying a model of abnormally elevated IMP (simulated compartment syndrome). IMP was elevated by venous obstruction induced by a thigh tourniquet of a casted leg. IMP was also measured during injections of 0.1 ml of saline into the muscle through the catheters. IMP at baseline was 5.1 (SD = 2.6) mmHg measured with the fiber-optic technique and 7.1 (SD = 2.5) mmHg with the needle-injection technique (p < 0.001). It increased to 48.5 (SD = 6.9) mmHg and 47.6 (SD = 6.6) mmHg respectively, during simulated compartment syndrome. IMP increased significantly following injection of 0.1 ml of saline, measured by both techniques. It remained increased 1 min after injection. The fiber-optic technique was able to record pulse-synchronous IMP oscillations. The fiber-optic technique may be used for IMP measurements in a muscle with both normal and abnormally elevated IMP. It has good dynamic properties allowing for measurement of IMP oscillations. Saline injection used with needle-injection systems to ensure catheter patency compromises IMP readings at least one minute after injection.
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Optical Fibre Pressure Sensors in Medical Applications. SENSORS 2015; 15:17115-48. [PMID: 26184228 PMCID: PMC4541926 DOI: 10.3390/s150717115] [Citation(s) in RCA: 81] [Impact Index Per Article: 8.1] [Reference Citation Analysis] [Abstract] [Key Words] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/01/2015] [Revised: 07/01/2015] [Accepted: 07/02/2015] [Indexed: 12/13/2022]
Abstract
This article is focused on reviewing the current state-of-the-art of optical fibre pressure sensors for medical applications. Optical fibres have inherent advantages due to their small size, immunity to electromagnetic interferences and their suitability for remote monitoring and multiplexing. The small dimensions of optical fibre-based pressure sensors, together with being lightweight and flexible, mean that they are minimally invasive for many medical applications and, thus, particularly suited to in vivo measurement. This means that the sensor can be placed directly inside a patient, e.g., for urodynamic and cardiovascular assessment. This paper presents an overview of the recent developments in optical fibre-based pressure measurements with particular reference to these application areas.
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Abraham AC, Villegas DF, Kaufman KR, Donahue TLH. Internal pressure of human meniscal root attachments during loading. J Orthop Res 2013; 31:1507-13. [PMID: 23775981 PMCID: PMC3902857 DOI: 10.1002/jor.22408] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 10/19/2012] [Accepted: 05/14/2013] [Indexed: 02/04/2023]
Abstract
This study investigated the internal fluid pressure of human cadaver meniscal root attachments. A pressure micro-sensor was implanted inside each attachment site. Tibiofemoral joints were compressed to 2× body weight at various flexion angles and pressure recorded for 20 min. The anterior cruciate ligament (ACL) was then transected and joints retested. Lastly, a longitudinal incision of the lateral posterior (LP) horn was made and the joint retested. Ramp pressure was defined as the pressure when 2× body weight was reached, and equilibrium pressure was recorded at the end of the hold period. The medial posterior (MP) attachment was subjected to greater ramp pressure than the medial anterior (p = 0.002) and greater equilibrium pressure than all other root attachment sites (p < 0.001). Flexion angle had a significant effect on pressure as full extension was greatest at ramp (p = 0.040). Transection of the ACL decreased ramp pressure in the LP attachment (p = 0.025) and increased equilibrium pressure (p = 0.031) in the MP attachment. The results suggest that repair strategies should be developed which reconstruct the MP attachments to be sufficient to withstand large pressures. Furthermore, since meniscal pressure is highest at full extension, this fact should be considered when prescribing rehabilitation following repair of an attachment.
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Affiliation(s)
- Adam C. Abraham
- Department of Mechanical Engineering, Colorado State University, Fort Collins, Colorado 80523
| | - Diego F. Villegas
- Department of Mechanical Engineering, Universidad del Turabo, Gurabo, Puerto Rico 00778
| | - Kenton R. Kaufman
- Biomechanics and Motion Analysis Lab, Orthopedic Surgery, Mayo Clinic, Rochester, Minnesota 59905
| | - Tammy L. Haut Donahue
- Department of Mechanical Engineering, Colorado State University, Fort Collins, Colorado 80523
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Morrow DA, Odegard GM, Kaufman KR. Use of a Poroelastic Model to Predict Intramuscular Pressure. POROMECHANICS V : PROCEEDINGS OF THE FIFTH BIOT CONFERENCE ON POROMECHANICS, JULY 10-12, 2013, VIENNA, AUSTRIA. BIOT CONFERENCE ON POROMECHANICS (5TH : 2013 : VIENNA, AUSTRIA) 2013; 2013:2174-2183. [PMID: 25541627 PMCID: PMC4275105 DOI: 10.1061/9780784412992.256] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/31/2022]
Abstract
Measurement of individual muscle tension in a clinical setting has yet to be achieved. Previous investigators have suggested that the tension in skeletal muscle, comprised of approximately 70% fluid, could be determined using interstitial muscle fluid pressure (IMP). A computational model is needed to aid in understanding IMP distribution in muscles of varying geometry and contractile states without exhaustive testing. The first aim of this study was to determine a set of transversely isotropic material properties (i.e., permeability, relaxed modulus, and drained Poisson's ratio) for excised skeletal muscle using inverse finite element analysis with a poroelastic constitutive formulation on tension data from either longitudinal or transverse uniaxial load-relaxation tests of skeletal muscle tissue. The second aim was to compare pore pressure estimated from a model to experimental pressure measurements to assess its ability to accurately predict IMP. Results of this study indicated that skeletal muscle was transversely isotropic under load-relaxation as demonstrated by significant differences in the drained Poisson's ratio. It was also noted that the drained Poisson's ratios under both longitudinal and transverse loading were negative in these tests of excised muscle tissue. Pore pressure calculated with this model provided a good prediction of the development of IMP. These results point to the benefit of using a poroelastic model of skeletal muscle to predict IMP.
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Affiliation(s)
- D A Morrow
- Motion Analysis Laboratory, Department of Orthopedic Surgery, Mayo Clinic, 200 First Street SW, Rochester, MN 55906
| | - G M Odegard
- Department of Mechanical Engineering-Engineering Mechanics, Michigan Technological University, 1400 Townsend Drive, Houghton, MI 49931
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