{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,25]],"date-time":"2026-06-25T09:26:50Z","timestamp":1782379610441,"version":"3.54.5"},"reference-count":44,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2018,1,19]],"date-time":"2018-01-19T00:00:00Z","timestamp":1516320000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This work focuses on the proof-mass mechanical structural design improvement of a tri-axial piezoresistive accelerometer specifically designed for head injuries monitoring where medium-G impacts are common; for example, in sports such as racing cars or American Football. The device requires the highest sensitivity achievable with a single proof-mass approach, and a very low error (&lt;1%) as the accuracy for these types of applications is paramount. The optimization method differs from previous work as it is based on the progressive increment of the sensor proof-mass mass moment of inertia (MMI) in all three axes. Three different designs are presented in this study, where at each step of design evolution, the MMI of the sensor proof-mass gradually increases in all axes. The work numerically demonstrates that an increment of MMI determines an increment of device sensitivity with a simultaneous reduction of cross-axis sensitivity in the particular axis under study. This is due to the linkage between the external applied stress and the distribution of mass (of the proof-mass), and therefore of its mass moment of inertia. Progressively concentrating the mass on the axes where the piezoresistors are located (i.e., x- and y-axis) by increasing the MMI in the x- and y-axis, will undoubtedly increase the longitudinal stresses applied in that areas for a given external acceleration, therefore increasing the piezoresistors fractional resistance change and eventually positively affecting the sensor sensitivity. The final device shows a sensitivity increase of about 80% in the z-axis and a reduction of cross-axis sensitivity of 18% respect to state-of-art sensors available in the literature from a previous work of the authors. Sensor design, modelling, and optimization are presented, concluding the work with results, discussion, and conclusion.<\/jats:p>","DOI":"10.3390\/s18010289","type":"journal-article","created":{"date-parts":[[2018,1,22]],"date-time":"2018-01-22T04:51:13Z","timestamp":1516596673000},"page":"289","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Mechanical Structural Design of a MEMS-Based Piezoresistive Accelerometer for Head Injuries Monitoring: A Computational Analysis by Increments of the Sensor Mass Moment of Inertia"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7375-8208","authenticated-orcid":false,"given":"Marco","family":"Messina","sequence":"first","affiliation":[{"name":"Maritime and Mechanical Engineering Department, Liverpool John Moores University, James Parsons Building Byrom Street, Liverpool L3 3AF, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8055-4457","authenticated-orcid":false,"given":"James","family":"Njuguna","sequence":"additional","affiliation":[{"name":"Centre for Advanced Materials Engineering, School of Engineering, Robert Gordon University, Aberdeen AB10 7GJ, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chrysovalantis","family":"Palas","sequence":"additional","affiliation":[{"name":"Maritime and Mechanical Engineering Department, Liverpool John Moores University, James Parsons Building Byrom Street, Liverpool L3 3AF, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2018,1,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"5132","DOI":"10.1143\/JJAP.47.5132","article-title":"First-Principles Study on Piezoresistance Effect in Silicon Nanowires","volume":"47","author":"Nakamura","year":"2008","journal-title":"Jpn. J. Appl. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Sasaki, S., Seki, T., Imanaka, K., Kimata, M., Toriyama, T., Miyano, T., and Sugiyama, S. (2007, January 28\u201331). Batteryless-Wireless Mems Sensor System with a 3d Loop Antenna. Proceedings of the 2007 IEEE Sensors, Atlanta, GA, USA.","DOI":"10.1109\/ICSENS.2007.4388384"},{"key":"ref_3","first-page":"299","article-title":"Dynamic Response Criteria for Ice Hockey Helmet Design","volume":"Volume V-B","author":"Bishop","year":"1976","journal-title":"Biomechanics"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1080\/00913847.1979.11948439","article-title":"The Ice Hockey Helmet: How Effective Is It","volume":"7","author":"Bishop","year":"1979","journal-title":"Phys. Sportsmed."},{"key":"ref_5","first-page":"19","article-title":"Changes in the Centre of Mass and Moment of Inertia of a Headform Induced by a Hockey Helmet and Face Shield","volume":"8","author":"Bishop","year":"1983","journal-title":"Can. J. Appl. Sport Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"600","DOI":"10.1097\/00005373-196609000-00005","article-title":"Tolerance Curves of Acceleration and Intracranial Pressure and Protective Index in Experimental Head Injury","volume":"6","author":"Gurdjian","year":"1966","journal-title":"J. Trauma Acute Care Surg."},{"key":"ref_7","unstructured":"Hodgson, V.R. (1973). Biomechanical Study of Football Head Impacts Using a Human Head Model: A Final Report Prepared for Nocsae, National Operating Committee on Standards for Athletic Equipment (NOCSAE)."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"15","DOI":"10.3233\/BME-1993-3102","article-title":"Energy Absorption Characteristics of Football Helmets under Low and High Rates of Loading","volume":"3","author":"Myers","year":"1993","journal-title":"Bio-Med. Mater. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1197\/aemj.10.1.85","article-title":"Does Soccer Headgear Attenuate the Impact When Heading a Soccer Ball?","volume":"10","author":"Naunheim","year":"2003","journal-title":"Acad. Emerg. Med."},{"key":"ref_10","first-page":"185","article-title":"Intracranial Pressure and Acceleration Accompanying Head Impacts in Human Cadavers","volume":"113","author":"Gurdjian","year":"1961","journal-title":"Surg. Gynecol. Obstet."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"604","DOI":"10.1111\/j.1553-2712.2001.tb00171.x","article-title":"Do Football Helmets Reduce Acceleration of Impact in Blunt Head Injuries?","volume":"8","author":"Lewis","year":"2001","journal-title":"Acad. Emerg. Med."},{"key":"ref_12","first-page":"437","article-title":"Are Helmets Protective in High Impact Collisions?","volume":"7","author":"Lewis","year":"2000","journal-title":"Acad. Emerg. Med."},{"key":"ref_13","first-page":"5","article-title":"Measurement of Impact Acceleration: Mouthpiece Accelerometer Versus Helmet Accelerometer","volume":"42","author":"Higgins","year":"2007","journal-title":"J. Athl. Train."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Knox, T. (2004). Validation of Earplug Accelerometers as a Means of Measuring Head Motion, SAE International.","DOI":"10.4271\/2004-01-3538"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"672","DOI":"10.1227\/01.NEU.0000108782.68099.29","article-title":"The Development of a Method to Measure Head Acceleration and Motion in High-Impact Crashes","volume":"54","author":"Olvey","year":"2004","journal-title":"Neurosurgery"},{"key":"ref_16","unstructured":"Corporation, D. (2018, January 18). Delphi\u2019s Innovative Earpiece Sensor System Becomes Safety Requirement for Indy Racing League Drivers. Available online: http:\/\/www.prnewswire.com\/news-releases\/delphis-innovative-earpiece-sensor-system-becomes-safety-requirement-for-indy-racing-league-drivers-74498057.html."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Begeman, P., Melvin, J., Troxel, T., and Mellor, A. (2006). Frequency Response and Coupling of Earpiece Accelerometers in the Human Head, SAE International.","DOI":"10.4271\/2006-01-3657"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1367","DOI":"10.4271\/2008-01-2978","article-title":"Improving Earpiece Accelerometer Coupling to the Head","volume":"1","author":"Salzar","year":"2008","journal-title":"SAE Int. J. Passeng. Cars Mech. Syst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"652","DOI":"10.4271\/2008-01-2976","article-title":"New Sensors to Track Head Acceleration During Possible Injurious Events","volume":"1","author":"Knox","year":"2009","journal-title":"SAE Int. J. Passeng. Cars Electron. Electr. Syst."},{"key":"ref_20","unstructured":"Messina, M. (2013). Design and Optimization of a Novel Tri-Axial Miniature Ear-Plug Piezoresistive Accelerometer with Nanoscale Piezoresistors. [Ph.D. Thesis, Cranfield University]."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Messina, M., and Njuguna, J. (2012, January 8\u201312). Potential of Silicon Nanowires Structures as Nanoscale Piezoresistors in Mechanical Sensors. Proceedings of the IOP Conference Series: Materials Science and Engineering, Miskolc-Lillaf\u00fcred, Hungary.","DOI":"10.1088\/1757-899X\/40\/1\/012038"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1201","DOI":"10.1109\/TMECH.2012.2200258","article-title":"Design and Simulation of a Novel Biomechanic Piezoresistive Sensor with Silicon Nanowires","volume":"18","author":"Messina","year":"2013","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_23","unstructured":"Messina, M., and Njuguna, J. (2014). High Performance Tri-Axial Piezoresistive Accelerometer. (EP2741088A1), Patent."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1109\/JPROC.2009.2013612","article-title":"Review: Semiconductor Piezoresistance for Microsystems","volume":"97","author":"Barlian","year":"2009","journal-title":"Proc. IEEE"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1109\/T-ED.1982.20659","article-title":"A Graphical Representation of the Piezoresistance Coefficients in Silicon","volume":"29","author":"Kanda","year":"1982","journal-title":"IEEE Tran. Electron Devices Soc."},{"key":"ref_26","unstructured":"Wilson, J.S. (2004). Sensor Technology Handbook, Elsevier."},{"key":"ref_27","unstructured":"Mason, W.P., Forst, J.J., and Tornillo, L.M. (1962). Recent Developments in Semiconductor Strain Transducers. Semiconductor and Conventional Strain Gauges, Academic Press."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Amarasinghe, R., Dao, D.V., Dau, V.T., Tung, B.T., and Sugiyama, S. (2009, January 21\u201325). Sensitivity Enhancement of Piezoresistive Micro Acceleration Sensors with Nanometer Stress Concentration Regions on Sensing Elements. Proceedings of the Solid-State Sensors, Actuators and Microsystems Conference, Denver, CO, USA.","DOI":"10.1109\/SENSOR.2009.5285847"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1103\/PhysRev.94.42","article-title":"Piezoresistance Effect in Germanium and Silicon","volume":"94","author":"Smith","year":"1954","journal-title":"Phys. Rev."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1103\/PhysRev.80.72","article-title":"Deformation Potentials and Mobilities in Non-Polar Crystals","volume":"80","author":"Bardeen","year":"1950","journal-title":"Phys. Rev."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1002\/j.1538-7305.1955.tb01472.x","article-title":"Transport Properties of a Many-Valley Semiconductor","volume":"34","author":"Herring","year":"1955","journal-title":"Bell Labs Tech. J."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"944","DOI":"10.1103\/PhysRev.101.944","article-title":"Transport and Deformation-Potential Theory for Many-Valley Semiconductors with Anisotropic Scattering","volume":"101","author":"Herring","year":"1956","journal-title":"Phys. Rev."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Maluf, N. (2002). An Introduction to Microelectromechanical Systems Engineering, IOP Publishing.","DOI":"10.1088\/0957-0233\/13\/2\/701"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1063\/1.1702605","article-title":"Piezoresistive Properties of Silicon Diffused Layers","volume":"34","author":"Tufte","year":"1963","journal-title":"J. Appl. Phys."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1109\/T-ED.1982.20660","article-title":"Nonlinearity of the Piezoresistance Effect of P-Type Silicon Diffused Layers","volume":"29","author":"Kazuji","year":"1982","journal-title":"IEEE Trans. Electron Devices"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"727","DOI":"10.1063\/1.1729524","article-title":"Piezoresistance of Diffused Layers in Cubic Semiconductors","volume":"34","author":"Kerr","year":"1963","journal-title":"J. Appl. Phys."},{"key":"ref_37","unstructured":"Senturia, S.D. (2007). Microsystem Design, Springer Science & Business Media."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1109\/84.846703","article-title":"1\/F Noise Considerations for the Design and Process Optimization of Piezoresistive Cantilevers","volume":"9","author":"Harkey","year":"2002","journal-title":"J. Microelectromech. Syst."},{"key":"ref_39","unstructured":"Marian, B., Ilie, I., Lupu, B., and Comes, M. (2008, January 7\u201311). Signal Conditioner for Piezoelectric Sensors. Proceedings of the 31st International Spring Seminar on Electronics Technology, Budapest, Hungary."},{"key":"ref_40","first-page":"95","article-title":"The Bakerian Lecture: Experimental Determination of the Laws of Magneto-Electric Induction in Different Masses of the Same Metal, and of Its Intensity in Different Metals","volume":"123","author":"Hunter","year":"1833","journal-title":"Philos. Trans. R. Soc. Lond."},{"key":"ref_41","unstructured":"Viet, D.D., Okada, S., Dau, V.T., Toriyama, T., and Sugiyama, S. (November, January 31). Development of a 3-Dof Silicon Piezoresistive Micro Accelerometer. Proceedings of the 2004 International Symposium on Micro-Nanomechatronics and Human Science, 2004 and The Fourth Symposium Micro-Nanomechatronics for Information-Based Society, Nagoya, Japan."},{"key":"ref_42","unstructured":"Freescale Semiconductor (2018, January 18). Accelerometer Terminology Guide (2017). Available online: http:\/\/cache.freescale.com\/files\/sensors\/doc\/support_info\/SENSORTERMSPG.pdf."},{"key":"ref_43","unstructured":"Craig, L., Desmulliez, M.P.Y., Hoff, L., Elle, O.J., and Fosse, E. (2009, January 1\u20133). Mems Three-Axis Accelerometer: Design, Fabrication and Application of Measuring Heart Wall Motion. Proceedings of the 2009 Symposium on Design, Test, Integration & Packaging of MEMS\/MOEMS, Rome, Italy."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"939","DOI":"10.1007\/s10544-007-9072-4","article-title":"Ultraminiature Encapsulated Accelerometers as a Fully Implantable Sensor for Implantable Hearing Aids","volume":"9","author":"Chen","year":"2007","journal-title":"Biomed. Microdevices"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/1\/289\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T14:51:52Z","timestamp":1760194312000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/1\/289"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1,19]]},"references-count":44,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2018,1]]}},"alternative-id":["s18010289"],"URL":"https:\/\/doi.org\/10.3390\/s18010289","relation":{"has-preprint":[{"id-type":"doi","id":"10.20944\/preprints201712.0126.v1","asserted-by":"object"}]},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1,19]]}}}