Stiness properties of the human lumbar spine: A lumped parameter model Leslie Nicholson a, * , Christopher Maher a , Roger Adams a , Nhan Phan-Thien b a The School of Physiotherapy, The Faculty of Health Sciences, The University of Sydney, East Street, P.O. Box 170, Lidcombe, New South Wales 2141, Australia b The Department of Mechanical Engineering, The University of Singapore, Singapore Received 21 August 2000; accepted 19 December 2000 Abstract Objective. To characterise with a mechanical model, the force±displacement response of the human lumbar spine to postero± anterior loading. Design. Single case with repetition. Background. Previous attempts to characterise the spine's force±displacement response have been simplistic and only considered the loading curve. These approaches ignored valuable information such as viscosity, non-linear elasticity and inertia of the lumbar spine. Methods. The Spinal Assessment Machine applied a postero±anterior load to the spines of 23 asymptomatic subjects and measured the force±displacement response. The data was analysed by two methods; by a traditional linear regression of part of the loadingcurveandbyanewmethodwhereanequationincludingnon-linearstinessanddampingwasusedtocharacterisethewhole force±displacement relationship. Results. The equation developed was found to account for virtually all of the variance in the raw data R 2 > 0:993). Four ele- ments derived by the equation determine the contributions of linear elasticity, non-linear elasticity, linear viscosity and non-linear viscosity to the overall stiness. Conclusions. Consideringtheexcellent®tofthenewequationtotherawdataanditspoorcorrelationwithexistingmeasures,itis proposed that the traditional measures provide an incomplete description of the force±displacement response. Relevance Therapists use their perception of the force±displacement response of the spine to select the type of manipulative treatment to apply. To study this aspect of patient care, devices capable of measuring spinal stiness have been developed, however to date the obtained data has been analysed only simply. A lumped parameter mechanical model incorporating non-linear damping and stiness provides a more complete description of the force±displacement response and thus may oer added insight into the ma- nipulative treatment of spinal pain. Ó 2001 Elsevier Science Ltd. All rights reserved. Keywords: Measurements; Perception; Viscosity; Stiness and tests 1. Introduction Whenpushingonthespineoflowbackpainpatients, manual therapists collect information about the pain elicited and the stiness they perceive. The information gained from a pushing technique termed the postero± anterior PA) pressure test [1] is used for clinical diag- nosis; both to select the region of the spine towards which treatment will be directed and to select the most appropriate technique to be used [1,2]. In the quest to better understand the response of the spine to a PA pressure, a number of devices have been constructed which are capable of loading the spine in- vivo) in a manner similar to the PA pressure test. These allow variables such as force, frequency of oscillation and displacement to be precisely controlled. The ®rst such device, called the ``spinal physiotherapy simulator'' SPS), was designed by Lee and Svensson [3]. It was the prototype for the ``spinal assessment machine'' SAM) that was built to be a portable, lighter, and smaller Clinical Biomechanics 16 2001) 285±292 www.elsevier.com/locate/clinbiomech * Corresponding author. E-mail address: l.nicholson@cchs.usyd.edu.au L. Nicholson). 0268-0033/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII:S0268-003300)00117-0