IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-24, NO. 6, NOVEMBER 1977 A Non-Invasive Technique for Detecting Stress Waves in Bone Using the Piezoelectric Effect SUBRATA SAHA AND RODERIC S. LAKES Abstract-A stress wave propagating in a long bone is accompanied by a traveling electrical charge generated as a result of the piezoelectric character of bone. An electromagnetic device has been developed which can detect the magnetic fields associated with this charge and which is capable of monitoring stress waves in bone in vivo. The field measurement is independent of the mechanical properties of the soft tissue overlying the bone, so that difficulties previously encountered with vibration and wave propagation tests to determine in vivo proper- ties of bone are avoided. Applications to the diagnosis of bone dis- orders are discussed. I. INTRODUCTION E LASTIC wave propagation techniques have been a subject of considerable investigation as experimental methods for the diagnosis of bone disorders. The objective of such experi- mentation is to non-invasively determine the in vivo mechani- cal properties of bone tissue. The development of a viable technique of this type would provide information currently unavailable from radiography and would be of use in the diagnosis of osteoporosis [13, [21 and of fracture healing. As early as 1958, Anast et al. [31 propagated ultrasonic waves .across fracture sites in living subjects; however the lack of statistical significance of this work has been criticized [4] . Experiments in which physical properties of bone have been successfully correlated with wave propagation parameters [5], [6], [7], [8] have generally involved excised specimens and are therefore not directly applicable to clinical situations. More recently, instrumented hammers and accelerometers have been used to determine the propagation speed of stress pulses in bone in vivo [9]. However no correlation with disease states was obtained. The delay of an ultrasonic wave across a fracture site has been found to be too small to cause a measurable change in the average propagation velocity, partic- ularly when the delays associated with soft tissue in vivo are considered [101. Amplitude attenuation appears to be a more suitable measure of the degree of union. Other authors have attempted to use impedance tests to determine the in vivo mechanical properties of bone [11]. A major drawback inherent in these approaches is the soft tissue through which the pulses or ultrasonic waves must be propagated to excite the bone and to be detected [Fig. 11. The variations in the quantity and quality of soft tissue from patient to patient constitute a complicating variable which cannot be easily evaluated [121 . The present research is aimed at developing a technique for the detection of stress waves in Manuscript received July 23, 1976; revised January 10, 1977. This work was supported by USPHS Research Grant 5R01 AM 18360. The authors are with the Department of Engineering and Applied Science, Yale University, New Haven, CT 06520. MECHANICAL EXCITATION SENSORS \BONE SOFT TISSUE FRACTURE Fig. 1. Generalized wave propagation scheme for assessing fracture healing. living bone, which is independent of the mechanical properties of the soft tissue and therefore is not subject to these limita- tions. The technique is based on a measurement of the magnetic field generated by a stress wave as a result of the piezoelectric effect in bone. The measurement of artificially induced magnetic fields used here is to be distinguished from techniques such as magnetocardiography [13], [141 in which naturally occurring magnetic fields resulting from currents in the heart, are detected. II. THE PIEZOELECTRIC EFFECT Piezoelectric response in a material is said to occur if the electric displacement vector Di depends not only on the elec- tric field E but also on the stress tensor Ujk. The constitutive equation for linear piezoelectricity with stress and electric field as independent variables is: Di = dijk usk+ KijEj where Ki1 is the dielectric permittivity tensor and dik is the piezoelectric tensor. In general these coupling coefficients will depend on frequency as a result of relaxation effects, so that K and d must be regarded as complex quantities. A number of authors have suggested alternative nomencla- ture to describe the electromechanical behavior of bone, in view of the uncertainty regarding the mechanisms responsible for such behavior, and in view of recently observed deviations from classical piezoelectric response [15]. Nevertheless, in the interest of brevity, in the present work we shall use the term "piezoelectric" to describe stress or strain related polar- izations in bone. The existence of piezoelectric behavior in dry bone was reported by Fukada and Yasuda [16] in 1957; more recently the effect has also been observed in wet bone [171, [18], [19]. The magnitude of the d coefficients, which are a measure of the strength of piezoelectric coupling, is known to depend on temperature, frequency, and relative humidity for compact bone. The largest piezoelectric coefficients for bone are those associated with shearing deformations. For compact bone at body temperature and 97% relative humidity, Re [dl23] is of 508