James L. Buchanan

DETERMINATION OF THE PARAMETERS OF CANCELLOUS BONE USING LOW FREQUENCY ACOUSTIC MEASUREMENTS

The Biot model is widely used to model poroelastic media. Several authors have studied its applicability to cancellous bone. In this article the feasibility of determining the Biot parameters of cancellous bone by acoustic interrogation using frequencies in the 5–15 kHz range is studied. It is found that the porosity of the specimen can be determined with a high degree of accuracy. The degree to which other parameters can be determined accurately depends upon porosity.

Determination of the parameters of cancellous bone using high frequency acoustic measurements

The Biot model is widely used to model poroelastic media. Several authors have tested its applicability to cancellous bone, but to do so requires a priori estimation of the parameters of the Biot model, which is an uncertain and expensive endeavor. A method of computing acoustic pressure in the low 100 kHz range is developed.

Recovery of the parameters of cancellous bone by inversion of effective velocities, and transmission and reflection coefficients

Estimating the parameters of an elastic or poroelastic medium from reflected or transmitted acoustic data is an important but difficult problem. Use of the Nelder–Mead simplex method to minimize an objective function measuring the discrepancy between some observable and its value calculated from a model for a trial set of parameters has been tried by several authors. In this paper, the difficulty with this direct approach, which is the existence of numerous local minima of the objective function, is documented for the in vitro experiment in which a specimen in a water tank is subject to an ultrasonic pulse. An indirect approach, based on the numerical solution of the equations for a set of ‘effective’ velocities and transmission coefficients, is then observed empirically to ameliorate the difficulties posed by the direct approach.

Transient reflection and transmission of ultrasonic wave in cancellous bone

Cancellous bone is known to be poroelastic in structure. Ultrasonic wave propagation in cancellous bone can be formulated by using Biots equations. In this paper we present some results in our ongoing research on the reflection and transmission of ultrasonic waves in cancellous bone. We investigate the relations among reflected waves, transmitted waves and Biot coefficients. We present an algorithm for the determination of the porosity of cancellous bone.

Identification, by the intersecting canonical domain method, of the size, shape and depth of a soft body of revolution located within an acoustic waveguide

The Rayleigh hypothesis is employed to solve the forward problem of scattering of a known, arbitrary acoustic wave from a body of revolution immersed in a shallow body of water. The acoustic wavefields obtained in this way are then employed as simulated data for the inverse problem of the determination of the (unknown) size, shape and depth of the immersed body, which is known to be acoustically soft, axisymmetric in shape and located on the vertical axis of a Cartesian reference system within the shallow-water waveguide. This fully 3D inverse problem is solved by the intersecting canonical domain, using multifrequency scattered field data, for two types of body: a non-convex (indented) spindle and a conical seamount.

TRANSMISSION LOSS IN THE FAR FIELD OVER A SEABED WITH RIGID SUBSTRATE ASSUMING THE BIOT SEDIMENT MODEL

A system of differential equations is derived from Biots constitutive and motion equations for a poroelastic material. The seabed is modeled as a poroelastic layer over a rigid substrate. A residue expansion for pressure in the far field is found in the case of constant parameters. The models prediction for transmission loss is examined for five different types of sediments.

RECOVERY OF THE POROELASTIC PARAMETERS OF CANCELLOUS BONE USING LOW FREQUENCY ACOUSTIC INTERROGATION

Cancellous bone is a porous type of bone found in the spine and at all articulating joints. It is a porous cellular solid, consisting of an irregular three-dimensional array of bony rods and plates, called trabeculae. Bone marrow fills the spaces of the pores. The study of cancellous bone is important, among other reasons, because the thinning of the trabeculae is a cause of osteoporosis. Hence determination of the porosity (pore space volume/total volume) of cancellous bone by acoustic interrogation would be useful in diagnosing osteoporosis. In view of the structure of cancellous bone Biot’s model of a poroelastic medium as an elastic frame with a connected pore space filled with fluid may be applicable. Williams 4 , McKelvie and Palmer 3 , and Hosokawa and Otani have compared the predictions of the Biot model for cancellous bone with experimental measurements. In order to do this the parameters upon which the Biot model depends had to be determined. Some of the parameters were measured, but others were estimates taken from the literature or based

Transmission loss in a shallow ocean over a two-layer seabed

Abstract Three mathematical models of a two-layer seabed are considered. The first assumes that both layers are elastic solids, the second that the upper layer is poroelastic while the substrate is elastic, and the third that both layers are poroelastic. The first and third models are found to produce reasonable agreement with data and each other, but the second model produces poor predictions because of mathematical incompatibilities of the poroelastic and elastic models.

Wavelet decomposition of transmitted ultrasound wave through a 1-D muscle-bone system

In the attempt for using ultrasound as a diagnostic device for osteoporosis, several authors have described the result of the in vitro experiment in which ultrasound is passed through a cancellous bone specimen placed in a water tank. However, in the in vivo setting, a patients cancellous bone is surrounded by cortical and muscle layers. This paper considers in the one-dimensional case (1) what effect the cortical bone segments surrounding the cancellous segment would have on the received signal and (2) what the received signal would be when a source and receiver are placed on opposite sides of a structure consisting of a cancellous segment surrounded by cortical and muscle layers. Mathematically this is accomplished by representing the received signal as a sum of wavelets which go through different reflection-transmission histories at the muscle-cortical bone and cortical-cancellous bone interfaces. The muscle and cortical bone are modeled as elastic materials and the cancellous bone as a poroelastic material described by the Biot-Johnson-Koplik-Dashen model. The approach presented here permits the assessment of which possible paths of transmission and reflection through the cortical-cancellous or muscle-cortical-cancellous complex will result in significant contributions to the received waveform. This piece of information can be useful for solving the inverse problem of non-destructive assessment of material properties of bone. Our methodology can be generalized to three-dimensional parallelly layered structure by first applying Fourier transform in the directions perpendicular to the transverse direction.

FINDING AN INCLUSION IN A SHALLOW OCEAN USING THE ICBA METHOD

In this paper we continue our investigation of the undetermined object problem in an acoustic wave guide. We consider objects which are deformed cylinders which may be represented, in terms of cylindrical coordinates, as Here δ is considered to be a small parameter. In order not to commit the inverse crime by using the same method for generating the field as in computing the image (the inversion procedure) we generate the acoustic field by using a perturbation method. The inverse imaging is done by the intersecting canonical domain method. Numerous experiments indicate that this method performs the inverse imaging well.