Research And Application On Ultrasonic Full Waveform Inversion In Bone Quantitative Techniques

Bone mineral density measurement is one of the important means to prevent and diagnose diseases of orthopedics.And the ultrasound quantitative techniques reflects the size of bone mineral density by using the propagation velocity of ultrasound in bone medium.It has the advantages of no radiation damage and low price.Traditional ultrasound quantitative measurement methods can not reflect the internal structure of bone.Combining tomography with ultrasound,bone parameters images of tissue cross-section can be obtained by inversion algorithm.Full waveform inversion algorithm is one of the most commonly used methods in seismic data processing for obtaining accurate parameters of the underground model.Compared with seismic data processing,ultrasonic quantitative measurement is mainly composed of four differences:(1)Seismic source is generally only 1OHz to 30Hz,and the frequency of ultrasonic source is usually more than IOOKHz.(2)Because the propagation velocity between the bone and the surrounding soft tissues is too large with narrow transition band and large mutation.,the inversion is easy to fall into the local minimum value and the phenomenon of cycle skipping.(3)In bone inversion,the grid scale is smaller,usually in the millimeter or micron scale.Therefore,a more accurate inversion algorithm is needed.In this paper,I improved the forward and inverse parts of the traditional full waveform inversion algorithm and innovatively applied the full waveform inversion algorithm to the quantitative techniques of bone ultrasound,which overcame the difficulties and needs of ultrasonic bone quantitative techniques.And the value and distribution of the velocity parameters and density parameters of bone tissue can be successfully obtained.In the forward part,a new hybrid-grids finite difference method is proposed in this dissertation.Through the wave field coupling of grid points,we can use conventional grids in the computational area and the staggered grids in perfectly matched layer absorbing region.At the same time,it takes both advantages of the former’s high computational efficiency and the latter’s high absorptive capacity of the reflected wave.Through a series of numerical experiments,the error between the conventional grids and the staggered grids was compared with the analytical solution of the acoustic wave.It was proved that the conventional grids is more efficient in the case of the same accuracy as the staggered grids.I also compared the absorption effect of the new hybrid grid method,the traditional perfectly matched layer conditions,the second-order perfectly matched layer conditions and the hybrid ABC conditions.It was proved that the absorption eflfect of the our hybrid grid method is not worse than the traditional perfectly matched layer conditions and the second-order perfectly matched layer conditions and is higher than the hybrid ABC conditions with shorter computational time and easier implementation.In the inversion part,I studied the Gauss Newton regularization method for time domain inversion comprehensively and discussed the influence of various factors on the inversion results in this paper.On the one hand,it was proved that the variation of the diffraction angle between the source and the receiving point can increase the coverage of the wave number by the simple bone cancellous inversion,also choosing the appropriate number of the source,the receivers and the time sampling rate can reduce the amount of computation without affecting the inversion effect.On the other hand,it was proved that the multiscale scale algorithm can avoid the cycle skipping and the local minimum of the object function when the difference between the initial model and the object model was too large,and successfully reconstruct the parameter image by the simple bone cortex inversion.At the same time,a new joint velocity-density inversion method is used to improve the inversion effect of density..Finally,the velocity inversion image and the density inversion image of approximate theoretical model of tibia and fibula and three-dimensional theoretical model of long bone were successfully obtained.The error between the object model and reconstructed model was about two percent.After adding some Gauss white noise,a good inversion image can still be obtained.Experiments show that the improved full waveform inversion algorithm is effective and robust in bone quantitative measurement.