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Background of QUS in cortical bone assessment
Osteoporosis has been recognized as a silent epidemic and there is increasing demand to mass screening and management. It results from a period of asymptotic bone loss and hence reduced bone strength. Currently, the mainly clinical assessment of osteoporosis relies on the Bone Mineral density (BMD) measured by dual X-ray absorptiometry (DXA) and quantitative X-ray computed tomography (QCT) (Frost et al., 2001; Kanis and Gluer, 2000; Marshall et al., 1996), which are ionizing radiation and relatively expense and bulky.
BMD is not sufficient to evaluate the strength of bone, while the remain part is due to bone micro structure and bone mechanical properties. Since ultrasound is a mechanical wave, it can be used to represent the mechanical properties of cortical bone through the variation of speed of sound, frequency attenuation, when it is propagating through the cortical bone. It is possible that ultrasound might give some architectural information about the bone and thus improve strength estimation. There is a growing interest in potential applications of quantitative ultrasound (QUS), because it is non-ionizing, relatively portable and relatively less expensive than DXA (Barkmann et al., 2008, 2009; Bauer, 1997; Frost et al., 2001; Hans and Krieg, 2008). This chapter will give a review of ultrasound in cortical bone assessment.
QUS measurements
Osteoporosis mainly caused by cortical loss shown in Fig. 1.1.1 (Bousson et al., 2006; Holzer et al., 2009; Mayhew et al., 2005) is currently diagnosed by dual X-ray absorptiometry (DXA) as a standard method for assessment of bone mineral density (BMD) (Greenfield, 1998). However, the BMD is not sufficient to evaluate the cortical bone strength (Siris et al., 2004), (Briot et al., 2013). Quantitative ultrasound (QUS) can be an effective mean to investigate the bone strength, which has played an increasing role in the assessment of bone status in past decades (Grimal et al., 2013; Mano et al., 2015; Stein et al., 2013). The QUS parameters known as broadband ultrasound attenuation (BUA) and speed of sound (SOS) are well correlated with the established variable bone mineral density (BMD) reported in (Enneman et al., 2014; Krieg and Didier, 2010; Olszynski et al., 2016; Prins et al., 2008; Töyräs et al., 2002). Currently, QUS is emerging an alternative tool to absorptiometry techniques to evaluation the risk of fracture and osteoporosis, some significant innovations of applying QUS in investigating of cortical bone statues will deliberate in following context. QUS is now showing a promising probability in clinical application as a predictor of hip fracture and osteoporosis (Hans and Krieg, 2008), (Hans and Baim, 2017). However, the performance of these techniques still has a large room to improve. The rapid development signal processing techniques provide us a potential tool to improve the performance of these method in aspects of accuracy, resolution and robust.
Speed of sound
The velocity of an ultrasound wave depend on both of the properties of the medium and the propagated mode. Cortical bone is a elastic modulus where the wave propagates containing a longitudinal and shear waves. The clinical velocity measurements including pulse-echoes and transmission technology by recording the travel time in a known distance, usually measured by X-ray based imaging method. In the bone application, the traveling time is denoted as time of flight (TOF), which usually measured by detect a specific reference point in the transmitted wave. As such reference points, the first point when a fixed or relative threshold is exceeded (Haiat et al., 2005), (Langton et al., 2001), (Nicholson et al., 1999), first or second maximum (Laugier et al.), envelope maximum (Le, 1999), zero crossing (Currey, 2001), (Rossman et al., 2001), or correlation maximum (Strelitzki et al., 1999) have been used. Alternatively, the phase velocity can be calculated in the frequency domain (Droin et al., 1998). In some application, the time of flight (TOF) as a single parameter measured by assuming a constant heel thickness and therefor the velocity measured is dependent upon heel width. using the SOS to evaluate the status of bone has been investigated for decades. The TOF measurements and pulse-echo techniques are the most common approach. In (ABENDSCHEIN and HYATT, 1972), Abendschein and Hyatt show a well correlation between the mechanical properties and elastically modulus of bovine cortical bone. Evans and Tavakoli has reported a highly significant correlation (r = 0.85) between velocity and physical density of bovine femur (Tavakoli and Evans, 1992). Njeh et al. and Bouxsein (Bouxsein and Radloff, 1997) have reported a significant correlation (r = 0.82 and 0.71) between ultrasound velocity and ultimate strength of human calcaneus.
There has also been investigated its correlation with established ionizing radia-tion measurements of BMD, the correlation is week reported in these investigations due to the other aspects of bone, such as density. The first study of using velocity and BMD to measure the hip fracture is reported in (Heaney, 1989), where it is observed that the velocity in calcaneus is sensitively.
BUA
It has been demonstrated that the attenuation of ultrasound over a frequency of 0.2 − 0.6 MHz is linear and its slope could different between normal and osteo-porotic subjects. The relationship between BUA and density of cancellous bone samples obtained from cadavers has been reported high correlated (r = 0.85) in (McCloskey et al., 1990). Most applications of evaluating BUA in vivo focus on the heel, where the calcaneus is approximately 90% composed of trabecular bone. A number of commercial calcanea BUA systems have been reported significant differ-ence between them ((Njeh et al., 2001)), some of them are shown in Fig. 1.2. The pulse-echo technique has also been applied to the analysis of the BUA in the cal-caneus trabecular bone ((Chaffa et al., 2000; Wear, 1999)). It is a roughly method based on the selection of the most appropriate time window before analysis of the echoes, this time window being evaluated from a particular depth within the calca-neus. To overcome the influence of multi-path transmission in the proximal femur of complex shape, a model-based estimation of the ultrasound parameters has been developed to evaluate the BUA ((Dencks et al., 2008)). However, the cortical bone, that represents about 80% of the human skeleton, plays an important role in the skeletal bio-mechanical stability ((Bala et al., 2014; Holzer et al., 2009; Zebaze et al., 2010)). (Han et al., 1996; Lakes et al., 1986; Lees and Klopholz, 1992; Sasso et al., 2008) has investigated the BUA of bovine femur cortical bone in vitro in the fre-quency range of 0.3-4.5 MHz. In plenty previously works ((McCloskey et al., 1990; Prins et al., 2008; Töyräs et al., 2002)), the linear dependence of the measured attenuation with frequency mainly occurs in the frequency range 200 ∼ 600 kHz. On the other hand, (Sasso et al., 2008) suggest that the BUA measurements performed around 4MHz are more sensitive to the cortical bone microstructure.
Cortical thickness
Since the cortical bone is mainly strength loading part, the thickness of the cortical bone is correlated with the mechanical strength of the bone and the risk of osteoporotic fractures. the thickness of cortical bone layer has been shown to significant correlated (r = 0.88) with the fracture load at distal radius (Augat et al., 2009). The thickness of cortical bone can be measured by the pQCT with ionizing radiation. So a cheap, radiation free method to measure the cortical thickness is valuable in clinical application.
Pulse-echo ultrasound measurements for the assessment of cortical bone thick-ness was proposed in (Wear, 2003) by using autocorrelation and cepstral methods, which are evaluated in human tibia samples and one volunteer, shown in Fig. 1.3(a). Further more, considering the in vivo ultrasound signal is more noisier than that obtained in vitro, autocorrelation method will exist false peak by the interferences, the envelop and cepstral methods are evaluated in a larger range of samples iv vivo in (Karjalainen et al., 2008a; Schousboe et al., 2016). The two methods have shown good correlation with the measurements by pQCT with almost same performance. However, the evaluation is based on the whose cortical thickness are distributed in a large range, it’s difficult to observed good correlation with pQCT when the cortical thickness is narrowed in smaller range. As we know, human radius cortical shell are more thiner the the tibia’s, and with smaller shift at the same time, which proposed a big challenge, caused by seriously overlapping of backscattered echoes, to envelop and cepstral methods. OMP shows promising performance to deal with serious overlapping by dividing the time delays of echoes in smaller interval and reconstructing the echo in each iteration. Firstly, the most correlated column with residual from the last iteration is been found , it corresponds to an echoes consisted of ultrasound parameters and its index indicates the time delay. So OMP can es-timate BUA and Co.Th. indicated by all the ultrasound parameters at the same time in relatively thin cortical bone, such as radius.
(Vallet et al., 2016) have used guided wave to estimated the radius cortical thick-ness by considering the cortical bone as a wave-guide and achieving the dispersion curve , this system can be used to estimate both of the cortical thickness and elastic parameter, which is shown in Fig. 1.3(b).
three model of QUS measurement
There are three different scheme using QUS to measure the cortical bone: Trans-verse transmission, axis transmission, pulse-echo, which are chosen according to different site of bone and the parameter needed to be measured. The scheme of these measured approaches is shown in Fig. 1.4.
Pulse-echo Ultrasound
The pulse-echo ultrasound is limited used in QUS parameter estimation, since the strong attenuation of bone, especially the trabecular bone. However, it is pop-ular in the estimating the thickness of cortical bone in (Karjalainen et al., 2008a; Schousboe et al., 2016; Wear, 2003), showing a good correlation with the thickness measured by pQCT. And the measured site is limited in tibia cortical bone and radius cortical bone, with a thin soft tissue. However, the pulse-echo ultrasound is very widely used in the industry domain to measure the properties and struc-ture of inspected medium. In this work, through combining with advanced signal processing algorithm, we try to improve the performance of pulse-echo ultrasound in accessing the cortical bone. And this the first time we try to use pulse-echo ultrasound to estimate the cortical thickness and BUA at the same time.
Transverse Transmission
Transverse transmission is the most widely use in measuring the SOS, TOF, BUA of bone, since the high contrast and attenuation of bone. varieties of BUA measurement are applied with transverse transmission, (Njeh et al., 2001) has compared six commercial instruments with transmission scheme in BUA measurements. The BUA is usually be applied at the bovine in vivo measurements, since of the bovine is mainly consist of trabecular bone. An important limitation of QUS is the measurement on peripheral skeletal sites, which can provide better hip fracture risk prediction. A QUS scanner has been developed by Barkmann et al (Barkmann et al., 2007) for direct assessment of skeletal properties at the proximal femur.
It has been report these transverse-transmission measurements could be used to discriminate the fractures, sharing the same performance with DXA (Barkmann et al., 2009). In recent research, the transverse transmission through the femur sites consist of two kinds of wave, direct wave and guided wave. The direct wave is through the trabecular bone, and the guided wave acts as a circumferential guided wave when propagating through the cortical bone. The circumferential guided wave has been tested ex-vivo on femurs (Grimal et al., 2013), and indicating that the time-of-flight of the FAS signal revealed a strong relationship with femur strength (R = 0.79). And the simulations of ultrasound propagation through the femoral neck has shown its connection with cortical porosity and thickness (Rohde et al., 2014). However, these research of transmission measurements at the proximal femur are performed by a pair of single-element transducers. Array systems can increase the flexibility of such QUS measurements and may enable a better estimation by adjusting for the impact of bone geometry (Rohde et al., 2014).
Axis transmission
Ultrasound axial transmission has been used to measure cortical bone in-vivo for decades. The time-of-flight of the first arriving signal (FAS) was initially used in clinical to evaluate the osteoporotic fracture (Talmant et al., 2009). However, the velocity of FAS depended on various bone properties , eg, cortical thickness, porosity, bone mineral density, and elasticity (Bossy et al., 2004b), and as so for, there isn’t sufficient physical interpretation of velocity of FAS connected with osteoporosis and fracture. Furthermore, to measure the FAS velocity with different frequency has been used to enhance the capacity of measuring the cortical bone properties (Egorov et al., 2014; Sarvazyan et al., 2009; Tatarinov et al., 2014). Recently, in some research the cortical bone can be considered as a waveguide for ultrasound (Lefebvre et al., 2002; Moilanen et al., 2003; Protopappas et al., 2007). More specifically, cortical bone is a multi-model waveguide when the ultrasonic range is between 100 kHZ and 2 MHz. The frequency-dependent propagation speed of each mode is determined by a specific combination of stiffness coefficients and thickness of the waveguide, which are more specifically for evaluating individual bone qualities. The dispersion curve of cortical bone, compared with appropri-ate waveguide modeling, can provide effective stiffness coefficients and cortical thickness (Foiret et al., 2012; Lefebvre et al., 2002; Moilanen et al., 2007). The estimation of waveguide thickness and elastic coefficients has been validated on bone mimicking phantoms and on ex-vivo human radius specimens (Foiret et al., 2012). In our laboratory, a novel divided with this method has been developed to measure the cortical thickness and elastic parameter in vivo (Bochud et al., 2017; Vallet et al., 2016).
Table of contents :
Abstract
1 Introduction
1.1 Background of QUS in cortical bone assessment
1.1.1 QUS measurements
1.1.2 three model of QUS measurement
1.1.3 the improvement of these thesis in bone parameters estimation
1.2 Background of ultrasound imaging in industrial and medical domain
1.2.1 ultrasound tomography
1.2.2 Full waveform inversion
1.2.3 Time domain topological energy
1.2.4 The improvement of cortical bone imaging in this thesis
2 Sparse signal processing in the evaluation of the cortical bone
2.1 Sparse signal processing
2.1.1 Signal model
2.1.2 Dictionary
2.1.3 Orthogonal Matching Pursuit
2.1.4 Adapted Orthogonal Matching Pursuit
2.2 Estimation of the Cortical Thickness and Broadband Ultrasound Attenuation
2.3 Numerical simulation of the OMP in the cortical bone assessment
2.3.1 2D numerical simulation
2.3.2 Application of OMP in imaging with a phased array transducer
2.4 Experimental validation
2.4.1 The sawbone plates
2.4.2 Ex-vivo measurement of the cortical bone
2.4.3 In-vivo measurement of the cortical bone
2.4.4 Results
2.5 Discussion
2.6 Appendix: Comparison between OMP and the envelop method
2.7 Appendix: Received in vivo signal and reconstruction by OMP
3 Cortical bone imaging by Time Domain Topological Energy
3.1 Time Domain Topological Gradient
3.1.1 Cost function
3.1.2 The topological gradient for linear elasticity and elastodynamics
3.1.3 Iterative process for the Time Domain Topological Gradient
3.2 Numerical simulations
3.2.1 Image of a 2D cross-section of cortical bone
3.3 Result Discussion
3.3.1 Velocity mismatch
3.3.2 Sampling frequency and time interval in TDTE integration
3.4 in vitro femur neck cortical bone validation
4 TDTE with Sparse Signal Processing for Cortical Bone Imaging
4.1 Sparse Signal Processing
4.1.1 Signal Model
4.1.2 Simplified version of OMP
4.1.3 Model based OMP without building dictionary
4.2 Additional processing
4.2.1 Envelope processing
4.2.2 Curve fitting
4.3 Numerical simulation
4.4 Experimental validation using the cortical bone phantom
4.5 Appendix
5 Iterative TDTE applied to cortical bone imaging
5.1 Iterative TDTE
5.2 Numerical simulation
5.2.1 Cortical bone with irregular internal boundary
5.3 bone phantom validation
5.4 Iterative TDTE of cortical bone with osteoporosis (pores inside cortical bone)
6 Quantitative Imaging of Cortical Bone by FullWaveform Inversion
6.1 Migration by adjoint method
6.1.1 The connection between imaging and adjoint kernels
6.1.2 Numerical implementation of sensitive kernels
6.2 Numerical imaging of cortical bone internal boundary by adjoint kernels
6.3 Full waveform inversion
6.4 Numerical Implement
6.4.1 pre-processing, post-processing, Nonlinear optimization
6.4.2 Numerical implement
7 Summary and conclusion
7.1 Summary
7.2 Comparation between TDTE, migration and full waveform inversion
Bibliography
