## 4 Discussion
### Transition to In Vivo Application  
Cortical bone has been proposed as significant predictor of a bone's mechanical strength because mechanical force given to a bone is carried primally by cortical bone [35]. Clinical studies showed an improvement of fracture prediction by measuring cortical thickness [36; 37; 38]. HR-pQCT is the most precise modality to measure cortical thickness at the tibia with a precision of 1.6% [38]. Our study showed a thickness precision estimation of 5.7%. We expect that the clinical precision of the MF approach could be larger than for controlled simulations; however, HR-pQCT uses ionizing radiation and is extremely expensive compared with ultrasound imaging. [PERSON] et al. [39] proposed a similar refraction measurement method and reported precision values for _Ct.Th_ of 8.5% for measurements on porous plate-shaped skull bone phantoms. In contrast, our study considered bone curvature and bone tilt with a better precision value of 5.67%, which can be attributed to the PAC methods, the use of a higher frequency (4 vs. 2.25 MHz), and the consideration of an effective aperture [19]. In addition to cortical thickness, ultrasonic wave-speed in cortical bone has been proposed as a biomarker for bone quality [10; 40; 41; 42]. Bidirectional axial transmission techniques use a probe with several ultrasonic transmitters and receivers to measure waves traveling in the longitudinal direction of long bones. An in vivo study by [PERSON] et al. used a bidirectional axial transmission technique (BDAT) to estimate the cortical thickness and porosity, and they reported those parameters as suitable biomarkers for fracture discrimination in postmenopausal women [43]. The QUS device Bindex(r) calculates the apparent cortical thickness at the distal radius and tibia using BDAT and reported the correlation with BMD (r \(\geq\) 0.71, \(p\) < 0.001, 0.20 < R\({}^{2}\) < 0.55) [44]. [PERSON] et al. [41] showed that the velocity of the first arriving signal (vFAS) is a significant biomarker for fracture discrimination and to predict fracture risk in vivo. Inter-operator precision (repeated measurements by different operators) for FAS velocities were reported at \(\sim\)7%, respectively. In our study we report the precision value for different simulation models (precision of radial cortical speed of sound was 9.8%), which have been simulated only once. Compared with axial transmission techniques, the multi-focus measurement estimates cortical thickness and speed of sound within the imagined plane and provides image guidance. Another approach to measure _Ct.Th_ and _Ct.v\({}_{11}\)_ using corrected refraction was proposed by [PERSON] et al. [14] using a single-element excitation, full-array waveform capture, and an adapted Kirchhoff migration developed by seismologists to image the earth subsurface. The method was validated in vivo on two young healthy subjects. No precision or accuracy values were reported. In two separate studies, [PERSON] et al[PERSON] [11; 45] proposed the estimation of an apparent _Ct.Th_ from _TOF_ between periosteal and endosteal bone interface at the tibia using a constant predefined speed of sound in cortical bone of 3565 m/s. This approach fails to capture the microstructural changes in porous bone structures and changes in _Ct.v\({}_{11}\)_. In contrast, our method estimates _Ct.Th_ and _Ct.v\({}_{11}\)_ independently; however, in this study, a very simple pore structure was assumed. Further studies should therefore target bone models with more realistic pore diameter distributions. Recently, [PERSON] et al. proposed a cortical backscatter model to retrieve the intracortical pore size distribution non-invasively in the tibia midshaft [46]. These findings were further supported by another study on the same set of bones, which suggested that cortical thinning and backscatter parameters describing the presence and accumulation of large cortical pores in the tibia provide similar or better predictions of proximal femur stiffness and ultimate force than _aBMD_[20].