## 2 Materials and Methods
### Classical Digital Signal Processing  
The presence of an open growth plate before its full ossification affects the ultrasonic wave propagation through the forearm and the wrist, which needs to be detected by an algorithm. Instead of previous approaches used by other researchers and vendors of bone age ultrasound devices, we do not measure the average speed of sound of an ultrasound wave through the bone to correlate this value with empirically determined speed of sound values for certain ossification states and bone ages. Our approach is based on the fact that the ultrasound signal differs more while the ultrasound transducer is moved over an open growth plate than it changes while being moved over fully ossified bone. Hence, the analysis must look for signal differences caused by changes in relative orientation of  
Figure 6: STARD 2015 flowchart of the study cohort. Exclusion criteria were previous fracture of the left wrist, hand, or underarm; precocious puberty; pubertats tarda; growth hormone deficiency; congenital adrenal hyperplasia; previous radio- or chemotherapy; previous high-dose steroid therapy; Turner syndrome; Down syndrome; transgender individuals undergoing/previous hormone therapy; tall stature individuals undergoing hormone therapy; non-treated hyper- or hypothyroidism or severe obesity (BMI > 40).  
the bone and the US transducers during transducer movements. In subjects with an open growth plate, the measurements may differ more significantly from the signals measured next to the epiphyseal gap, through the bone, or around the bone. This can be caused by less attenuation and change in US propagation speed due to different stages of ossification or changes in bone surface structure that reflect and diffract the US wave at the boundaries of the growth plate. The presence of a growth plate potentially leads to larger changes in reflectivity or ratio of transmitted US waves as the reflectivity and intensity of transmitted US waves differ more than the signal changes while moving over an ossified growth plate. A growth plate without full ossification results in a slower US wave as it travels through more non-bony tissue and less-ossified bone tissue. Due to the lateral extension of the acoustic beam, parts of the wave still travel through the bone tissue located outside the growth plate. This results in an overlay of both traveling paths, with the signal through the open growth plate submerging into the other signal (see Figure 7).  
The exact location of a potentially open growth plate varies between individuals. However, in order to detect full growth plate ossification, identifying the exact location of the growth plate is not necessary, only its potential influence on signal change when the transducer moves across it.  
Our classical signal processing approach computes the integral changes in signal amplitude of the received signals over all measurements during transducer motion over the possible open growth plate area. It also computes the sum of all differences over each consequential A-scan difference and the sum of all changes over all A-scans. All permutations of transmit/receive ultrasound transducer elements are used for both transmission scans through the wrist/arm and reflection measurements on a single side using the same array transducer. According to our hypothesis, these integrated changes of subsequent measurements during the movement should be higher in subjects with an open growth plate compared to those with a fully ossified growth plate.  
Figure 7: The left forearm is placed in the device with the transducers of the motorized sled positioned around the assumed location of the growth plate (left). The acoustic wave propagation through the growth plate (blue) and the radius bone (pink) is depicted in the enlarged detail inset on the right.