Use of smoothing splines for analysis of backscattered ultrasonic waveforms: Application to monitoring of steroid treatment of dystrophic mice

Duchenne muscular dystrophy (DMD) is an Xlinked genetic disease characterized by progressive weakness and wasting of skeletal and cardiac muscle; boys present with weakness by the age of 5 years and, if left untreated, are unable to walk without assistance by the age of 10 years. Therapy for DMD has been primarily palliative, with oral steroids emerging as a first-line approach even though this treatment has serious side-effects. Consequently, low-cost imaging technology suitable for improved diagnosis and treatment monitoring of DMD would be of great value, especially in remote and underserved areas. Previously, we reported use of the logarithm of the signal energy, log [E
_f
], and a new method for ultrasound signal characterization using entropy, H
_f
, to monitor prednisolone treatment of skeletal muscle in a dystrophindeficient mouse model. Three groups were studied: mdx mice treated with prednisolone, a control group of mdx mice treated with saline, and a control group of wild-type mice treated with saline. It was found that both log [E
_f
] and H
_f
were required to statistically differentiate the three groups. In the current study, we show that preprocessing of the raw ultrasound using optimal smoothing splines before computation of either log [E
_f
] or a rapidly computable variant of Hf, denoted I
_f
,
_∞
, permits delineation of all three groups by either metric alone. This opens the way to the ultimate goal of this study, which is identification and implementation of new diagnostically sensitive algorithms on the new generation of low-cost hand-held clinical ultrasonic imaging systems.