The paper describes an investigation of a subjectively distinguishable element of high speed jet noise known as ‘crackle’. ‘Crackle’ cannot be characterized by the normal spectral description of noise. It is shown to be due to intense spasmodic short-duration compressive elements of the wave form. These elements have low energy spread over a wide frequency range. The crackling of a large jet engine is caused by groups of sharp compressions in association with gradual expansions. The groups occur at random and persist for some 10−1s, each group containing about 10 compressions, typically of strength 5 × 10−3 atmos at a distance of 50 m. The skewness of the amplitude probability distribution of the recorded sound quantifies crackle, though the recording process probably changes the skewness level. Skewness values in excess of unity have been measured; noises with skewness less than 0·3 seem to be crackle free. Crackle is uninfluenced by the jet scale, but varies strongly with jet velocity and angular position. The jet temperature does not affect crackle, neither does combustion. Supersonic jets crackle strongly whether or not they are ideally expanded through convergent-divergent nozzles. Crackle is formed (we think) because of local shock formation due to nonlinear wave steepening at the source and not from long-term nonlinear propagation. Such long-term effects are important in flight, where they are additive. Some jet noise suppressors inhibit crackle.

Introduction In this study, we aimed to investigate the feasibility of gadoxetate low‐temporal resolution (LTR) DCE‐MRI for voxel‐based hepatic extraction fraction (HEF) quantification for liver sparing radiotherapy using a deconvolution analysis (DA) method. Methods The accuracy and consistency of the deconvolution implementation in estimating liver function was first assessed using simulation data. Then, the method was applied to DCE‐MRI data collected retrospectively from 64 patients (25 normal liver function and 39 cirrhotic patients) to generate HEF maps. The normal liver function patient data were used to measure the variability of liver function quantification. Next, a correlation between HEF and ALBI score (a new model for assessing the severity of liver dysfunction) was assessed using Pearson's correlation. Differences in HEF between Child‐Pugh score classifications were assessed for significance using the Kruskal–Wallis test for all patient groups and Mann–Whitney U ‐test for inter‐groups. A statistical significance was considered at a P ‐value <0.05 in all tests. Results The results showed that the implemented method accurately reproduced simulated liver function; root‐mean‐square error between estimated and simulated liver response functions was 0.003, and the coefficient‐of‐variance of HEF was <20%. HEF correlation with ALBI score was r = −0.517, P < 0.0001, and HEF was significantly decreased in the cirrhotic patients compared to normal patients ( P < 0.0001). Also, HEF in Child‐Pugh B/C was significantly lower than in Child‐Pugh A ( P = 0.024). Conclusion The study demonstrated the feasibility of gadoxetate LTR‐DCE MRI for voxel‐based liver function quantification using DA. HEF could distinguish between different grades of liver function impairment and could potentially be used for functional guidance in radiotherapy.

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