Entropic Imaging of Cataract Lens: An In Vitro Study

Abstract

Phacoemulsification is a common surgical method for treating advanced cataracts. Determining the optimal phacoemulsification energy depends on the hardness of the lens involved. Previous studies have shown that it is possible to evaluate lens hardness via ultrasound parametric imaging based on statistical models that require data to follow a specific distribution. To make the method more system-adaptive, nonmodel-based imaging approach may be necessary in the visualization of lens hardness. This study investigated the feasibility of applying an information theory derived parameter – Shannon entropy from ultrasound backscatter to quantify lens hardness. To determine the physical significance of entropy, we performed computer simulations to investigate the relationship between the signal-to-noise ratio (SNR) based on the Rayleigh distribution and Shannon entropy. Young's modulus was measured in porcine lenses, in which cataracts had been artificially induced by the immersion in formalin solution in vitro. A 35-MHz ultrasound transducer was used to scan the cataract lenses for entropy imaging. The results showed that the entropy is 4.8 when the backscatter data form a Rayleigh distribution corresponding to an SNR of 1.91. The Young's modulus of the lens increased from approximately 8 to 100 kPa when we increased the immersion time from 40 to 160 min (correlation coefficient r = 0.99). Furthermore, the results indicated that entropy imaging seemed to facilitate visualizing different degrees of lens hardening. The mean entropy value increased from 2.7 to 4.0 as the Young's modulus increased from 8 to 100 kPa (r = 0.85), suggesting that entropy imaging may have greater potential than that of conventional statistical parametric imaging in determining the optimal energy to apply during phacoemulsification.

Effects of Fatty Infiltration of the Liver on the Shannon Entropy of Ultrasound Backscattered Signals

“…The RF data were used for entropy imaging by using a standard sliding window algorithm [30,31] as follows: (i) A square window within the data was used to acquire local RF signals. Different ultrasound systems may produce different dynamic ranges of RF signals (i.e., y max − y min ); therefore, signal normalization was performed to limit the variance of signal amplitudes between −1 and 1; (ii) The normalized RF signals were used for establishing the probability density function w(y) (the statistical histogram using 200 bins was used; the width of a bin was 0.01) and calculating the RF data-based entropy value (denoted by H R ) by using Equation (1), which was assigned as the new pixel located in the center of the window; (iii) The window was moved across the entire range of image data in steps of the number of pixels corresponding to a 50% window overlap ratio, and the first step was repeated to yield a H R parametric map.…”

“…The uncompressed envelope images with normalized amplitude between 0 and 1 were also used for constructing the parametric images of entropy (denoted by H E ) using the same algorithmic procedure, as shown in Figure 1. The side length of the square sliding window was determined as being three times the transducer pulse length (6.9 mm), as suggested for ensuring stable estimations for statistical parameters [30,31]. The programming was implemented using MATLAB software (Version R2012a, MathWorks, Inc., Natick, MA, USA).…”

“…One requisite of using statistical models to fit echo amplitude distributions is that the ultrasound envelope data must conform to the used distribution [29][30][31][32]. This requirement may not always be satisfied in practice because different systems have different hardware and software designs for envelope detection.…”

Ultrasound Detection of Scatterer Concentration by Weighted Entropy

“…One constraint to employing physically based statistical models for fitting the backscattered envelopes is that the distribution of the backscatter envelope data must conform to the used distribution [13,[17][18][19]. This requirement may not always be satisfied because adjusting the settings in an ultrasound system or using nonlinear signal processing approaches (e.g., logarithmic compression) may alter the statistical distribution of raw data.…”

“…Hughes first proposed using information (Shannon) entropy for analyzing ultrasound signals, indicating that entropy can be used to quantitatively characterize the changes in the microstructures of scattering media [22][23][24][25][26]. Entropy is also a function of probability density; therefore, it may be related to distribution parameters to reflect the physical meaning of backscattered statistics to some degree [17,19]. Compared with the distribution parameters, entropy is estimated using the raw waveform of ultrasound radiofrequency (RF) data returned from a scattering medium (not envelope data), thereby preventing the possible effects of the demodulation method on parameter estimation.…”