Question

In: Statistics and Probability

A ultrasound technician (also known as diagnostic medical sonographers) have the knowledge and responsibility to perform...

A ultrasound technician (also known as diagnostic medical sonographers) have the knowledge and responsibility to perform ultrasound examinations utilizing a technology that creates detailed and dynamic images of the body's internal organs using high frequency sound waves. How can probability help these professionals perform their job duties?

(Be sure to include how probability is set up, what conclusions you can draw as you figure the probability, and any potential challenges in establishing probability statistics in your scenario).

Solutions

Expert Solution

1. LINK:- https://www.ncbi.nlm.nih.gov/pubmed/22559607

PURPOSE: Ultrasound temperature estimation based on probability variation of backscatter data.

we assumed that the degree of variation in the probability distribution of the backscattered signals is temperature dependent.

METHODS: Experiments on agar phantoms and tissue samples using a temperature-regulated water tank and a microwave ablation system. During heating, raw images of the backscattered-signal envelope of each phantom and tissue at temperatures ranging between 37?°C and 45?°C were acquired to construct the parametric matrix based on the ratio of the change in the Nakagami parameter (RCN), which was used as a quantitative measure of the backscatter statistics. The absolute value of the RCN (ARCN) matrix was obtained, to which a polynomial approximation was applied to obtain the ARCN(pa) image.

RESULTS: The results showed that the RCN matrix locally increased or decreased with increasing temperature, indicating bidirectional changes in the backscatter statistics. Also the ARCN significantly increased with the temperature, demonstrating that the magnitude of the variation in the probability distribution of the backscattered-signal envelope is a monotonic function of temperature.

2. LINK:- https://www.nature.com/articles/srep39379

Purpose:- Statistical Characterization of the Medical Ultrasound Echo Signals

Method:- This model based on the assumption that the human tissue is composed of a large number of scattering cells, both the magnitudes and the phases of the backscattered ultrasound echoes from the cells are statistically independent and obey the normal distribution1. The joint probability density function of these two components, representing the distribution function of the echo signal, results in a Rayleigh distribution1.

By applying the concept of the set theory, every single value of yi occupy a space point xi along the vertical scanning line as yi?=?AiSin(x) within each half period. The probability distribution of y depends on the number of the corresponding space point xi it occupies. As a result, the probability distribution of y for one half period of the waveform AiSin(x) is H(x)???H(x???Ai), where H(x) is the Heaviside step function with the amplitude of one (Fig. 1c). Re-expressing the function in the P(y) domain, Ai is substituted by yi. Then the total probability density function of y is equivalent to the summation of H(y?+yi)???H(y???yi), which is

3. LINK:- http://iopscience.iop.org/article/10.1088/0031-9155/49/6/011/meta

PURPOSE:-The use of the compound probability density function in ultrasonic tissue characterization

a compound probability density function (pdf) was proposed to model the envelope of the ultrasonic backscattered echo from tissues.The usefulness of this parameter for tissue characterization has been explored through computer simulation of ultrasonic A scans and analyses of the data collected from tissue-mimicking phantoms.


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