Ultrasound imaging has emerged as a pivotal modality in medical diagnostics due to its safety, real-time capabilities, and absence of ionizing radiation. This paper presents a comprehensive analysis of echocardiogram image segments obtained from tissue, blood, valve, and combined tissue and blood regions, using curve-fitting techniques utilizing genetic algorithm. The genetic algorithm convergence data, including generation number, cumulative fitness function evaluations, \({R}^{2}\) values, and fitted curve parameters, are documented and analyzed. Furthermore, the optimization results for various probability distribution functions (PDFs) are presented, offering insights into the mean and standard deviation of generation counts, function evaluations, \({R}^{2}\) values, and fitted distribution parameters for Gamma, Gaussian, exponential, and bimodal distributions. The findings show the suitability of the Gamma distribution for modeling the histograms of ultrasound image segments of blood regions, supported by \({R}^{2}\) values ranging from 0.71 to 0.99. Additionally, the study evaluates the goodness of fit for three PDFs—Gaussian, exponential, and bimodal—for the tissue, valve, and combined tissue and blood region, providing insights into the performance of these distributions. Metrics such as \({R}^{2}\) , MAE, AIC, and BIC are presented for each case and compared to evaluate their ability for classification tasks. The work underscores the potential for more specialized PDF models, incorporating hybrid approaches and machine learning techniques, to further enhance the analysis of cardiac ultrasound image segments.