Based on allometric theory and scaling laws, numerous mathematical models have been proposed to study ontogenetic growth patterns of animals. Although deterministic models have provided valuable insight into growth dynamics, animal growth often deviates from strict deterministic patterns due to stochastic factors such as genetic variation and environmental fluctuations. In this study, we extend a general model for ontogenetic growth proposed by West et al. to stochastic models for ontogenetic growth by incorporating stochasticity using white noise. According to data variance fitting for stochasticity, we propose two stochastic models for ontogenetic growth, one is for determinate growth and one is for indeterminate growth. To develop a universal stochastic process for ontogenetic growth across diverse species, we approximate stochastic trajectories of two stochastic models and apply random time change and obtain a geometric Brownian motion with a multiplier of an exponential time factor. We conduct detailed mathematical analysis and numerical analysis for our stochastic models. Our stochastic models predict well not only average growth, but also variations of growth within species. This stochastic framework may be extended to studies of other growth phenomena.

This paper provides an alternative Slope-Deflection equation for performing the static analysis of the indeterminate structures. While the conventional Slope-Deflection method introduced in undergraduate structural analysis course involves the use of fixed end moments in the Slope-Deflection equations, the proposed method employs the slope of a simply supported beam to obtain the unknown moments at the joints. Three numerical examples of continuous beams with different load configurations are chosen and the efficacy of the proposed equations is demonstrated. From the perspective of undergraduate structural analysis course in Civil Engineering education, the approach proposed in this paper offers two advantages: (1) prior knowledge of fixed beams is not required and (2) the concepts gained from determinate structural analysis are directly applicable.

Evaluation of biliary strictures remains a challenge due to the low sensitivity of standard diagnostic work up, but the introduction of direct single-operator cholangioscopy (DSOC) changed this paradigm. Aim of our study was to evaluate diagnostic performance of DSOC and DSOC-targeted biopsies, intraductal ultrasound (IDUS) and brush cytology in patients with indeterminate biliary stricture (IBS). We evaluated patients who underwent advanced diagnostic work up for IBS in our endoscopy unit from ‘01/2018 to ‘12/2022; all patients had at least one previous attempt to characterize the biliary stricture. Final diagnosis was based on surgical pathology and/or clinical and radiological follow-up of at least 12 months. A total of 57 patients with a mean age of 67.2 ± 10.0 years were included, with a mean follow up of 18.2 ± 18.1 months. IBS were mostly located in the distal common bile duct (45.6%) and final diagnosis was consistent with malignancy in 35 patients (61.4%). DSOC and IDUS showed a significantly higher accuracy (89.5% and 82.7% respectively) compared to standard cytology (61.5%, p <0.05). In our experience, DSOC visualization and IDUS both demonstrated an optimal diagnostic yield in the differentiation of IBS, with an acceptable safety profile both quantitatively and qualitatively.

Background: Fine-needle aspiration cytology (FNAC) is widely used to diagnose and monitor thyroid nodules. The Bethesda System for Reporting Thyroid Cytopathology (TBSRTC) is the standard for interpreting FNAC specimens. The risk of malignancy in Bethesda III nodules also known as Atypia of Undetermined Significance (AUS) varies significantly throughout several studies published worldwide. This retrospective study examines the risk of cancer in thyroid FNAC categorized as Bethesda III, as identified in the final histopathology of thyroidectomy specimens at a single endocrine surgery center. Methods: This retrospective cohort analysis included 1038 consecutive patients who underwent elective thyroid surgery with complete follow up data between January 2020 and March 2024. Preoperative data on clinical and pathological characteristics have been collected. The final histopathology report from the thyroidectomy specimen was compared to the results of the preoperative FNAC on nodules that were judged to be Bethesda category III. Statistical methods were performed using SPSS version 29. Results: A total of 670 ultrasound-guided FNACs (64.5%) performed during the study period were included in the final analysis. The study population was predominantly female, represented by 79.6% of patients with a mean age of 42.5 (SD 12.1), while 20.4% were male and significantly older with mean age 45.13 years (p = 0.02). The FNAC inadequacy rate was 5.1%, which was associated with a high risk of malignancy (6 out of 34, 17.6%). Out of the total sample size of 170 patients classified as group III, 57 were found to have malignancies in final surgical histopathology, representing 33.5% of the cases within this category. The secondary gender-related outcome analysis showed that female patients classified under the Bethesda II category had a significantly higher risk of malignancy, with a rate of 21.2%, compared to males who had a malignancy rate of 3.4% in the same Bethesda category (p = 0.001, chi square test). However, female had more better prognostic non-invasive tumors than male (p = 0.02, chi square test). Conclusion: The study's results indicate that Bethesda categories II and III are associated with a higher risk of malignancy in comparison to the reports of the first and third editions of the TBSRTC, particularly for female patients classified under category II.

Introduction – Molecular tests can contribute to improve the preoperative diagnosis of thyroid nodules. Tests available are expensive and not adapted to different population. Aim – This study aimed to compare the cyto-histological genetic profile, and to evaluate the reliability of molecular tests on Ultrasound-guided Fine Needle Aspiration Cytology (US-FNAC) in accurately diagnosing differentiated thyroid carcinomas (DTCs) and predicting biologic behavior of papillary thyroid carcinomas (PTCs). Material and methods – The series included 259 patients with paired cyto-histological samples totalizing 518 samples. The genetic alterations were analyzed by PCR/Sanger sequencing. The association with clinicopathologic features was evaluated in PTCs. Results/Discussion – From the 259 patients included, histologies were 50 (19.3%) benign controls and 209 (80.7%) DTCs cases, from which 182 were PTCs; cytologies were 5.8% non-diagnostic, 18.2% benign, 39% indeterminate and 37.1% malignant. In histology, indeterminate nodules (n=101) were 22.8% benign and 77.2% malignant. Mutation frequencies in cytology and histology specimens were, respectively, TERTp: 3.7% vs. 7.9%; BRAF: 19.5% vs. 25.1%; RAS: 11% vs. 17.5%. The overall cyto-histological agreement of the genetic mutations was 94.9%, Cohen’s k=0.67, and in indeterminate nodules 95.7%, k=0.64. The identified mutations exhibited a discriminative ability in diagnosing DTC with a specificity of 100% for TERTp and BRAF, and of 94% for RAS, albeit with low sensitivity. TERTp and BRAF mutations were associated with aggressive clinicopathological features and tumor progression in PTCs (p<0.001). The obtained good cyto-histological agreement suggests that molecular analysis in US-FNAC may anticipate the genetic profile and the behavior of thyroid tumors, confirming malignancy and contributing to refer patients towards surgery.

Stem/progenitor cell transplantation is a potential novel therapeutic strategy to induce angiogenesis in ischemic tissue, which can prevent major amputation in patients with advanced peripheral artery disease (PAD). Thus, clinicians can use cell therapies worldwide to treat PAD. However, some cell therapy studies did not report beneficial outcomes. Clinical researchers suggested that classical risk factors and comorbidities may adversely affect the efficacy of cell therapy. Some studies have indicated that the response to stem cell therapy varies among patients even in those harboring limited risk factors. This suggested the role of undetermined risk factors, including genetic alterations, somatic mutations, and clonal hematopoiesis. Personalized stem cell-based therapy can be developed by analyzing individual risk factors. These approaches must consider several clinical biomarkers and perform studies (such as genome-wide association studies (GWAS)) on disease-related genetic traits and integrate the findings with those of transcriptome-wide association studies (TWAS) and whole-genome sequencing in PAD. Additional unbiased analyses with state-of-the-art computational methods, such as machine learning-based patient stratification, are suited for predictions in clinical investigations. The integration of these complex approaches into a unified analysis procedure for the identification of responders and non-responders before stem cell therapy, which can decrease treatment expenditure, is a major challenge to increase the efficacy of therapies.