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. 2025 Aug 19;16(1):1583.
doi: 10.1007/s12672-025-03402-5.

Biproximate ellipsoid formula with transrectal ultrasound: a superior method for PSA density in gray zone prostate cancer detection

Xin Wang  1 , Jinxiao Sun  2   3 , Dandan Xu  4 , Hao Zhu  5
Affiliations

Biproximate ellipsoid formula with transrectal ultrasound: a superior method for PSA density in gray zone prostate cancer detection

Xin Wang et al. Discov Oncol. .

Abstract

Purpose: This study aimed to enhance prostate cancer (PCa) detection in patients with prostate-specific antigen (PSA) levels within the "gray zone" (4-10 ng/mL) by comparing PSA density (PSAD) calculations derived from the traditional ellipsoid formula (TEF) and the biproximate ellipsoid formula (BPEF).

Materials and methods: A total of 99 patients were enrolled. All participants underwent transrectal ultrasound (TRUS) for prostate volume estimation, followed by PSAD calculation using both the BPEF and TEF methods. The BPEF method, which incorporates well-defined anatomical landmarks, was assessed for its accuracy in prostate volume measurement and diagnostic performance for PCa compared to TEF. Inter- and intra-observer consistency were also evaluated for both approaches.

Results: Both BPEF and TEF reliably measured prostate volume, however, BPEF demonstrated superior accuracy and higher consistency in inter- and intra-observer assessments. PSAD calculated using BPEF (BPEF-PSAD) exhibited significantly greater diagnostic performance than TEF-PSAD, with an area under the curve (AUC) of 0.84. At the optimal diagnostic threshold of 0.15 ng/mL/cm³, BPEF-PSAD achieved a sensitivity of 88.89% and a specificity of 74.60%, enhancing the discrimination between PCa and benign prostatic hyperplasia (BPH). Multivariate logistic regression analysis identified BPEF-PSAD as an independent predictor of PCa.

Conclusions: The study concluded that the BPEF method, when combined with TRUS, improves the accuracy of PSA density measurements, potentially reducing unnecessary biopsies in patients with intermediate PSA levels, particularly in cases where MRI is unavailable or contraindicated.

Keywords: Biproximate ellipsoid formula; PSA density; PSA gray zone; Prostate cancer; Transrectal ultrasound.

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Conflict of interest statement

Declarations. Ethics approval and consent to participate: The study protocol was approved by the Ethics Committee of Wuxi Second Hospital of Traditional Chinese Medicine, with ethical approval number 2023SWJJ03. The study adhered to all relevant guidelines and regulations, including the Declaration of Helsinki. Informed consent was obtained from all individual participants included in the study. Consent for publication: Not applicable. Competing interests: The authors declare no competing interests.

Figures

Fig. 1
Fig. 1
Representative transrectal ultrasound images demonstrating BPEF measurement technique across different pathological conditions. Images (a) and (c) show axial views displaying the prostate’s transverse and anteroposterior diameters at maximum dimensions. Images (b) and (d) show sagittal views for superior-inferior diameter measurement, calculated as the sum of distances above and below the vesico-prostatic line (indicated by red lines). Images (a) and (b) are from a 70-year-old male patient with surgically confirmed BPH, demonstrating irregular prostate morphology with median lobe enlargement and intravesical protrusion (BPEF-calculated volume: 57.34 cm³). Images (c) and (d) are from a 68-year-old male patient with surgically confirmed (PCa (BPEF-calculated volume: 46.83 cm³)
Fig. 2
Fig. 2
Performance of PSAD calculated by using BPEF formulas-derived volume for detection of lesions
See this image and copyright information in PMC

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