Multi-parametric MRI-based Radiomics Predicts the Risk of Recurrent Lower Urinary Tract Obstruction after Benign Prostatic Hyperplasia Surgery

Multi-parametric MRI-based Radiomics Predicts the Risk of Recurrent Lower Urinary Tract Obstruction after Benign Prostatic Hyperplasia Surgery | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Multi-parametric MRI-based Radiomics Predicts the Risk of Recurrent Lower Urinary Tract Obstruction after Benign Prostatic Hyperplasia Surgery Jia Wang, Yun-Feng Zhang, Han He, Wenbo Zhang, Hongde Hu, Qidong Wang, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7093079/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 5 You are reading this latest preprint version Abstract Objective To explore the effectiveness of multi-parameter magnetic resonance imaging (MRI) radiomics in forecasting the likelihood of recurrence after surgery in benign prostatic hyperplasia (BPH). Material and Methods This retrospective study enrolled 134 pathologically confirmed BPH patients from Gansu Provincial People's Hospital (2018–2021), divided into training and validation sets. ROIs were delineated on T2-WI, DWI, and ADC sequences to extract 312 radiomic features. Dimensionality reduction and feature selection were performed using regularization and LASSO regression LR, SVM, and Naive Bayes classifiers were employed to build models, evaluated by ROC-AUC, calibration curves, and decision curve analysis (DCA) for performance, goodness of fit, and clinical utility. Results 30 radiomics features closely related to recurrence were ultimately selected. The AUC of the LR model was 0.953 in the training set and 0.931 in the validation set. For the SVM model, the AUC was 0.982 in the training set and 0.926 in the validation set. For NaiveBayes model, the AUC was 0.850 in the training set and 0.828 in the validation set. Calibration curves indicated good model fitting, and DCA curves showed significant clinical net benefit. Conclusion Multi-parameter MRI radiomics can predict the risk of postoperative recurrence in benign prostatic hyperplasia. benign prostatic hyperplasia recurrence magnetic resonance imaging radiomics machine learning Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 1. Introduction Benign prostatic hyperplasia (BPH) is the most common non-malignant cause of urinary obstruction in middle-aged and older men [ 1 ]. Histological studies confirm that the prevalence of BPH increases with age, typically starting after the age of 40 [2]. In the male population, more than half are affected by the condition after the age of 60, with the prevalence rising to 83% by the age of 80 [ 3 ]. Correspondingly, urinary problems such as difficulty urinating are more common in older men, with approximately 50% of BPH patients experiencing moderate to severe lower urinary tract symptoms. The progression of BPH significantly reduces the quality of life in older men. For patients with severe benign prostatic hyperplasia (BPH), or those whose lower urinary tract symptoms have significantly impaired their quality of life, surgical intervention may be considered [ 4 , 5 ], especially when medications are ineffective or not preferred. As the gold standard for BPH treatment, Transurethral Resection of the Prostate (TURP) can effectively relieve lower urinary tract symptoms in over 70% of patients [ 6 ]. However, this procedure is not curative, and postoperative recurrence of obstruction symptoms may occur due to residual prostate tissue growth or other factors [ 7 ]. Research shows that approximately 2.3%-4.3% of patients require reoperation within a year after TURP [ 8 ], and this percentage rises to around 14.5% within five years [ 9 ]. Therefore, accurately assessing the risk of recurrent urinary tract obstruction following TURP is crucial for optimizing the diagnosis, treatment strategies, and prognosis of BPH patients. Radiomics is an emerging technology that combines medical imaging with computer science, aiming to extract key information from imaging data to advance precision medicine [ 10 , 11 ]. This technology encompasses the entire process of image acquisition, storage, analysis, and interpretation, with the goal of assisting clinical decision-making and improving diagnostic accuracy and treatment management. By integrating image processing, machine learning, and artificial intelligence, radiomics demonstrates significant potential in optimizing medical diagnosis and disease management. To assess the risk of recurrent lower urinary tract obstruction following BPH surgery, this study developed a predictive model that leverages the predictive advantages of radiomics and explores its clinical application value. 2. Materials and Methods This study was approved by the Medical Ethics Committee of Gansu Provincial People's Hospital, and the requirement for informed consent from participants was waived 2.1 Participants This study retrospectively collected clinical and imaging data from patients diagnosed with benign prostatic hyperplasia (BPH) at Gansu Provincial People's Hospital and Gansu Provincial Second People's Hospital between January 2017 and January 2021, followed by a 3-year follow-up. Inclusion criteria: (1) Pathologically confirmed initial diagnosis of BPH; (2) Patients who received transurethral resection of the prostate (TURP); (3) All MRI examinations completed within 2 weeks before pathological confirmation (to exclude confounding factors); (4) Complete clinical data. Exclusion criteria: (1) Missing key MRI sequences; (2) Presence of other prostate diseases; (3) Lower urinary tract obstruction caused by other conditions; (4) Loss to follow-up. Recurrence criteria (must meet at least two objective indicators, confirmed by cystoscopy or MRI): Clinical symptoms: such as difficulty urinating, acute urinary retention, or an International Prostate Symptom Score (IPSS) ≥ 8; Imaging abnormalities: bladder neck stenosis (diameter ≥ 10mm); Urodynamic abnormalities: maximum urinary flow rate ≤ 10mL/s, or bladder outlet obstruction index (BOOI) ≥ 40; Secondary complications: residual urine volume >50mL, or ≥ 3 urinary tract infections per year, or obstructive renal dysfunction (serum creatinine >1.5 times the baseline value). After rigorous screening (see Fig. 1 ), a total of 320 BPH patients who met the criteria were included for further analysis. 2.2 Image preprocessing and lesion segmentation This study is based on preoperative T2-weighted imaging (T2WI), diffusion-weighted imaging (DWI), and apparent diffusion coefficient (ADC) sequences for multimodal MRI analysis. The raw DICOM data were corrected for magnetic field inhomogeneity artifacts using N4 bias field correction, followed by isotropic resampling (resolution 1×1×1 mm³) through linear interpolation to achieve spatial registration between cases. The regions of interest (ROIs) in the prostate hyperplasia area were independently delineated by two urological radiologists with over 5 years of experience using ITK-SNAP software (v3.8.0) (Fig. 2 ). The data were included in subsequent analysis after confirming the labeling consistency through intra-class correlation coefficient (ICC) testing (ICC > 0.85). Relevant MRI device parameters (magnetic field strength, slice thickness, TR/TE) are detailed in Appendix S1. Inter-observer consistency evaluation: To ensure the robustness and reproducibility of feature extraction, two imaging diagnosis experts (one with 30 years of experience in BPH MRI diagnosis as a chief urologist, and the other with 5 years of experience in MRI interpretation as a senior imaging physician) independently completed the ROI segmentation. A random sampling method was used to select 30 cases for a double-blind segmentation experiment. The radiomic features extracted from the segmentation results were used to quantify inter-observer consistency [ 12 ], with statistical analysis conducted via Kappa test and ICC. The ICC value range is 0–1, with values closer to 1 indicating better repeatability (ICC > 0.8 meets clinical research stability standards) [ 13 ]. This dual statistical validation mechanism ensures the clinical translational potential of the image feature extraction process. 2.3 Feature Extraction and Model Construction The PyRadiomics package ( http://www.radiomics.io/pyradiomics.html ) was used to extract radiomic features from three imaging sequences. A total of 312 raw imaging features were obtained, covering first-order histograms, shape features, Gray Level Co-occurrence Matrix (GLCM), Gray Level Run Length Matrix (GLRLM), Gray Level Size Zone Matrix (GLSZM), Gray Level Dependence Matrix (GLDM), and Neighborhood Gray Tone Difference Matrix (NGTDM). The data were standardized using Z-score normalization. The Spearman correlation coefficient was used to assess the inter-observer consistency of the extracted features, and reliable features with a correlation coefficient greater than 0.9 were retained for subsequent analysis. Key features were selected using the stepwise Lasso algorithm based on accuracy and were iteratively evaluated for significance. The patient data were divided into a training cohort from Gansu Provincial People's Hospital (93 cases) and a testing cohort from Gansu Provincial Second People's Hospital (41 cases). Finally, predictive models were built using Logistic Regression (LR), Support Vector Machine (SVM), and Naive Bayes classifiers. 2.4 Model Evaluation The model was built based on the training set and evaluated on the validation set. The predictive accuracy was measured by plotting the Receiver Operating Characteristic (ROC) curve and calculating the Area Under the Curve (AUC). Additionally, Decision Curve Analysis (DCA) and calibration curves were generated to assess the clinical net benefit and examine the goodness of fit of the model 2.5 Statistical Analysis Data following a normal distribution were expressed as mean (± standard deviation), while skewed data were described using the median and interquartile range. The comparison of metric data between groups was based on distribution characteristics, with different methods selected: an independent samples t-test was used for normally distributed data with equal variances, and the Mann-Whitney U test was applied for skewed data or unequal variances. The classification performance of the model was evaluated by calculating the area under the receiver operating characteristic curve (AUC). Additionally, decision curve analysis (DCA) was used to assess the clinical relevance of the model. Statistical significance was set at a P-value of < 0.05. 3. Results 3.1. Clinical Characteristics Based on the exclusion criteria mentioned earlier, 186 BPH patients were excluded, resulting in 134 patients eligible for analysis. Recurrence was determined by the occurrence of secondary surgery, and of the included patients, 58 experienced recurrence. As shown in Table 1 , no statistically significant differences in clinical characteristics were observed between the training and validation sets (P>0.05). Table 1 Comparison of clinical characteristics of BPH patients between the training and validation sets. various train(n = 93) test(n = 41) Z value P value age 68.00(63.00,72.00) 69.00(64.00,75.00) -1.122 0.262 Volume 66.50(38.94,96.53) 74.00(58.40,97.00) -1.415 0.157 tPSA 10.96(5.41,18.89) 12.08(6.84,21.47) -0.777 0.437 TP 66.30(62.112,71.55) 69.10(63.55,72.50) -1.251 0.211 ALB 39.20(35.70,42.80) 40.00(36.36,42.75) -0.570 0.569 ALP 69.00(60.50,78.50) 71.00(66.00,85.00) -1.827 0.068 UA 381.00(299.00,426.50) 382.00(318.00,433.00) -0.116 0.908 Scr 76.90(67.40,88.20) 79.10(71.75,98.75) -1.029 0.304 Fbg 3.20(2.84,4.59) 3.36(2.99,3.95) -0.493 0.622 NEUT 3.91(3.07,5.97) 4.55(3.23,6.76) -0.995 0.320 Lym 1.28(0.99,1.77) 1.34(0.99,1.94) -0.377 0.706 M 0.47(0.35,0.60) 0.47(0.37,0.69) -0.527 0.598 Hb 147.00(130.50,158.50) 150.00(132.00,164.00) -1.126 0.560 PLT 189.00(147.00,218.00) 183.00(154.50,218.00) -0.058 0.954 BMI 23.39(21.58,24.85) 24.20(21.67,24.64) -0.618 0.536 TP:Total Protein;UA: Uric Acid;ALP:Alkaline phosphatase;ALB:Albumin;UA:UricAcid;Fbg:Fibrinogen;NEUT:Neutrophil;Lym:lymphocyte;PLT:Platelet;HB: Hemoglobin;M:Monocyte. 3.2 Feature Selection A total of 312 radiomics features were extracted from T2WI, DWI, and ADC images for each patient. To optimize the model's hyperparameters (including the number of features), we performed 5-fold cross-validation on the training set. Feature selection was conducted using the LASSO regression model (Figs. 3 a, b), resulting in the identification of 30 radiomics features significantly associated with recurrence (Fig. 4 ). Based on these selected features, prediction models were built using various classifiers 3.3 Model Performance ROC analysis showed that the LR model achieved AUCs of 0.953 for the training set and 0.931 for the validation set (Fig. 5 a). The SVM model had AUCs of 0.982 (training set) and 0.926 (validation set) (Fig. 5 b). The NaiveBayes model had AUCs of 0.850 (training set) and 0.828 (validation set) (Fig. 5 c). Calibration and decision curve analysis (DCA) indicated that all models had good fit and clinical applicability (Figs. 6 a-c; Figs. 7 a-c). The predicted probability distributions for each sample in the validation set are shown in Figs. 8 a-c. A summary of the model details is provided in Table 2 . 4. Discussion BPH is a common cause of urinary obstruction in middle-aged and older men. Some patients may progress to severe BPH, for which transurethral resection of the prostate (TURP) is an effective method to relieve lower urinary tract symptoms. However, some patients may experience a recurrence of symptoms post-surgery, significantly affecting their quality of life. Therefore, accurately predicting the risk of recurrent lower urinary tract obstruction due to BPH is essential for guiding clinical decision-making and optimizing treatment outcomes. BPH recurrence is associated with many factors such as age, medication, prostate volume, and individual differences between patients and surgeons, making the assessment of recurrence risk complicated [ 14 , 15 ]. Radiomics involves using advanced algorithms to extract concealed information from medical images, which aids clinicians in making more precise diagnoses and evaluating patient prognosis, thereby enhancing the capabilities of traditional imaging to some degree [ 16 ]. Radiomics has shown good performance in the diagnosis and prognosis assessment of various urological diseases such as kidney cancer, bladder cancer, and prostate cancer, making it possible for us to evaluate the recurrence status of BPH [ 17 – 19 ]. Radiomics feature analysis is a method that uses imaging techniques to quantify the physical properties of tissues, encompassing aspects such as density, shape, and size. For example, calculating tumor volume and shape factors helps assess the nature of lesions. Blood flow and perfusion-related features provide information about blood circulation, particularly perfusion indicators, which can evaluate tumor blood supply and assist in determining its malignancy. Texture features describe the spatial relationships between image pixels, used to distinguish different texture patterns and identify lesions. Shape and boundary features are crucial for defining the contours of objects, especially when delineating the boundaries of tumors or lesions. Density and intensity features reflect optical density or intensity differences in an imaging area, aiding in the distinction between normal and abnormal tissues. Physiological parameter-related features provide information on metabolic rate, blood oxygen levels, and other physiological processes, which are important for assessing tissue function and status. Therefore, these features collectively reflect various biological characteristics of lesions, which may explain why they can assess disease progression. MRI has significant advantages in the diagnosis and treatment of prostate diseases. This study extracted radiomic features from retrospectively acquired MRI images (particularly T2-weighted imaging (T2WI), diffusion-weighted imaging (DWI), and apparent diffusion coefficient (ADC) sequences). Based on these features, we developed a machine learning model to accurately predict the risk of lower urinary tract obstruction recurrence in benign prostatic hyperplasia (BPH) patients after transurethral resection of the prostate (TURP). Decision curve analysis (DCA) and calibration curve results confirmed that the model has good clinical application value and calibration performance. Additionally, we employed standard classifiers such as logistic regression (LR), support vector machine (SVM), and naïve Bayes. The results showed that all three classifiers demonstrated robust predictive performance in predicting the risk of lower urinary tract obstruction recurrence due to BPH. This highlights the predictive potential of radiomics-based models and their ability to support clinical decision-making with precision. This study has several limitations. First, its retrospective design may introduce selection bias, highlighting the need for prospective validation in future studies. Second, all study samples were collected from a single province, which could limit the model's generalizability. To improve clinical applicability, future research should include larger sample sizes from multiple centers beyond the province. 5. Conclusions The machine learning model, which is based on multi-parameter radiomics extracted from MRI, exhibits predictive value for predicting the risk of postoperative lower urinary tract obstruction recurrence in patients diagnosed with benign prostatic hyperplasia . Abbreviations AUC: Area under the curve ADC: Apparent diffusion coefficient ALP: Alkaline phosphatase ALB: Albumin BMI: Body mass index BPH: Benign prostatic hyperplasia DCA: decision curve analysis DICOM: Digital Imaging and Communications in Medicine DWI: Diffusion weighted imaging Lasso ： Least absolute shrinkage and selection operator logistic regression LR ： Logistic Regression MRI: Multiparametric Magnetic Resonance Imaging NaiveBayes ： Naive Bayes Classifier ROC: Receiver operating characteristic PSA: Prostate specificantigen ROI: Regions of interest SVM ： Support Vector Machine XGBoost ： Extreme Gradient Boosting Declarations Acknowledgments This study sincerely thanks Gansu Provincial Hospital, Lanzhou University, and Gansu University of Chinese Medicine for their guidance and support throughout the project. We also appreciate the technical assistance provided by the Onekey AI platform. Funding A demonstration study on the application of domestic high-end endoscopic system and minimally invasive instruments in precision minimally invasive surgery technology for urinary diseases（2022YFC2407305） Scientific Research Foundation of Gansu Provincial People's Hospital (23GSSYD-12) Natural Science Foundation of Gansu Province (23JRRA1170) Study on synergistic effect of targeted delivery of dictinine and exosomes in the treatment of prostate cancer（24GSSYE-7） Construction of prostate cancer early warning model and its application based on AI multimodal imaging and liquid biopsy（25JRRA318） Authors ’ contributions Guarantor of integrity of the entire study: WJ,ZFH; Design of the research programme: ZFH,ZYF; literature retrieve: WJ,HH; information collection of BPH patients: ZWB,HHD,WQD; manuscript preparation: ZYF,WJ; manuscript review: ZFH. All authors read and approved the final manuscript. Data availability All data supporting the findings of this study are available within the paper and its Supplementary material. Ethics approval and consent to participate: The Ethics Committee of Gansu Provincial Hospital approved this retrospective study, and the need for informed consent was waived. All procedures were conducted in compliance with the applicable guidelines and regulations Competing interests: All authors declare that they have no competing interests. References Csikós E, Horváth A, Ács K, Papp N, Balázs VL, Dolenc MS, Kenda M, Kočevar Glavač N, Nagy M, Protti M, Mercolini L, Horváth G, Farkas Á, On Behalf Of The Oemonom. Treatment of Benign Prostatic Hyperplasia by Natural Drugs. Molecules. 2021 Nov 25;26(23):7141. doi: 10.3390/molecules26237141. PMID: 34885733; PMCID: PMC8659259. Berry MJ，Coffey DS，Walsh PC，and Ewing LL．The development of human benign prostatic hyperplasia with age．J Urol，1984，132：474-478． Gu FL；Xia TL；Kong XT．Preliminary study of the frequency of benign prostatic hyperplasia and prostatic cancer in China．Urology,1994，44：688-691． Borborglu PG, Kane CJ，Ward JF，Roberts JL，Sands JP. Immediate and postoperative complications of transurethral prostatectomy in 1990s．J Urol，1999，162：1307-1310． Jonler M, Riehmann M, Brinkmann R, Bruskewitz RC. Benign prostatic hyperplasia. Endocrinol Metab Clin North Am. 1994 Dec;23(4):795-807. PMID: 7535688. Kim SJ, Al Hussein Alawamlh O, Chughtai B, Lee RK. Lower Urinary Tract Symptoms Following Transurethral Resection of Prostate. Curr Urol Rep. 2018 Aug 20;19(10):85. doi: 10.1007/s11934-018-0838-4. PMID: 30128964. Heiman J, Snead WM, DiBianco JM. Persistent Lower Urinary Tract Symptoms After BPH Surgery. Curr Urol Rep. 2024 Jun;25(6):125-131. doi: 10.1007/s11934-024-01202-y. Epub 2024 Apr 5. PMID: 38578550. Mebust WK, Holtgrewe HL, Cockett AT, Peters PC. Transurethral prostatectomy: immediate and postoperative complications. a cooperative study of 13 participating institutions evaluating 3,885 patients. 1989. J Urol. 2002 Feb;167(2 Pt 2):999-1003; Rassweiler J, Teber D, Kuntz R, Hofmann R. Complications of transurethral resection of the prostate (TURP)--incidence, management, and prevention. Eur Urol. 2006 Nov;50(5):969-79; discussion 980. Lambin P, Leijenaar RTH, Deist TM, et al. Radiomics: the bridge between medical imaging and personalized medicine. Nat Rev Clin Oncol. 2017 Dec;14(12):749-762. Aerts HJWL, Velazquez ER, Leijenaar RTH, et al. Decoding tumour phenotype by noninvasive imaging using a quantitative radiomics approach. Nat Commun. 2014;5:4006. Aerts HJ, Velazquez ER, Leijenaar RT, et al. Decoding tumour phenotype by noninvasive imaging using a quantitative radiomics approach[J]. Nat Commun. 2014;5:4006. Nakanishi R, Akiyoshi T, Toda S, et al. Radiomics Approach Outperforms Diameter Criteria for Predicting Pathological Lateral Lymph Node Metastasis After Neoadjuvant (Chemo)Radiotherapy in Advanced Low Rectal Cancer[J]. Ann Surg Oncol. 2020;27(11):4273-4283. Oelke M, Bachmann A, Descazeaud A, Emberton M, Gravas S, Michel MC, N'dow J, Nordling J, de la Rosette JJ; European Association of Urology. EAU guidelines on the treatment and follow-up of non-neurogenic male lower urinary tract symptoms including benign prostatic obstruction. Eur Urol. 2013 Jul;64(1):118-40. Madersbacher S, Alivizatos G, Nordling J, Sanz CR, Emberton M, de la Rosette JJ. EAU 2004 guidelines on assessment, therapy and follow-up of men with lower urinary tract symptoms suggestive of benign prostatic obstruction (BPH guidelines). Eur Urol. 2004 Nov;46(5):547-54. Gillies RJ, Kinahan PE, Hricak H. Radiomics: Images are more than pictures, they are data. Radiology. 2016;278(2):563-577. Xu Q, Zhu Q, Liu H, et al. Differentiating Benign from Malignant Renal Tumors Using T2- and Diffusion-Weighted Images: A Comparison of Deep Learning and Radiomics Models Versus Assessment from Radiologists[J]. J Magn Reson Imaging. 2022 Apr;55(4):1251-1259. Fan TW, Malhi H, Varghese B,et al.Computed tomography-based texture analysis of bladder cancer: differentiating urothelial carcinoma from micropapillary carcinoma[J]. Abdom Radiol (NY). 2019 Jan;44(1):201-208. Zhang GM, Han YQ, Wei JW, et al.Radiomics Based on MRI as a Biomarker to Guide Therapy by Predicting Upgrading of Prostate Cancer From Biopsy to Radical Prostatectomy[J]. J Magn Reson Imaging. 2020 Oct;52(4):1239-1248. Aerts HJ, Velazquez ER, Leijenaar RT, et al. Decoding tumour phenotype by noninvasive imaging using a quantitative radiomics approach. Nat Commun. 2014 Jun 3;5:4006. Lambin P, Rios-Velazquez E, Leijenaar R, et al. Radiomics: extracting more information from medical images using advanced feature analysis. Eur J Cancer. 2012 Mar;48(4):441-6. Parmar C, Grossmann P, Bussink J，et al.Sci Rep. 2015 Aug 17;5:13087. Panebianco V, Barchetti F, Sciarra A,et al. Multiparametric magnetic resonance imaging vs. standard care in men being evaluated for prostate cancer: a randomized study. Urol Oncol. 2015 Jan;33(1):17.e1-17.e7. Appendix Appendix S1 is not available with this version Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviewers invited by journal 04 Sep, 2025 Editor invited by journal 04 Aug, 2025 Editor assigned by journal 14 Jul, 2025 Submission checks completed at journal 14 Jul, 2025 First submitted to journal 10 Jul, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7093079","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":511174724,"identity":"3457fd82-980d-4649-9592-912c311e84c6","order_by":0,"name":"Jia Wang","email":"","orcid":"","institution":"Gansu University of Chinese Medicine","correspondingAuthor":false,"prefix":"","firstName":"Jia","middleName":"","lastName":"Wang","suffix":""},{"id":511174725,"identity":"3bfa0442-b2dc-48fa-b506-a15f8c64720f","order_by":1,"name":"Yun-Feng Zhang","email":"","orcid":"","institution":"Lanzhou University","correspondingAuthor":false,"prefix":"","firstName":"Yun-Feng","middleName":"","lastName":"Zhang","suffix":""},{"id":511174726,"identity":"75b54ce8-73cd-4360-93f1-d2662582eef8","order_by":2,"name":"Han He","email":"","orcid":"","institution":"Lanzhou University","correspondingAuthor":false,"prefix":"","firstName":"Han","middleName":"","lastName":"He","suffix":""},{"id":511174727,"identity":"33df7c85-0b44-4079-b4d2-1f4ffa46ea84","order_by":3,"name":"Wenbo Zhang","email":"","orcid":"","institution":"Gansu University of Chinese Medicine","correspondingAuthor":false,"prefix":"","firstName":"Wenbo","middleName":"","lastName":"Zhang","suffix":""},{"id":511174728,"identity":"5cc222e8-38e6-43d7-a72f-2a6460ae13c5","order_by":4,"name":"Hongde Hu","email":"","orcid":"","institution":"Lanzhou University","correspondingAuthor":false,"prefix":"","firstName":"Hongde","middleName":"","lastName":"Hu","suffix":""},{"id":511174729,"identity":"138a9989-327a-409a-aed4-78fafafb4b33","order_by":5,"name":"Qidong Wang","email":"","orcid":"","institution":"Gansu University of Chinese Medicine","correspondingAuthor":false,"prefix":"","firstName":"Qidong","middleName":"","lastName":"Wang","suffix":""},{"id":511174730,"identity":"41649878-0c96-49d9-a44a-9f2769c842b4","order_by":6,"name":"Feng-Hai Zhou","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA6UlEQVRIie3NMWrDMBTG8c8Y7Ayv9qoQ8BlecTCFDr3KK4Fm8RDo0hOkS3KXZsvoItDkA3go1FDwlMFrQEPtFEonJd0K1X+QeEI/HuDz/cESyHhVQFgHbXt6EzeJvklUhiy/JZG6jMRloWDfMjZX5kmsRhqXjOPeQegwEOpyNslDI6Qx3Rw42NYOosYtSt+/vG+KRpQGNyWHwfoc4YEYKlbCGneXEfkiEBm2qHOEuscbVDqfGsqVVEtSdbd63TpIGi92DazOEkPXfW9vs/R5sWuPDgJM5jP7Y6TxqFwAiD969wefz+f7930CkDhNgxe+ZowAAAAASUVORK5CYII=","orcid":"","institution":"Gansu Provincial Hospital","correspondingAuthor":true,"prefix":"","firstName":"Feng-Hai","middleName":"","lastName":"Zhou","suffix":""}],"badges":[],"createdAt":"2025-07-10 12:38:10","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7093079/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7093079/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":91189642,"identity":"c96e4f36-3fcc-48ad-8bd6-aeefcbdc110f","added_by":"auto","created_at":"2025-09-12 14:31:48","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":101451,"visible":true,"origin":"","legend":"\u003cp\u003eshows the recruitment process of the patients\u003c/p\u003e","description":"","filename":"Fig.1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7093079/v1/6d2a7836926ac7844a39c9be.jpg"},{"id":91189647,"identity":"96aeda38-6d91-4bf7-8e1e-520e63be6f00","added_by":"auto","created_at":"2025-09-12 14:31:48","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":106252,"visible":true,"origin":"","legend":"\u003cp\u003eThe two physicians annotate the image shown in Figure 1. The urologist's annotations are in green, while the radiologist's are in red.\u003c/p\u003e","description":"","filename":"Fig.2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7093079/v1/f44814425411b48711c1a1fc.jpg"},{"id":91191861,"identity":"e00ad13e-8a48-44f1-bd11-9fd03ec8be66","added_by":"auto","created_at":"2025-09-12 14:39:48","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":156369,"visible":true,"origin":"","legend":"\u003cp\u003eshows the process of selecting the tuning parameter (λ) in the Lasso model.\u003c/p\u003e","description":"","filename":"Fig.3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7093079/v1/f8872f7be8e124b909ef7883.jpg"},{"id":91189649,"identity":"2e9ec197-3010-46b0-bbe8-0112623b22db","added_by":"auto","created_at":"2025-09-12 14:31:48","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":781338,"visible":true,"origin":"","legend":"\u003cp\u003edisplays the final selected features and their corresponding weights in the model.\u003c/p\u003e","description":"","filename":"Fig.4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7093079/v1/bf48e278b072490f50503904.jpg"},{"id":91189651,"identity":"dd3c964c-e7e4-4bdd-84aa-3d00c0ccbc81","added_by":"auto","created_at":"2025-09-12 14:31:48","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":210595,"visible":true,"origin":"","legend":"\u003cp\u003eROC curve analysis demonstrates that the models have excellent predictive performance.\u003c/p\u003e","description":"","filename":"Fig.5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7093079/v1/b11bd030911c2b9714584c9e.jpg"},{"id":91191862,"identity":"a081b863-cbc4-4733-a364-d6de29370017","added_by":"auto","created_at":"2025-09-12 14:39:48","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":188126,"visible":true,"origin":"","legend":"\u003cp\u003eDecision Curve Analysis (DCA) curve analysis demonstrates that these models have similar clinical net benefits, and the LR model has the highest clinical value.\u003c/p\u003e","description":"","filename":"Fig.6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7093079/v1/3404067bb03e2c860d70b2a5.jpg"},{"id":91189655,"identity":"6e356ee3-820d-4579-a13e-a1f8e514a67e","added_by":"auto","created_at":"2025-09-12 14:31:48","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":126132,"visible":true,"origin":"","legend":"\u003cp\u003eindicates that the model has good fitting and calibration abilities.\u003c/p\u003e","description":"","filename":"Fig.7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7093079/v1/17916db32440f5b566fb123a.jpg"},{"id":91191864,"identity":"47c5d7c3-bced-4d5a-8470-a56070af4265","added_by":"auto","created_at":"2025-09-12 14:39:48","extension":"jpg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":224680,"visible":true,"origin":"","legend":"\u003cp\u003edepicts the probability distribution of the model on the validation set (where 1 represents BPH recurrence, 0 represents normal state, and the intersection indicates cases where the model predicted a deviation).\u003c/p\u003e","description":"","filename":"Fig.8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7093079/v1/49b1644c67b848205be69e20.jpg"},{"id":91196675,"identity":"ad4d25ba-9d72-4c2a-acb5-8837f18a66d9","added_by":"auto","created_at":"2025-09-12 15:03:48","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2581757,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7093079/v1/6375d8e3-b410-4cb5-a4f7-e8d9116f0b3d.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Multi-parametric MRI-based Radiomics Predicts the Risk of Recurrent Lower Urinary Tract Obstruction after Benign Prostatic Hyperplasia Surgery","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eBenign prostatic hyperplasia (BPH) is the most common non-malignant cause of urinary obstruction in middle-aged and older men [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. Histological studies confirm that the prevalence of BPH increases with age, typically starting after the age of 40 [2]. In the male population, more than half are affected by the condition after the age of 60, with the prevalence rising to 83% by the age of 80 [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Correspondingly, urinary problems such as difficulty urinating are more common in older men, with approximately 50% of BPH patients experiencing moderate to severe lower urinary tract symptoms. The progression of BPH significantly reduces the quality of life in older men.\u003c/p\u003e\u003cp\u003eFor patients with severe benign prostatic hyperplasia (BPH), or those whose lower urinary tract symptoms have significantly impaired their quality of life, surgical intervention may be considered [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e5\u003c/span\u003e], especially when medications are ineffective or not preferred. As the gold standard for BPH treatment, Transurethral Resection of the Prostate (TURP) can effectively relieve lower urinary tract symptoms in over 70% of patients [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. However, this procedure is not curative, and postoperative recurrence of obstruction symptoms may occur due to residual prostate tissue growth or other factors [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. Research shows that approximately 2.3%-4.3% of patients require reoperation within a year after TURP [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e8\u003c/span\u003e], and this percentage rises to around 14.5% within five years [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. Therefore, accurately assessing the risk of recurrent urinary tract obstruction following TURP is crucial for optimizing the diagnosis, treatment strategies, and prognosis of BPH patients.\u003c/p\u003e\u003cp\u003eRadiomics is an emerging technology that combines medical imaging with computer science, aiming to extract key information from imaging data to advance precision medicine [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. This technology encompasses the entire process of image acquisition, storage, analysis, and interpretation, with the goal of assisting clinical decision-making and improving diagnostic accuracy and treatment management. By integrating image processing, machine learning, and artificial intelligence, radiomics demonstrates significant potential in optimizing medical diagnosis and disease management.\u003c/p\u003e\u003cp\u003eTo assess the risk of recurrent lower urinary tract obstruction following BPH surgery, this study developed a predictive model that leverages the predictive advantages of radiomics and explores its clinical application value.\u003c/p\u003e"},{"header":"2. Materials and Methods","content":"\u003cp\u003eThis study was approved by the Medical Ethics Committee of Gansu Provincial People's Hospital, and the requirement for informed consent from participants was waived\u003c/p\u003e\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003e2.1 Participants\u003c/h2\u003e\u003cp\u003e This study retrospectively collected clinical and imaging data from patients diagnosed with benign prostatic hyperplasia (BPH) at Gansu Provincial People's Hospital and Gansu Provincial Second People's Hospital between January 2017 and January 2021, followed by a 3-year follow-up. Inclusion criteria: (1) Pathologically confirmed initial diagnosis of BPH; (2) Patients who received transurethral resection of the prostate (TURP); (3) All MRI examinations completed within 2 weeks before pathological confirmation (to exclude confounding factors); (4) Complete clinical data. Exclusion criteria: (1) Missing key MRI sequences; (2) Presence of other prostate diseases; (3) Lower urinary tract obstruction caused by other conditions; (4) Loss to follow-up. Recurrence criteria (must meet at least two objective indicators, confirmed by cystoscopy or MRI): Clinical symptoms: such as difficulty urinating, acute urinary retention, or an International Prostate Symptom Score (IPSS)\u0026thinsp;\u0026ge;\u0026thinsp;8; Imaging abnormalities: bladder neck stenosis (diameter\u0026thinsp;\u0026ge;\u0026thinsp;10mm); Urodynamic abnormalities: maximum urinary flow rate\u0026thinsp;\u0026le;\u0026thinsp;10mL/s, or bladder outlet obstruction index (BOOI)\u0026thinsp;\u0026ge;\u0026thinsp;40; Secondary complications: residual urine volume \u0026amp;gt;50mL, or \u0026ge;\u0026thinsp;3 urinary tract infections per year, or obstructive renal dysfunction (serum creatinine \u0026amp;gt;1.5 times the baseline value).\u003c/p\u003e\u003cp\u003eAfter rigorous screening (see Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), a total of 320 BPH patients who met the criteria were included for further analysis.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003e2.2 Image preprocessing and lesion segmentation\u003c/h2\u003e\u003cp\u003eThis study is based on preoperative T2-weighted imaging (T2WI), diffusion-weighted imaging (DWI), and apparent diffusion coefficient (ADC) sequences for multimodal MRI analysis. The raw DICOM data were corrected for magnetic field inhomogeneity artifacts using N4 bias field correction, followed by isotropic resampling (resolution 1\u0026times;1\u0026times;1 mm\u0026sup3;) through linear interpolation to achieve spatial registration between cases. The regions of interest (ROIs) in the prostate hyperplasia area were independently delineated by two urological radiologists with over 5 years of experience using ITK-SNAP software (v3.8.0) (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). The data were included in subsequent analysis after confirming the labeling consistency through intra-class correlation coefficient (ICC) testing (ICC \u0026amp;gt; 0.85). Relevant MRI device parameters (magnetic field strength, slice thickness, TR/TE) are detailed in Appendix S1.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eInter-observer consistency evaluation: To ensure the robustness and reproducibility of feature extraction, two imaging diagnosis experts (one with 30 years of experience in BPH MRI diagnosis as a chief urologist, and the other with 5 years of experience in MRI interpretation as a senior imaging physician) independently completed the ROI segmentation. A random sampling method was used to select 30 cases for a double-blind segmentation experiment. The radiomic features extracted from the segmentation results were used to quantify inter-observer consistency [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e12\u003c/span\u003e], with statistical analysis conducted via Kappa test and ICC. The ICC value range is 0\u0026ndash;1, with values closer to 1 indicating better repeatability (ICC \u0026amp;gt; 0.8 meets clinical research stability standards) [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. This dual statistical validation mechanism ensures the clinical translational potential of the image feature extraction process.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\u003ch2\u003e2.3 Feature Extraction and Model Construction\u003c/h2\u003e\u003cp\u003eThe PyRadiomics package (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://www.radiomics.io/pyradiomics.html\u003c/span\u003e\u003cspan address=\"http://www.radiomics.io/pyradiomics.html\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e) was used to extract radiomic features from three imaging sequences. A total of 312 raw imaging features were obtained, covering first-order histograms, shape features, Gray Level Co-occurrence Matrix (GLCM), Gray Level Run Length Matrix (GLRLM), Gray Level Size Zone Matrix (GLSZM), Gray Level Dependence Matrix (GLDM), and Neighborhood Gray Tone Difference Matrix (NGTDM).\u003c/p\u003e\u003cp\u003eThe data were standardized using Z-score normalization. The Spearman correlation coefficient was used to assess the inter-observer consistency of the extracted features, and reliable features with a correlation coefficient greater than 0.9 were retained for subsequent analysis. Key features were selected using the stepwise Lasso algorithm based on accuracy and were iteratively evaluated for significance. The patient data were divided into a training cohort from Gansu Provincial People's Hospital (93 cases) and a testing cohort from Gansu Provincial Second People's Hospital (41 cases). Finally, predictive models were built using Logistic Regression (LR), Support Vector Machine (SVM), and Naive Bayes classifiers.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\u003ch2\u003e2.4 Model Evaluation\u003c/h2\u003e\u003cp\u003eThe model was built based on the training set and evaluated on the validation set. The predictive accuracy was measured by plotting the Receiver Operating Characteristic (ROC) curve and calculating the Area Under the Curve (AUC). Additionally, Decision Curve Analysis (DCA) and calibration curves were generated to assess the clinical net benefit and examine the goodness of fit of the model\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\u003ch2\u003e2.5 Statistical Analysis\u003c/h2\u003e\u003cp\u003eData following a normal distribution were expressed as mean (\u0026plusmn;\u0026thinsp;standard deviation), while skewed data were described using the median and interquartile range. The comparison of metric data between groups was based on distribution characteristics, with different methods selected: an independent samples t-test was used for normally distributed data with equal variances, and the Mann-Whitney U test was applied for skewed data or unequal variances. The classification performance of the model was evaluated by calculating the area under the receiver operating characteristic curve (AUC). Additionally, decision curve analysis (DCA) was used to assess the clinical relevance of the model. Statistical significance was set at a P-value of \u0026amp;lt; 0.05.\u003c/p\u003e\u003c/div\u003e"},{"header":"3. Results","content":"\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\u003ch2\u003e3.1. Clinical Characteristics\u003c/h2\u003e\u003cp\u003eBased on the exclusion criteria mentioned earlier, 186 BPH patients were excluded, resulting in 134 patients eligible for analysis. Recurrence was determined by the occurrence of secondary surgery, and of the included patients, 58 experienced recurrence. As shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, no statistically significant differences in clinical characteristics were observed between the training and validation sets (P\u0026gt;0.05).\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eComparison of clinical characteristics of BPH patients between the training and validation sets.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"5\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003evarious\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003etrain(n\u0026thinsp;=\u0026thinsp;93)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003etest(n\u0026thinsp;=\u0026thinsp;41)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eZ value\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eP value\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eage\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e68.00(63.00,72.00)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e69.00(64.00,75.00)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e-1.122\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.262\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eVolume\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e66.50(38.94,96.53)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e74.00(58.40,97.00)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e-1.415\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.157\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003etPSA\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e10.96(5.41,18.89)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e12.08(6.84,21.47)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e-0.777\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.437\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eTP\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e66.30(62.112,71.55)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e69.10(63.55,72.50)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e-1.251\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.211\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eALB\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e39.20(35.70,42.80)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e40.00(36.36,42.75)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e-0.570\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.569\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eALP\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e69.00(60.50,78.50)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e71.00(66.00,85.00)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e-1.827\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.068\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eUA\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e381.00(299.00,426.50)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e382.00(318.00,433.00)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e-0.116\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.908\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eScr\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e76.90(67.40,88.20)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e79.10(71.75,98.75)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e-1.029\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.304\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eFbg\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e3.20(2.84,4.59)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e3.36(2.99,3.95)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e-0.493\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.622\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eNEUT\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e3.91(3.07,5.97)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e4.55(3.23,6.76)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e-0.995\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.320\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eLym\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1.28(0.99,1.77)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.34(0.99,1.94)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e-0.377\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.706\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eM\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.47(0.35,0.60)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.47(0.37,0.69)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e-0.527\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.598\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eHb\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e147.00(130.50,158.50)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e150.00(132.00,164.00)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e-1.126\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.560\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePLT\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e189.00(147.00,218.00)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e183.00(154.50,218.00)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e-0.058\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.954\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eBMI\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e23.39(21.58,24.85)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e24.20(21.67,24.64)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e-0.618\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.536\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003ctfoot\u003e\u003ctr\u003e\u003ctd colspan=\"5\"\u003eTP:Total Protein;UA: Uric Acid;ALP:Alkaline phosphatase;ALB:Albumin;UA:UricAcid;Fbg:Fibrinogen;NEUT:Neutrophil;Lym:lymphocyte;PLT:Platelet;HB: Hemoglobin;M:Monocyte.\u003c/td\u003e\u003c/tr\u003e\u003c/tfoot\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\u003ch2\u003e3.2 Feature Selection\u003c/h2\u003e\u003cp\u003eA total of 312 radiomics features were extracted from T2WI, DWI, and ADC images for each patient. To optimize the model's hyperparameters (including the number of features), we performed 5-fold cross-validation on the training set. Feature selection was conducted using the LASSO regression model (Figs.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea, b), resulting in the identification of 30 radiomics features significantly associated with recurrence (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). Based on these selected features, prediction models were built using various classifiers\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\u003ch2\u003e3.3 Model Performance\u003c/h2\u003e\u003cp\u003eROC analysis showed that the LR model achieved AUCs of 0.953 for the training set and 0.931 for the validation set (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea). The SVM model had AUCs of 0.982 (training set) and 0.926 (validation set) (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eb). The NaiveBayes model had AUCs of 0.850 (training set) and 0.828 (validation set) (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ec). Calibration and decision curve analysis (DCA) indicated that all models had good fit and clinical applicability (Figs.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ea-c; Figs.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ea-c). The predicted probability distributions for each sample in the validation set are shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ea-c. A summary of the model details is provided in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003cp\u003e\u003cimg src=\"data:image/png;base64,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\"\u003e\u003c/p\u003e\n"},{"header":"4. Discussion","content":"\u003cp\u003eBPH is a common cause of urinary obstruction in middle-aged and older men. Some patients may progress to severe BPH, for which transurethral resection of the prostate (TURP) is an effective method to relieve lower urinary tract symptoms. However, some patients may experience a recurrence of symptoms post-surgery, significantly affecting their quality of life. Therefore, accurately predicting the risk of recurrent lower urinary tract obstruction due to BPH is essential for guiding clinical decision-making and optimizing treatment outcomes.\u003c/p\u003e\u003cp\u003eBPH recurrence is associated with many factors such as age, medication, prostate volume, and individual differences between patients and surgeons, making the assessment of recurrence risk complicated [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e14\u003c/span\u003e, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. Radiomics involves using advanced algorithms to extract concealed information from medical images, which aids clinicians in making more precise diagnoses and evaluating patient prognosis, thereby enhancing the capabilities of traditional imaging to some degree [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. Radiomics has shown good performance in the diagnosis and prognosis assessment of various urological diseases such as kidney cancer, bladder cancer, and prostate cancer, making it possible for us to evaluate the recurrence status of BPH [\u003cspan additionalcitationids=\"CR18\" citationid=\"CR16\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e19\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eRadiomics feature analysis is a method that uses imaging techniques to quantify the physical properties of tissues, encompassing aspects such as density, shape, and size. For example, calculating tumor volume and shape factors helps assess the nature of lesions. Blood flow and perfusion-related features provide information about blood circulation, particularly perfusion indicators, which can evaluate tumor blood supply and assist in determining its malignancy. Texture features describe the spatial relationships between image pixels, used to distinguish different texture patterns and identify lesions. Shape and boundary features are crucial for defining the contours of objects, especially when delineating the boundaries of tumors or lesions. Density and intensity features reflect optical density or intensity differences in an imaging area, aiding in the distinction between normal and abnormal tissues. Physiological parameter-related features provide information on metabolic rate, blood oxygen levels, and other physiological processes, which are important for assessing tissue function and status. Therefore, these features collectively reflect various biological characteristics of lesions, which may explain why they can assess disease progression.\u003c/p\u003e\u003cp\u003eMRI has significant advantages in the diagnosis and treatment of prostate diseases. This study extracted radiomic features from retrospectively acquired MRI images (particularly T2-weighted imaging (T2WI), diffusion-weighted imaging (DWI), and apparent diffusion coefficient (ADC) sequences). Based on these features, we developed a machine learning model to accurately predict the risk of lower urinary tract obstruction recurrence in benign prostatic hyperplasia (BPH) patients after transurethral resection of the prostate (TURP). Decision curve analysis (DCA) and calibration curve results confirmed that the model has good clinical application value and calibration performance. Additionally, we employed standard classifiers such as logistic regression (LR), support vector machine (SVM), and na\u0026iuml;ve Bayes. The results showed that all three classifiers demonstrated robust predictive performance in predicting the risk of lower urinary tract obstruction recurrence due to BPH. This highlights the predictive potential of radiomics-based models and their ability to support clinical decision-making with precision.\u003c/p\u003e\u003cp\u003eThis study has several limitations. First, its retrospective design may introduce selection bias, highlighting the need for prospective validation in future studies. Second, all study samples were collected from a single province, which could limit the model's generalizability. To improve clinical applicability, future research should include larger sample sizes from multiple centers beyond the province.\u003c/p\u003e"},{"header":"5. Conclusions","content":"\u003cp\u003eThe machine learning model, which is based on multi-parameter radiomics extracted from MRI, exhibits predictive value for predicting the risk of postoperative lower urinary tract obstruction recurrence in patients diagnosed with benign prostatic hyperplasia .\u003c/p\u003e"},{"header":"Abbreviations","content":"\u003cp\u003e\u003cstrong\u003eAUC:\u0026nbsp;\u003c/strong\u003eArea under the curve\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eADC:\u0026nbsp;\u003c/strong\u003eApparent diffusion coefficient\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eALP:\u0026nbsp;\u003c/strong\u003eAlkaline phosphatase\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eALB:\u0026nbsp;\u003c/strong\u003eAlbumin\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eBMI:\u0026nbsp;\u003c/strong\u003eBody mass index\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eBPH:\u0026nbsp;\u003c/strong\u003eBenign prostatic hyperplasia\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDCA:\u0026nbsp;\u003c/strong\u003edecision curve analysis\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDICOM:\u0026nbsp;\u003c/strong\u003eDigital Imaging and Communications in Medicine\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDWI:\u0026nbsp;\u003c/strong\u003eDiffusion weighted imaging\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eLasso\u003c/strong\u003e\u003cstrong\u003e：\u003c/strong\u003eLeast absolute shrinkage and selection operator logistic regression\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eLR\u003c/strong\u003e\u003cstrong\u003e：\u003c/strong\u003eLogistic Regression\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMRI:\u003c/strong\u003e Multiparametric Magnetic Resonance Imaging\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eNaiveBayes\u003c/strong\u003e\u003cstrong\u003e：\u003c/strong\u003eNaive Bayes Classifier\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eROC:\u0026nbsp;\u003c/strong\u003eReceiver operating characteristic\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ePSA:\u0026nbsp;\u003c/strong\u003eProstate specificantigen\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eROI:\u0026nbsp;\u003c/strong\u003eRegions of interest\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSVM\u003c/strong\u003e\u003cstrong\u003e：\u003c/strong\u003eSupport Vector Machine\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eXGBoost\u003c/strong\u003e\u003cstrong\u003e：\u003c/strong\u003eExtreme Gradient Boosting\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgments\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis study sincerely thanks Gansu Provincial Hospital, Lanzhou University, and Gansu University of Chinese Medicine for their guidance and support throughout the project. We also appreciate the technical assistance provided by the Onekey AI platform.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eA demonstration study on the application of domestic high-end endoscopic system and minimally invasive instruments in precision minimally invasive surgery technology for urinary diseases（2022YFC2407305）\u003c/p\u003e\n\u003cp\u003eScientific Research Foundation of Gansu Provincial People\u0026apos;s Hospital (23GSSYD-12)\u003c/p\u003e\n\u003cp\u003eNatural Science Foundation of Gansu Province (23JRRA1170)\u003c/p\u003e\n\u003cp\u003eStudy on synergistic effect of targeted delivery of dictinine and exosomes in the treatment of prostate cancer（24GSSYE-7）\u003c/p\u003e\n\u003cp\u003eConstruction of prostate cancer early warning model and its application based on AI multimodal imaging and liquid biopsy（25JRRA318）\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthors\u003c/strong\u003e\u003cstrong\u003e\u0026rsquo;\u003c/strong\u003e\u003cstrong\u003econtributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eGuarantor of integrity of the entire study: WJ,ZFH; Design of the research programme: ZFH,ZYF; literature retrieve: WJ,HH; information collection of BPH patients: ZWB,HHD,WQD; manuscript preparation: ZYF,WJ; manuscript review: ZFH. All authors read and approved the final manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData availability\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll data supporting the findings of this study are available within the paper and its Supplementary material.\u003c/p\u003e\n\u003cp\u003eEthics approval and consent to participate: The Ethics Committee of Gansu Provincial Hospital approved this retrospective study, and the need for informed consent was waived. All procedures were conducted in compliance with the applicable guidelines and regulations\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests:\u003c/strong\u003e All authors declare that they have no competing interests.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eCsik\u0026oacute;s E, Horv\u0026aacute;th A, \u0026Aacute;cs K, Papp N, Bal\u0026aacute;zs VL, Dolenc MS, Kenda M, Kočevar Glavač N, Nagy M, Protti M, Mercolini L, Horv\u0026aacute;th G, Farkas \u0026Aacute;, On Behalf Of The Oemonom. Treatment of Benign Prostatic Hyperplasia by Natural Drugs. Molecules. 2021 Nov 25;26(23):7141. doi: 10.3390/molecules26237141. PMID: 34885733; PMCID: PMC8659259. \u003c/li\u003e\n\u003cli\u003eBerry MJ，Coffey DS，Walsh PC，and Ewing LL．The development of human benign prostatic hyperplasia with age．J Urol，1984，132：474-478．\u003c/li\u003e\n\u003cli\u003eGu FL；Xia TL；Kong XT．Preliminary study of the frequency of benign prostatic hyperplasia and prostatic cancer in China．Urology,1994，44：688-691．\u003c/li\u003e\n\u003cli\u003eBorborglu PG, Kane CJ，Ward JF，Roberts JL，Sands JP. Immediate and postoperative complications of transurethral prostatectomy in 1990s．J Urol，1999，162：1307-1310．\u003c/li\u003e\n\u003cli\u003eJonler M, Riehmann M, Brinkmann R, Bruskewitz RC. Benign prostatic hyperplasia. Endocrinol Metab Clin North Am. 1994 Dec;23(4):795-807. PMID: 7535688.\u003c/li\u003e\n\u003cli\u003eKim SJ, Al Hussein Alawamlh O, Chughtai B, Lee RK. Lower Urinary Tract Symptoms Following Transurethral Resection of Prostate. Curr Urol Rep. 2018 Aug 20;19(10):85. doi: 10.1007/s11934-018-0838-4. PMID: 30128964. \u003c/li\u003e\n\u003cli\u003eHeiman J, Snead WM, DiBianco JM. Persistent Lower Urinary Tract Symptoms After BPH Surgery. Curr Urol Rep. 2024 Jun;25(6):125-131. doi: 10.1007/s11934-024-01202-y. Epub 2024 Apr 5. PMID: 38578550.\u003c/li\u003e\n\u003cli\u003eMebust WK, Holtgrewe HL, Cockett AT, Peters PC. Transurethral prostatectomy: immediate and postoperative complications. a cooperative study of 13 participating institutions evaluating 3,885 patients. 1989. J Urol. 2002 Feb;167(2 Pt 2):999-1003;\u003c/li\u003e\n\u003cli\u003eRassweiler J, Teber D, Kuntz R, Hofmann R. Complications of transurethral resection of the prostate (TURP)--incidence, management, and prevention. Eur Urol. 2006 Nov;50(5):969-79; discussion 980. \u003c/li\u003e\n\u003cli\u003eLambin P, Leijenaar RTH, Deist TM, et al. Radiomics: the bridge between medical imaging and personalized medicine. Nat Rev Clin Oncol. 2017 Dec;14(12):749-762. \u003c/li\u003e\n\u003cli\u003eAerts HJWL, Velazquez ER, Leijenaar RTH, et al. Decoding tumour phenotype by noninvasive imaging using a quantitative radiomics approach. Nat Commun. 2014;5:4006.\u003c/li\u003e\n\u003cli\u003eAerts HJ, Velazquez ER, Leijenaar RT, et al. Decoding tumour phenotype by noninvasive imaging using a quantitative radiomics approach[J]. Nat Commun. 2014;5:4006. \u003c/li\u003e\n\u003cli\u003eNakanishi R, Akiyoshi T, Toda S, et al. Radiomics Approach Outperforms Diameter Criteria for Predicting Pathological Lateral Lymph Node Metastasis After Neoadjuvant (Chemo)Radiotherapy in Advanced Low Rectal Cancer[J]. Ann Surg Oncol. 2020;27(11):4273-4283.\u003c/li\u003e\n\u003cli\u003eOelke M, Bachmann A, Descazeaud A, Emberton M, Gravas S, Michel MC, N\u0026apos;dow J, Nordling J, de la Rosette JJ; European Association of Urology. EAU guidelines on the treatment and follow-up of non-neurogenic male lower urinary tract symptoms including benign prostatic obstruction. Eur Urol. 2013 Jul;64(1):118-40.\u003c/li\u003e\n\u003cli\u003eMadersbacher S, Alivizatos G, Nordling J, Sanz CR, Emberton M, de la Rosette JJ. EAU 2004 guidelines on assessment, therapy and follow-up of men with lower urinary tract symptoms suggestive of benign prostatic obstruction (BPH guidelines). Eur Urol. 2004 Nov;46(5):547-54. \u003c/li\u003e\n\u003cli\u003eGillies RJ, Kinahan PE, Hricak H. Radiomics: Images are more than pictures, they are data. Radiology. 2016;278(2):563-577. \u003c/li\u003e\n\u003cli\u003eXu Q, Zhu Q, Liu H, et al. Differentiating Benign from Malignant Renal Tumors Using T2- and Diffusion-Weighted Images: A Comparison of Deep Learning and Radiomics Models Versus Assessment from Radiologists[J]. J Magn Reson Imaging. 2022 Apr;55(4):1251-1259.\u003c/li\u003e\n\u003cli\u003eFan TW, Malhi H, Varghese B,et al.Computed tomography-based texture analysis of bladder cancer: differentiating urothelial carcinoma from micropapillary carcinoma[J]. Abdom Radiol (NY). 2019 Jan;44(1):201-208. \u003c/li\u003e\n\u003cli\u003eZhang GM, Han YQ, Wei JW, et al.Radiomics Based on MRI as a Biomarker to Guide Therapy by Predicting Upgrading of Prostate Cancer From Biopsy to Radical Prostatectomy[J]. J Magn Reson Imaging. 2020 Oct;52(4):1239-1248.\u003c/li\u003e\n\u003cli\u003eAerts HJ, Velazquez ER, Leijenaar RT, et al. Decoding tumour phenotype by noninvasive imaging using a quantitative radiomics approach. Nat Commun. 2014 Jun 3;5:4006. \u003c/li\u003e\n\u003cli\u003eLambin P, Rios-Velazquez E, Leijenaar R, et al. Radiomics: extracting more information from medical images using advanced feature analysis. Eur J Cancer. 2012 Mar;48(4):441-6. \u003c/li\u003e\n\u003cli\u003eParmar C, Grossmann P, Bussink J，et al.Sci Rep. 2015 Aug 17;5:13087. \u003c/li\u003e\n\u003cli\u003ePanebianco V, Barchetti F, Sciarra A,et al. Multiparametric magnetic resonance imaging vs. standard care in men being evaluated for prostate cancer: a randomized study. Urol Oncol. 2015 Jan;33(1):17.e1-17.e7. \u003c/li\u003e\n\u003c/ol\u003e"},{"header":"Appendix","content":"\u003cp\u003eAppendix S1 is not available with this version\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"bmc-medical-imaging","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"bmim","sideBox":"Learn more about [BMC Medical Imaging](http://bmcmedimaging.biomedcentral.com/)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/bmim/default.aspx","title":"BMC Medical Imaging","twitterHandle":"BMC_series","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"em","reportingPortfolio":"BMC Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"benign prostatic hyperplasia, recurrence, magnetic resonance imaging, radiomics, machine learning","lastPublishedDoi":"10.21203/rs.3.rs-7093079/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7093079/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\u003cb\u003eObjective\u003c/b\u003e\u003c/p\u003e\u003cp\u003eTo explore the effectiveness of multi-parameter magnetic resonance imaging (MRI) radiomics in forecasting the likelihood of recurrence after surgery in benign prostatic hyperplasia (BPH).\u003c/p\u003e\u003cp\u003e\u003cb\u003eMaterial and Methods\u003c/b\u003e\u003c/p\u003e\u003cp\u003eThis retrospective study enrolled 134 pathologically confirmed BPH patients from Gansu Provincial People's Hospital (2018\u0026ndash;2021), divided into training and validation sets. ROIs were delineated on T2-WI, DWI, and ADC sequences to extract 312 radiomic features. Dimensionality reduction and feature selection were performed using regularization and LASSO regression LR, SVM, and Naive Bayes classifiers were employed to build models, evaluated by ROC-AUC, calibration curves, and decision curve analysis (DCA) for performance, goodness of fit, and clinical utility.\u003c/p\u003e\u003cp\u003e\u003cb\u003eResults\u003c/b\u003e\u003c/p\u003e\u003cp\u003e30 radiomics features closely related to recurrence were ultimately selected. The AUC of the LR model was 0.953 in the training set and 0.931 in the validation set. For the SVM model, the AUC was 0.982 in the training set and 0.926 in the validation set. For NaiveBayes model, the AUC was 0.850 in the training set and 0.828 in the validation set. Calibration curves indicated good model fitting, and DCA curves showed significant clinical net benefit.\u003c/p\u003e\u003cp\u003e\u003cb\u003eConclusion\u003c/b\u003e\u003c/p\u003e\u003cp\u003eMulti-parameter MRI radiomics can predict the risk of postoperative recurrence in benign prostatic hyperplasia.\u003c/p\u003e","manuscriptTitle":"Multi-parametric MRI-based Radiomics Predicts the Risk of Recurrent Lower Urinary Tract Obstruction after Benign Prostatic Hyperplasia Surgery","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-09-12 14:31:43","doi":"10.21203/rs.3.rs-7093079/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewersInvited","content":"","date":"2025-09-04T10:14:25+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-08-04T08:54:06+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-07-14T11:40:18+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-07-14T11:38:59+00:00","index":"","fulltext":""},{"type":"submitted","content":"BMC Medical Imaging","date":"2025-07-10T12:24:12+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"bmc-medical-imaging","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"bmim","sideBox":"Learn more about [BMC Medical Imaging](http://bmcmedimaging.biomedcentral.com/)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/bmim/default.aspx","title":"BMC Medical Imaging","twitterHandle":"BMC_series","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"em","reportingPortfolio":"BMC Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"455a4318-e265-4a31-a923-4bc6bba966c5","owner":[],"postedDate":"September 12th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2025-09-12T14:31:43+00:00","versionOfRecord":[],"versionCreatedAt":"2025-09-12 14:31:43","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7093079","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7093079","identity":"rs-7093079","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}