## 1 Introduction  
Over the last decade, there have been significant advancements in multi-parametric prostate MRI (mpMRI) [1, 2] and machine learning (ML) applications in mpMRI [3, 4, 5]. While mpMRI has high sensitivity and specificity for the detection of prostate cancer, accurate discrimination between high-risk prostate cancer (hrPCA, defined as Gleason grade \(\geq\)4 + 3 in this study and others [6, 7]) and low-grade/benign prostate lesions remains challenging and is paramount for clinical management [8, 9]. Methods to distinguish hrPCA from low-grade/benign PCA are important as low-grade/benign prostate lesions can be managed with active surveillance instead of invasive treatment. Many recent publications report highly accurate machine learning algorithms for the classification of prostate lesions on MRI that appear to successfully address this diagnostic obstacle, with areas under the receiver operating characteristic curve (AUCs) of 80-98% [10].  
Recently, a consortium of the American Association of Physicists in Medicine (AAPM), the SPIE (the International Society for Optics and Photonics), and the National Cancer Institute (NCI) conducted ProstateX and ProstateX-2 Challenges [11]. They published publicly available image datasets of annotated mpMRI lesions (as identified by radiologist) and their subsequent MRI-guided biopsy results [12], asking challenge participants to classify lesions as hrPCA or \"benign\" and to predict the lesion Gleason grade. Top-trained algorithms (models) developed using the challenge image data also reached accuracies of >90% in the classification of hrPCA versus \"benign\" lesions [11; 13; 14].  
While ProstateX and other mpMRI ML results appear promising, caution is warranted as the majority of these studies are single-institutional studies, often using a single MRI scanner manufacturer [15; 16; 17]. A systematic review of ML algorithms in mpMRI noted the paucity of multi-institutional studies [18]. The need for multi-institutionally trained models using heterogeneous image data is being recognized [19; 20], spurring the development of the field of federated learning [21]. The purpose of this study was to determine the efficacy of highly accurate ML classification models trained on prostate image data from one institution and tested on image data from another institution. The highly accurate model used was a subset of a machine learning algorithm called a convolutional neural network: the Residual Neural Network (ResNet). The broader impact of single- and multi-institutional training data on model performance was also assessed.  
This study tested the effects of single- and multi-institutional studies by training a series of models to classify high risk Prostate Cancer (hrPCA) on the open-source ProstateX-2 dataset, local institutional dataset, and combined dataset including data from both. Models were then tested on corresponding data from each of the three subsets and compared to one another through statistical testing. Sub-analysis was performed on the PZ and TZ regions of the prostate. Finally, the results were analyzed and discussed in the broader context of the need for heterogeneous datasets.  
The results of this study serve to identify the need for heterogeneous or multi-institutional training datasets for broadly applicable clinical models. Additionally, this study draws attention to an important concern, which is the potential lack of generalizability of models trained on single-institutional or homogeneous datasets.