Segmenting blood vessels is an important step in a wide variety of tasks in medical image analysis. Patch-based convolutional neural networks (CNNs) are often used for vascular detection, but the impact of patch size and choice of CNN architecture have not been addressed in detail in previous studies. In this study, we aim to investigate the impact of patch size and CNN architecture on the accuracy of vascular detection from contract enhanced computed tomography (CT). We targeted the renal arteries as the primary focus of detection. We conducted experiments using contrast enhanced abdominal CT data of 30 cases. For the experiments, arteries in pre-defined regions of interest were manually labeled to build a dataset of input CT images and ground truth labels. We repeated the experiments with four patch sizes and two patch-based 3D CNN architectures (U-Net-like model and a simple sequential model) and evaluated the differences. Moreover, a Hessian-based line enhancing method was included in the evaluation to compare this non-deep learning method with the CNNs. The experimental results showed that patch size had a significant impact on detection accuracy. U-Net-like model showed peak accuracy at a certain patch size, unlike the sequential model that plateaued at large patch sizes. Although both CNNs outperformed Hessian-based line enhancement by a large margin, Hessian-based line enhancement achieved good recall when enhancing vessel structures not included in the CNN training. Our experiments show that different network architectures have different characteristics regarding their response to various patch sizes and vessel structures unseen during training.