The interpretation of image data plays a critical role during acute brain stroke diagnosis, and promptly defining the requirement of a surgical intervention will drastically impact the patient's outcome. However, determining stroke lesions purely from images can be a daunting task. Many studies proposed automatic segmentation methods for brain stroke lesions from medical images in different modalities, though heretofore results do not satisfy the requirements to be clinically reliable. We investigate the segmentation of brain stroke lesions using a geometric deep learning model that takes advantage of the intrinsic interconnected diffusion features in a set of multi-modal inputs consisting of computer tomography (CT) perfusion parameters. We propose a geometric deep learning model for the segmentation of ischemic stroke brain lesions that employs spline convolutions and unpooling/pooling operators on graphs to excerpt graph-structured features in a fully convolutional network architecture. In addition, we seek to understand the underlying principles governing the different components of our model. Accordingly, we structure the experiments in two parts: an evaluation of different architecture hyperparameters and a comparison with state-of-the-art methods. The ablation study shows that deeper layers obtain a higher Dice coefficient score (DCS) of up to 0.3654. Comparing different pooling and unpooling methods shows that the best performing unpooling method is the proportional approach, yet it often smooths the segmentation border. Unpooling achieves segmentation results more adapted to the lesion boundary corroborated with systematic lower values of Hausdorff distance. The model performs at the level of state-of-the-art models without optimized training methods, such as augmentation or patches, with a DCS of . We proposed and evaluated an end-to-end trainable fully convolutional graph network architecture using spline convolutional layers for the ischemic stroke lesion prediction. We propose a model that employs graph-based operations to predict acute stroke brain lesions from CT perfusion parameters. Our results prove the feasibility of using geometric deep learning to solve segmentation problems, and our model shows a better performance than other models evaluated. The proposed model achieves improved metric values for the DCS metric, ranging from 8.61% to 69.05%, compared with other models trained under the same conditions. Next, we compare different pooling and unpooling operations in relation to their segmentation results, and we show that the model can produce segmentation outputs that adapt to irregular segmentation boundaries when using simple heuristic unpooling operations.