Transthoracic Echocardiography (TTE) is a crucial tool for assessing cardiac morphology and function quickly and non-invasively without ionising radiation. However, the examination is subject to intra- and inter-user variability and recordings are often limited to 2D imaging and assessments of end-diastolic and end-systolic volumes. We have developed a novel, fully automated machine learning-based framework to generate a personalised 4D (3D plus time) model of the left ventricular (LV) blood pool with high temporal resolution. A 4D shape is reconstructed from specific 2D echocardiographic views employing deep neural networks, pretrained on a synthetic dataset, and fine-tuned in a self-supervised manner using a novel optimisation method for cross-sectional imaging data. No 3D ground truth is needed for model training. The generated digital twins enhance the interpretation of TTE data by providing a versatile tool for automated analysis of LV volume changes, localisation of infarct areas, and identification of new and clinically relevant biomarkers. Experiments are performed on a multicentre dataset that includes TTE exams of 144 patients with normal TTE and 314 patients with acute myocardial infarction (AMI). The novel biomarkers show a high predictive value for survival (area under the curve (AUC) of 0.82 for 1-year all-cause mortality), demonstrating that personalised 3D shape modelling has the potential to improve diagnostic accuracy and risk assessment.