Ventricular tachycardia (VT) and fibrillation (VF) are dangerous cardiac arrhythmias. It is thought that a single re-entrant wave of excitation (a scroll wave) that rotates around a phase singularity (a filament) underlies VT, and that breakdown of this wave into multiple wavelets results in the transition from VT to VF (Jalife 2000). We examined effects of cardiac geometry and architecture (fibre and sheet structure – see Gilbert et al. 2007) on scroll wave dynamics by quantifying the scroll wave filament in two heterogeneous models of the human left ventricular free wall – a simple cuboid model with a rule-based architecture, and a wedge model with geometry and architecture reconstructed from human diffusion tensor MRI data. For each, excitation was described using a biophysically-detailed human model (ten Tusscher et al. 2004), and propagation of excitation was either isotropic (no architecture), anisotropic (fibre structure only) or orthotropic (fibre and sheet structure). Figure 1A shows snapshots of orthotropic re-entrant activity in the cuboid and wedge geometries after 2 s of activity. Filament trajectories on the epicardial surfaces of the geometries were used to examine meander of the scroll wave filament. For both models, changing from isotropy through to orthotropy rescales the meander in the sheet normal direction. The lengths of the scroll wave filaments during 1 second of simulation are shown in Fig. 1B. Oscillations of filament length are evident even in isotropic simulations, a consequence of heterogeneous excitation kinetics in the models. For both models, filament length increases as anisotropy and then orthotropy are introduced. Filament curvature increases with anisotropy then orthotropy in the wedge (from 0.8 to 3.8 /mm), although this pattern is not seen in the cuboid. Conversely, filament twist increases with anisotropy then orthotropy in the cuboid (1.0 to 5.8 °/mm) but not in the wedge. Maximum twist along a single filament increases in both models as anisotropy and then orthotropy are introduced – from 51 to 445° in the cuboid, and from 64 to 161° in the wedge. Increases in filament length, curvature and twist can result in breakdown of the wave into the multiple wavelets that underlie VF (Clayton et al. 2006). We conclude that different cardiac geometries and architectures result in different re-entrant scroll wave dynamics. Hence, simulations of VT and VF should take into account the complex geometry and fibre and sheet structure of the ventricles.