3D phase diagram in vectorcardiography

Abstract

The article is intended to propose the new technique for analysis and visualization of vectorcardiograms based on the 3D phase diagrams. The regular Frank 3D lead system was considered as the signal source to construct 3D vector space. The three cardio signals from the lead system, representing the currents in the body, and the three integrated in time signals, representing the corresponding charge flows, were used to form 3D phase diagram. This diagram is considered as a new compact description of the dipole object properties in the 3D space, combining simultaneously information about the charge movements and the changes in values and orientation of the current. The regular properties, like the angular momentum of the charge flow and the dipole strength vectors and their covariance can be evaluated from the real vectorcardiogram. Based on the set of vectorcardiograms for 8 healthy controls and 7 myocardial infarction patients the 3D phase diagrams and their statistical parameters are evaluated and discussed. An example is given of the technique implementation for the comparison of the 3D phase diagrams in a control and a myocardial infarction patient.

Walking with robot-generated haptic forces in a virtual environment: a new approach to analyze lower limb coordination

“…The magnitude of the angular velocity is plotted perpendicular to the angular position trajectory, thus making an angular velocity trace visible in the 3D phase diagram. This is achieved by multiplying the angular velocity by a transformation matrix seen in Goussev [41] given below to display the corresponding perpendicular angular velocity magnitude, visible throughout the gait cycle [41].…”