The characterisation of blood rotation in a human heart chamber based on statistical analysis of vorticity maps Kelvin K.L. Wong a,c , Richard M. Kelso b , Stephen G. Worthley c , Prashanthan Sanders c , Jagannath Mazumdar a and Derek Abbott a a Center for Biomedical Engineering and School of Electrical & Electronics Engineering, University of Adelaide, SA 5005, Australia; b School of Mechanical Engineering, Sports Engineering Group, University of Adelaide, SA 5005, Australia; c Cardiovascular Research Centre and School of Medicine, University of Adelaide, SA 5005, Australia ABSTRACT Modelling of non-stationary cardiac structures is complicated by the complexity of their intrinsic and extrinsic motion. The first known study of haemodynamics due to the beating of heart was made by Leonardo Da Vinci, giving the idea of fluid-solid interaction by describing how vortices develop during cardiac structural interac- tion with the blood. Heart morphology affects in changes of cardio dynamics during the systolic and diastolic phrases. In a chamber of the heart, vortices are discovered to exist as the result of the unique morphological changes of the cardiac chamber wall by using flow-imaging techniques such as phase contrast magnetic reso- nance imaging. The first part of this paper attempts to quantify vortex characteristics by means of calculating vorticity numerically and devising two dimensional vortical flow maps. The technique relies on determining the properties of vorticity using a statistical quantification of the flow maps and comparison of these quantities based on different scenarios. As the characteristics of our vorticity maps vary depending on the phase of a car- diac cycle, there is a need for robust quantification method to analyse vorticity. In the second part of the paper, the approach is then utilised for examining vortices within the human right atrium. Our study has shown that a proper quantification of vorticity for the flow field can indicate the strength and number of vortices within a heart chamber. Keywords: Vorticity, Phase contrast magnetic resonance imaging, Histogram, Segmentation 1. INTRODUCTION A phase contrast magnetic resonance imaging (MRI) approach is used in this study for the flow imaging of right atrium in a healthy subject. The use of this velocity-encoded MR imaging method applied onto cardiac imaging of right atria enables a good assessment of vortices that exist in the cardiac chamber. Phase contrast MRI can produce cine-MR images that are presented in a movie. It is a non-invasive imaging technique that allows study of flow-related physiology and pathophysiology with good spatial and temporal resolutions. Velocity-encoded (VENC) phase contrast MRI allows three dimensional MR velocity mapping based on the intrinsic sensitivity of MRI to flow, and enables the acquisition of spatially registered functional information simultaneously with morphological information. 1 Three dimensional MRI based velocity mapping operates by registering three separate flow-sensitive volumes in the x, y and z orientations of the scan. The flow veloci- ties may be computed by determining the shift of phase pertaining to the collection of imaged blood proton spins and reconstructing the flow vectors in advanced visualisation packages. This concept has varying ter- minologies in literature: the most common being phase contrast MRI, while some studies labelled it as phase- velocity MRI. 2 In general, such MRI based techniques form a class of approach known as magnetic resonance Further author information: (Send correspondence to K.K.L. Wong) K.K.L. Wong: E-mail: kwong@eleceng.adelaide.edu.au, Telephone: +61 (8) 8303 6296 Biomedical Applications of Micro- and Nanoengineering IV and Complex Systems, edited by Dan V. Nicolau, Guy Metcalfe Proc. of SPIE Vol. 7270, 72700W · © 2008 SPIE · CCC code: 1605-7422/08/$18 · doi: 10.1117/12.810703 Proc. of SPIE Vol. 7270 72700W-1 2008 SPIE Digital Library -- Subscriber Archive Copy