Influence of Ventricular Pressure Drop on Mitral Annulus Dynamics Through the Process of Vortex Ring Formation ARASH KHERADVAR 1 and MORTEZA GHARIB 2 1 Department of Mechanical Engineering, University of South Carolina, 300 Main Street, Columbia, SC 29208, USA; and 2 Cardiovascular and Biofluid Dynamics Laboratory, California Institute of Technology, 1200 E California Blvd., Pasadena, CA 91125, USA (Received 23 January 2007; accepted 11 September 2007; published online 25 September 2007) Abstract—Several studies have suggested that the mitral annulus displacement and velocity in early diastole can be used as indicators of diastolic performance. The peak velocity of the mitral annulus away from the LV apex during early diastole, which indicates the rate of longitudinal expansion of the LV, is reduced in patients with impaired diastolic relaxation. With the intention of relating the trans- mitral flow to mitral annulus plane dynamics, we measured mitral annulus recoil force for different valve sizes, while applying an exponential pressure drop in a simplified model of the ventricle. The temporal changes in diameter of the valve during rapid filling phase were also considered. The process of ventricular vortex formation was studied together with the measurement of mitral annulus recoil force within different pressure drop conditions. Matching the vorticity contour plots with the recoil force measurements resulted in the fact that the magnitude of recoil is maximal once the vortex ring is about to pinch off, regardless of the valve size or the characteristics of ventricular pressure drop. This study showed that the mitral annulus recoil is maximal once occurs at the vortex formation time ranging from 3.5 to 4.5. It was also shown that the presence of leaflets would dissipate the annulus recoil force. Keywords—Vortex ring, Vortex formation time, Left ventri- cle, Diastole, Mitral annulus recoil. INTRODUCTION Dynamics of mitral valve annulus during diastole is a topic that has received much attention recently given its important effects on valve performance in addition to its close association with diastolic heart failure (HF). The current literature strongly supports the dynamic motion of the mitral annulus during diastole on the basis of the extensive studies performed in both experimental ani- mals and human subjects using roentgenogram marker imaging, 20,21 sonomicrometry, 22 MR Imaging, 36 and echocardiography. 45,46 The annulus motion is relative to the ventricular apex and is a function of ventricular chamber shape, the trans-mitral flow, the papillary muscles and the chordate, respectively. Several studies have suggested that the mitral annulus displacement 1,38 and velocity 47,51,58 in early diastole can be used as indicators of diastolic perfor- mance. 14,15,25,32 It has also been shown previously that during the development of HF, normal pattern of left ventricular (LV) filling would be altered due to the diastolic dysfunction. 2,10,42,43 This variation in trans- mitral flow would be reflected in diastolic motion of the mitral annulus measurable by Doppler tissue imaging (DTI). 41 The peak velocity of the mitral annulus away from the LV apex during early diastole (E M )—which indicates the rate of longitudinal LV expansion—is reduced in patients with impaired diastolic relaxation. 25 Several factors such as trans-mitral flow, ventricular compliance and papillary muscles can influence the mitral valve dynamics. The effect of trans-mitral flow can be analyzed through studying the characteristics of the trans-mitral vortex ring formed at early dias- tole. 5,30,53 Formation of a vortex ring due to the early diastolic flow was initially recognized by in vitro visu- alization of the trans-mitral flow 4,48 and subsequently confirmed by analyses based on color Doppler map- ping 34,56 and MR Imaging. 33,35 The early trans-mitral flow is considered a rapidly starting jet that forms a vortex ring. The process of vortex ring formation is described by the vortex formation time which is a non- dimensional parameter 18 : T  ¼  U D T p ð1Þ where  U is the mean velocity of the jet, T p is the pulse duration, and D is the diameter of the nozzle. The importance of this parameter lies in the fact that by increasing it beyond a certain range (~3.5–4.5) for a Address correspondence to Arash Kheradvar, Department of Mechanical Engineering, University of South Carolina, 300 Main Street, Columbia, SC 29208, USA. Electronic mail: arashkh@engr. sc.edu Annals of Biomedical Engineering, Vol. 35, No. 12, December 2007 (Ó 2007) pp. 2050–2064 DOI: 10.1007/s10439-007-9382-y 0090-6964/07/1200-2050/0 Ó 2007 Biomedical Engineering Society 2050