2-D Simulations of Valveless Pumping Using the Immersed Boundary Method

Flow driven by pumping without valves is examined, motivated by biomedical applications such as cardiopulmonary resuscitation (CPR) and the human fetus before the development of the heart valves. The direction of flow inside a loop of tubing that consists of (almost) rigid and flexible parts is investigated when the boundary of one end of the flexible segment is forced periodically in time. Despite the absence of valves, net flow around the loop may appear in these simulations. The amplitude and even the direction of this flow depend on the driving frequency of the periodic forcing. INTRODUCTION Pumping blood in one direction is the main function of the heart, and the heart is equipped with valves that ensure unidirectional flow. Is it possible, though, to pump blood without valves? This paper is intended to show by numerical simulation the possibility of a net flow which is generated by a valveless mechanism in a circulatory system. Simulations of valveless pumping are motivated by the physical experiments of Kilner [3]. He observed net flow in one direction is dependent upon the location of periodic forcing in his model, which is a loop of tubing of which part is almost rigid and the other part flexible. In agreement with Kilner, we find by numerical simulations that net flow can indeed be driven around such a loop by periodic forcing at one location, but we also find something new: the direction of the flow depends on the driving frequency of the periodic forcing. One of the applications of valveless pumping may be cardiopulmonary resuscitation (CPR). The blood flow during CPR has been explained by two conventional theories: thoracic pump and cardiac compression mechanisms. In the thoracic pump model, it has been reported that the heart is " a passive conduit for blood flow " during chest compression, with an open mitral valve throughout the cardiac cycle and anterograde (forward) transmitral blood flow even during chest compression [1]. However, in the theory of the cardiac pump model, the heart acts as a pump and its valves function normally [2]. Our computational model of valveless pumping may provide assistance in understanding the thoracic pump