Though mechanical circulatory support(MCS)devices,such as ventricular assist device(VAD)and total artificial heart(TAH),indeed provide heart failure patients with an alternative to transplantation,many complications are provided at the same time due to the non-pulsatile blood flow or high blood shear induced by those MCS.A novel spherical total artificial heart(TAH)based on the concept of hydraulic gerotor pump is proposed.This spherical TAH features volumetric pumping mechanism,pulsatile flow generating and low blood shear.It consists of four time-varying chambers partitioned by two orange shape wedges and one complex curve cut disk.The disk rotates as twice fast as the wedges,while all in the same direction.The TAH sucks in and pumps out blood through four ports located at the pump peripheral.This paper presents the fundamental equations which establish the geometric shape of the TAH,develop the range of the size specs,and show the analytical model for the time-varying chamber volume.