How to compute the total viscous energy loss from 3D velocity flow field ?
 

I am trying to compute the total energy viscous energy loss of the left ventricle . The velocity data is 3D velocity field acquired using 4D Flow MRI. I am wondering, when computing the cumulative energy loss should I sum the absolute (i.e. unsigned or non negative) values of the individual measurements or the signed ones?

To compute the energy loss of every point I use the following function:

E_loss=(S-(div(v)/3)*delta), where S is the strain rate tensor and delta is the Kronecker delta

Thanks in advance

I would like to clarify my question more.
I do understand the point that divergence has to be signed. My question is about getting the total E-loss over all points in the domain of interest (In my case, Left ventricle ) i.e. when summing up the E-loss of all (x,y,z) mesh points should I sum the signed or unsigned E-loss? On other words, does negative E-loss represent something?