Negative Jacobian

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  • Adam Baker
    Junior Member
    • Jan 2008
    • 29

    Negative Jacobian

    Hi,
    I wonder if you can determine the reason for the negative Jacobian error that this file generates. ErrorTest_8.feb works; it has active contraction of 0.2. ErrorTest_9.feb generates the error, with active contraction of 0.21. I would expect a negative Jacobian if the mesh were excessively distorted, but judging impressionistically from the output of ErrorTest_8.feb, I wouldn't expect an extra 0.01 to make a difference.

    Thanks,
    Adam
  • maas
    Lead Code Developer
    • Nov 2007
    • 3400

    #2
    Hi Adam,

    If you run the problem in debug mode (add -g2 at the end of your command line) you might get a better idea on what's going on. Debug mode dumps all iterations to the plotfile as well, not just the converged states. If you do this, you'll see that although ErrorTest_8.feb works fine, the first iteration causes a very large deformation (The model almost gets compressed completely onto itself). For this problem, FEBio can recover and still find the solution. For ErrorTest_9.feb however, the initial deformation on the first iteration is too large and generates a negative Jacobian. Now, the reason why this seamingly simple problem runs soo poorly, is probably due to the fact that the active contraction stiffness matrix has not been implemented yet. Until now, I've never had an example for which that actually causes a problem, but now I'll move this up in my todo list. I'll keep you posted.

    Cheers,

    Steve.
    Department of Bioengineering, University of Utah
    Scientific Computing and Imaging institute, University of Utah

    Comment

    • Adam Baker
      Junior Member
      • Jan 2008
      • 29

      #3
      Okay, that's good information to have, thanks. When I ramp it up more gradually the error doesn't occur. (Upon doing that, it seems like activation above 0.3 doesn't do much, so for this particular problem ramping will work.)

      Speaking of the active contraction model, after reviewing the theory manual and the Guccione & McCulloch (1993) paper, I'm not sure I understand how the two mesh (so to speak). Specifically I can't find where the theory manual's equations (5.30) and (5.31) come from. I'm probably just not quick enough at the algebra to see how the simpler equations in the theory manual were derived.

      Relatedly, and perhaps more pertinent to my particular application, it seems that Guccione & McCulloch hardwired a behavior specific to cardiac muscle into their model, in using a piecewise cross-bridge detachment function rather than a constant rate of detachment, as Lackner & Peskin (1986) do for skeletal muscle. I wonder if that could be a specifiable parameter. Alternately, would it be possible to have an option for a basic Hill-type model (like in LS-Dyna?).

      Thanks (and sorry),
      Adam

      Comment

      • maas
        Lead Code Developer
        • Nov 2007
        • 3400

        #4
        Hi Adam,

        Glad to hear you found a workaround.

        The equations (5.30) and (5.31) are taken litteraly from Guccione's paper (Mechanics of Active conctraction in Cardiac Muscle: Part II - Cylindrical Models of the Systolic Left Ventricle, Journal of Biomechanical Engineering, vol 115, FEB 1993, pg 82-90). In particular see eqs 8 and 9 on page 84 of this paper. The only difference between this model and FEBio's implementation is that the user needs to specify Ct with a loadcurve.

        You are also correct that this model is specific for cardiac muscle. I must admit I am not too familiar with other active contraction models so I'll have to do some more reading to answer your final question. If you want, you can request this as a new feature for FEBio, though.

        Cheers,

        Steve.
        Department of Bioengineering, University of Utah
        Scientific Computing and Imaging institute, University of Utah

        Comment

        • Adam Baker
          Junior Member
          • Jan 2008
          • 29

          #5
          Ah... part II. The theory manual reference is to "Mechanics of active contraction in cardiac muscle: part I - constitutive relations for fiber stress that describe deactivation." Sounds like BibTeX.

          I will add a feature request with some links.

          Adam

          Comment

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