AISIM 3 Rheology of the liver

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Le texte suivant (en anglais) est la synthèse d'un échange d'e-mail entre Marc Thiriet et Fiona Carter a propos de la rhéologie du foie.

there is two strategies, both useful for our work
(biomechanical modelling and augmented reality imaging)
1. in vitro experiments on the parenchyma and on the Glisson's capsule separately
   
   --> Dan Diane work
2. in vivo tests
   
   --> Fiona Carter study
Here is an e-mail exchange between Fiona Carter and Marc Thiriet

• Marc's question
  I would like to have further informations on your results my questions are
  1. curves ex or in vivo ?
  2. 0.172 MPa ex or in vivo value ? for what strain range ?

• Fiona's answer
  All of the stress-strain curves for human liver indentation tests are in-vivo. We have done no post-mortem studies in humans due to the fact that extensive investigations were performed on excised animal tissue and we really wanted to move on to look at living human tissue.
  The values in the table are ex-vivo for pig liver and in-vivo for human liver (curves for one subject shown). As I mentioned in my talk, you can only consider a linear relationship between stress and strain at very low levels of strain. For this reason I was pretty careful not to call this relationship Young's modulus - there is no single value for Young's modulus of biological tissue. The figures in the table indicate the gradient of the curve up to 10% strain. It is very important to note that once strain levels increase beyond this level, the initial linear gradient given will not characterise the tissue accurately. Thus far 8 patients with normal liver tissue have been examined and the initial linear gradient values have fallen in the range given. I also briefly mentioned that it may be possible to characterise more of the stress-strain curve by considering an exponential relationship. This analysis is ongoing in my department at present.

  Fiona Carter
  Research Assistant
  Dept. of Surgery
  Level 6
  Ninewells Hospital and Medical School
  DUNDEE DD1 9SY
  Scotland
  01382 660111 ext:32561
  f.j.carter@dundee.ac.uk
  

• Marc's question
  a rapid check give indeed a crude value of 2.e5 between .05 and 1
  the order of magnitude is 1.e3 higher than in vitro test given to us by Dan D.
  the specimen being tested in fluid. What is your opinion with this discrepency in vitro - not dry - vs. in vivo.

• Fiona's answer
  I think that I discussed these experiments with the person in question briefly during my visit to Sophia. It was my understanding that the methods for Dan's experiment involve cutting segments/sections out of intact liver tissue. It was not clear to me if this was human liver or animal liver and another important factor is how these sections were stored and how soon they were tested post-mortem. In pig liver, and to a lesser extent in human liver, there is a dense fibrous tissue network surrounding the liver lobules which acts as a support structure for the whole organ. Depending on the size of Dan's samples taken from the liver, a certain amount of this support structure will be lost and this may effect the measured compliance.
  In our in-vivo tests the organ was intact with it's normal blood supply still in place. I have found a marked increase in compliance when excised tissues have been reperfused before testing - this may be another part explanation in the differences between our results. Another structure which has vital importance for the liver's mechanical properties is the surface region (Glisson's capsule), which is made up of densely packed fibrous tissue (mainly collagen). The presence or absence of this layer has a marked affect on the tissue properties - if the surface capsule is removed or damaged you definitely will notice a marked reduction in tissue stiffness. Finally, I seem to recall that the liver samples in Dan's tests were impacted at high speeds. In our tests we merely indent the surface of an organ at speeds between 1-2mm/sec using a small blunt indentor. I would have thought that using a higher strain rate would in fact produce a higher value for the elastic modulus with the tissue behaving as a stiffer material - so I can't see why Dan's results would give a lower value than ours if this were the only difference !

  To summarise, I cannot fully explain why we are getting such vastly different results without knowing a little more about Dan's experimental methods. There could be a number of reasons for the disparity and I would be more than happy to discuss them further if you want to give me a few more clues.

• Marc's informations
  Dan's harmonic compression tests were performed on parenchyma cylindrical samples (height of 10mm, diameter of 20mm) without large vessels.
  The tests were carried out on specimens immerged in petroleum bath to avoid deshydratation and to put fluid inside the sample.
  The bath temperature was maintained at 25 degrees Celsius.o

• Fiona :
  It sounds like the tests you describe are to measure the bulk modulus of the liver tissue (this value should be approaching that of water - i.e. that the tissue is virtually incompressible). Our two centres approach' to the question of biomechanical measurement are fundamentally different. To cut out very small samples (with respect to the total size of the organ) and immerse them in petroleum is basically treating biological tissue as an engineering material. You would perform this sort of test on something like rubber where taking a small sample from the whole should not affect it's intrinsic properties. In our centre we try to devise tests that involve testing the tissue in it's natural physiologial state - i.e. with the blood supply and the fibrous support system intact, filled with and surrounded by natural body fluids and at body temperature (37.4 deg). It seems very clear to me that if you treat a complex biological tissue as a homogenous engineering material there will be difficulties in extrapolating the results to the systemic, in-vivo situation.
  There are a few issues here:
  1. Testing small tissue samples.
     It has been recognised since the mid 1960's biological tissue has very complex mechanical properties and that devising methods to tests these properties is problematic. Early methods of testing soft tissues (such as mesentery or muscle) involved cutting strips from an excised organ and performing simple extension tests (uniaxial) - see Fung, Am. J. Physiol. 1967 for good descriptions. When some investigators looked at tethering all the free edges of the specimen (biaxial tension tests) they found that the same material yielded quite different results - in general samples that were tethered around all free edges behaved as a stiffer material than those in uniaxial tension.
     The suggested reason is that, although you may need to treat biological tissue as homogenous for modelling purposes, the microscopic structure of the tissue is very complex. Tissue fibres which give mechanical support to the tissue, run through it in many directions. If a tissue is cut then these tissue fibres are damaged and some of the support is lost. One way to overcome this problem in extension tests is to fix all the free edges of the specimen - trying to mimic the in-vivo situation. This is still far from ideal though since any manipulation of the tissue (attaching hooks or stitches for example) will further damage the tissue and affect it's mechanical response to stress.
     Several centres studying soft tissue biomechanics have moved away from small sample testing and endeavour to devise methods to measure elasticity of whole organs or systems. These methods are generally very complex and involve large and expensive imaging methods - e.g the breast elastography techniques used at the Mayo Clinic (R Ehman) using MRI. At our centre we used simple methods initially to get some basic data about the tissues and then developed novel instrumentation to get information from the tissue in it's natural state.
     I suggest that one reason that the elasticity constant, from Dan's liver experiments, is lower than ours is because of the tissue samples tested. You mention that the samples were free of large blood vessels - these are an important support structure in the intact organ, both physiologically and mechanically. In our early tests on liver we looked at indenting the surface of an organ with the surface capsule removed - i.e. the surface raw or damaged - similar to Dan's liver samples. Indentation tests showed that the tissue compliance increased significantly - initial elastic modulus value around 0.03-0.06 MPa for sheep liver ex-vivo.
  2. Organ blood flow.
     Since 70-80% of biological tissue is made up of water then the fluid supply to the tissue is of vital importance. In pathological situations, an increased vascularity (blood flow) to an area will result in the local area becoming swollen and stiffer initially. Likewise, if blood supply is removed e.g. in an excised organ, then the tissue will be more flaccid and compliant. We have found that reperfusing excised tissue with a physiological fluid significantly affects it's elasticity (experiments with pig and sheep spleen). There are also subtle differences between reperfusing tissue with an isotonic solution and with water - water produces increased tissue swelling and stiffness even in dead tissue. This is partly due to osmosis, the means by which cells take up or release water. I am not sure what osmotic effect petroleum will have on liver tissue but I doubt that it will be improving the tissue's fluid balance.
  3. Speed of testing.
     Some authors have found that altering the rate of strain applied to the tissue sample affects the measured tissue stiffness. There is little agreement in this area however, we have found that reducing the indentation speed to 0.15mm/sec affects the measured tissue response as there is some stress relaxation occurring during the test. Since our interest is in surgical interventions with tissue, we have limited the speed of indentations between 1-2mm/sec and have found no variation in elastic response in this range. You have not mentioned the testing speed so I cannot comment much further here - except to say that it would probably not make much difference.
  4. Temperature.
     Again, there should be little difference in results due to temperature as our ex-vivo tests were performed at room temperature and the in-vivo tests at body temperature. It is expected that the high water content of biological tissue will be the main factor influencing how elasticity changes with lower temperature and the protein content of tissue influencing the elasticity at high temperature (denaturation or 'cooking' occuring).
  In summary, I think that the most important reason why Dan's experiments yield lower elasticity values than our experiments is due to the effect of cutting out small samples from the tissue. I suppose that I could try preparing similar samples here and testing them using our methods, to see if I get similar figures to Dan. If I get some time then I will have a look at this.

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  further to our correspondance, I did some test on samples of fresh pig liver Friday may 21st. Using cylindrical sections (20mm diam, 10mm depth) held in rigid containers I indented them using our testing methods. The results for tissue samples which still had the surface capsule, the initial gradient up to 10% strain was roughly 2kPa, removing the surface capsule roughly halves the initial gradient value (1kPa). I think that this simple test reinforces the idea that removing small sections of liver and testing them individually will give much lower values of elasticity.