Solid stress and elastic energy as measures of tumour mechanopathology

Tumors are not only more rigid than normal tissues, but they also store elastic energy and are under compressive and tensile forces. How do we measure these forces and the stored elastic energy? Do these new mechanical abnormalities affect the tumor growth and treatment? How do we deal with them?
Solid stress and elastic energy as measures of tumour mechanopathology

My motivation for joining the lab of Professor Rakesh Jain at the Massachusetts General Hospital as a postdoctoral fellow was his group’s 1997 discovery of solid stress in tumors [1]. Solid stress, a new mechanical abnormality in tumors, was defined as the physical forces contained and transmitted by the solid constituents of the tumor. The role of cancer cells in compressing blood and lymphatic vessels was demonstrated in Jain’s lab in 2004 [2]. Interestingly, this paper also reported that when the cancer cells were selectively killed in a mouse tumor model, the vessels opened up. This led to the hypothesis that the blood vessels in tumors are compressed by physical forces from their surroundings. These physical forces, however, could not be a result of fluid pressure, given that fluid can typically flow through the leaky vessels of tumours without impediment. It was not until 2012 that the first measurements of solid stress were made in solid tumors [3]: a partial cut in the tumor, made with a scalpel, resulted in an opening of the cut. This observation, together with subsequent work in Jain’s lab, showed that, by lowering the amount of collagen and hyaluronan (two proteins abundant in tumors), solid stress is reduced, the blood vessels are decompressed, and the oxygenation of tumors and drug delivery to them are increased [3–5]. Lowering solid stress, when combined with chemotherapy, was shown to improve the survival rate in preclinical models [4], and is currently being tested in patients in a phase-II clinical trial [6].

These results showed that targeting solid stress and normalizing the mechanical microenvironment of tumors can be a promising strategy in the fight against cancer. This was my main motivation for working on the mechanobiology of tumors with a focus on solid stress. However, unlike stiffness and fluid pressure, measuring solid stress, a first step in characterizing this new mechanopathology, is much more challenging. Using springs as an analogy for tumor mechanobiology has been helpful to understand this challenge and to explain the underlying concept in our paper in Nature Biomedical Engineering: A tumor can be stiff (rigid) as the spring in Fig. 1a, or soft (compliant) as in Fig. 1b. However, at the same time, it can be under compression as in Fig. 1c, or under tension as in Fig. 1d; therefore, independently of being soft or stiff, the tumor can be under compressive or tensile solid stresses. Similar to the springs that can store elastic energy when pushed or pulled, the tumors can also store elastic energy. Measuring the stiffness of the tumors (spring constant in our spring analogy) is straightforward and available at the macro, micro and even nanoscale. However, measuring the amount of solid stress (in our analogy, the magnitude of the weights in Fig. 1c and d), and the direction of the solid stress (compressive or tensile) is quite challenging, especially when the unloaded states of the tumors are not known. Our methods are based on the simple concept of unloading the tumor at the region of interest, observing how much the tumor (the spring in Fig. 1e) is relaxed by the unloading, and measuring the amount and direction of the displacement after the unloading. Using this approach, we are able to estimate the force by using Hooke’s law, and determine whether it is compressive or tensile.

In the paper, we introduced three methods in which the tumors are mechanically unloaded in different geometries: (i) in the planar-cut method, we unload the tumor by a cut through the plane of interest, and the resulting stress-induced deformation gives us a two-dimensional distribution map of the stress; (ii) in the slice method we cut the tumor as a thin slice at the plane of interest, and the tumor slice deforms and changes surface area in response to even small amounts of stress; and (iii) in the needle biopsy method, we create a void by punching the tumor (this method can be used to account for the forces that are exerted by the surrounding tissue on the tumor, as in brain tumors). Applying these methods on multiple primary and metastatic tumors such as those from breast, pancreas, colon, liver, brain and lymph-node tissues, in mice and humans, led to several findings: (1) the same cancer cells, when grown in different organs, gave rise to tumors with different levels of solid stress and stiffness, and interestingly, the stiffer tumors did not necessarily contain higher solid stress; (2) in a model of breast cancer, the solid stress was increased by tumor growth, whereas the stiffness did not show a trend; and (3) the normal brain tissue contributes substantially to the solid stress level in brain tumors. We believe that the engineering principles presented in this work will facilitate the study of the origins and consequences of solid stress in tumors and will potentially lead to the discovery of new therapeutics and treatment strategies for fighting cancer.

See the published paper here:

Nia, H. T. et al. Solid stress and elastic energy as measures of tumour mechanopathology. Nat. Biomed. Eng. 1, 0004 (2016).

Figure 1. Spring analogy for (a) stiff and (b) soft tumors. Independently of being soft or stiff, tumors can be under (c) compressive or (d) tensile solid stresses. (e) To measure the solid stress in tumors, the stress is released at the plane of interest (here shown for the planar-cut method), and the stress-induced displacement is used to calculate the solid stress via mathematical modeling.

Figure 2. Some of the key members of the team behind the paper. Top row, from left to right: Dr. Lance Munn, Dr. Dai Fukumura, Dr. Yves Boucher and Dr. Keehoon Jung; bottom row: Ms. Meenal Datta, Dr. Hadi Nia, Dr. Rakesh Jain and Dr. Giorgio Seano.


  1. Helmlinger, G., P.A. Netti, H.C. Lichtenbeld, R.J. Melder, and R.K. Jain, Solid stress inhibits the growth of multicellular tumor spheroids. Nature Biotechnology, 1997. 15(8): p. 778-783.
  2. Padera, T.P., B.R. Stoll, J.B. Tooredman, D. Capen, E. di Tomaso, and R.K. Jain, Pathology: cancer cells compress intratumour vessels. Nature, 2004. 427(6976): p. 695-695.
  3. Stylianopoulos, T., J.D. Martin, V.P. Chauhan, S.R. Jain, B. Diop-Frimpong, N. Bardeesy, B.L. Smith, C.R. Ferrone, F.J. Hornicek, Y. Boucher, L.L. Munn, and R.K. Jain, Causes, consequences, and remedies for growth-induced solid stress in murine and human tumors. Proceedings of the National Academy of Sciences, 2012. 109(38): p. 15101-15108.
  4. Chauhan, V.P., J.D. Martin, H. Liu, D.A. Lacorre, S.R. Jain, S.V. Kozin, T. Stylianopoulos, A.S. Mousa, X. Han, P. Adstamongkonkul, Z. Popovich, P. Huang, M. Bawendi, Y. Boucher, and R.K. Jain, Angiotensin inhibition enhances drug delivery and potentiates chemotherapy by decompressing tumour blood vessels. Nature Communications, 2013. 4.
  5. Chauhan, V.P., Y. Boucher, C.R. Ferrone, S. Roberge, J.D. Martin, T. Stylianopoulos, N. Bardeesy, R.A. DePinho, T.P. Padera, L.L. Munn, and R.K. Jain, Compression of Pancreatic Tumor Blood Vessels by Hyaluronan Is Caused by Solid Stress and Not Interstitial Fluid Pressure. Cancer Cell, 2014. 26(1): p. 14-15.
  6. Proton w/FOLFIRINOX-Losartan for Pancreatic Cancer; identifier NCT01821729. Available from:

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