Role of Constitutive Behavior and Tumor-Host Mechanical Interactions in the State of Stress and Growth of Solid Tumors

<div><p>Mechanical forces play a crucial role in tumor patho-physiology. Compression of cancer cells inhibits their proliferation rate, induces apoptosis and enhances their invasive and metastatic potential. Additionally, compression of intratumor blood vessels reduces the supply of oxygen, nutrients and drugs, affecting tumor progression and treatment. Despite the great importance of the mechanical microenvironment to the pathology of cancer, there are limited studies for the constitutive modeling and the mechanical properties of tumors and on how these parameters affect tumor growth. Also, the contribution of the host tissue to the growth and state of stress of the tumor remains unclear. To this end, we performed unconfined compression experiments in two tumor types and found that the experimental stress-strain response is better fitted to an exponential constitutive equation compared to the widely used neo-Hookean and Blatz-Ko models. Subsequently, we incorporated the constitutive equations along with the corresponding values of the mechanical properties - calculated by the fit - to a biomechanical model of tumor growth. Interestingly, we found that the evolution of stress and the growth rate of the tumor are independent from the selection of the constitutive equation, but depend strongly on the mechanical interactions with the surrounding host tissue. Particularly, model predictions - in agreement with experimental studies - suggest that the stiffness of solid tumors should exceed a critical value compared with that of the surrounding tissue in order to be able to displace the tissue and grow in size. With the use of the model, we estimated this critical value to be on the order of 1.5. Our results suggest that the direct effect of solid stress on tumor growth involves not only the inhibitory effect of stress on cancer cell proliferation and the induction of apoptosis, but also the resistance of the surrounding tissue to tumor expansion.</p></div

Effect of tumor constitutive behavior on tumor growth and state of stress.

<p>A) Model fit to the experimentally measured growth curve of SW620 tumors using the neo-Hookean and the exponential equation. B) Evolution of bulk solid stress in the tumor interior does not depend on the selection of the constitutive equation. Results using the Blatz-Ko material are omitted for clarity.</p

Experimental measurements for the elastic modulus and tan(<i>δ</i>) of the two tumor types.

<p>Experimental measurements for the elastic modulus and tan(<i>δ</i>) of the two tumor types.</p

Values of the mechanical properties of the two tumor types derived by fitting the model to the experimental stress-strain curves.

<p>Standard errors are shown in parenthesis.</p>a<p>The Poisson’s ratio was taken to be 0.2 <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0104717#pone.0104717-Roose1" target="_blank">[22]</a>.</p

Effect of tumor-host mechanical interactions on tumor state of stress and growth.

<p>Dependence of A) state of stress and B) growth rate of tumors on the mechanical properties of the host tissue. The host tissue was modeled as a compressible neo-Hookean material with Poisson’s ratio of 0.2 and three values of the shear modulus were used, <i>µ</i> = 10, 15 and 30 kPa. The stiffer the host tissue is, the higher the stress in the tumor and the lower its growth rate becomes.</p

Effect of relative stiffness of the tumor compared to the host tissue on solid stress and tumor growth.

<p>Dependence of A) the state of stress and B) tumor volume on the relative stiffness of the tumor compared to the normal tissue, <i>µ</i>*. Relative stiffness is the ratio of the tumor shear modulus to that of the host. Results correspond to day 5 of the simulations. Tumor solid stress increases with stiffening of the surrounding host tissue and reaches a plateau when the stiffness of the tumor becomes the same as or lower than the stiffness of the host (panel A). The tumor has to reach a critical stiffness compared with that of the normal tissue to be able to displace the tissue and grow (panel B).</p

Stress-strain response of tumors.

<p>Experimentally measured elastic stress-strain response of MCF10CA1a and SW620 tumors in unconfined compression. Data show individual tumor behavior.</p

An Unusual Michael-Induced Skeletal Rearrangement of a Bicyclo[3.3.1]nonane Framework of Phloroglucinols to a Novel Bioactive Bicyclo[3.3.0]octane

A novel skeletal rearrangement of bicyclo[3.3.1]nonane-2,4,9-trione (<b>16</b>) to an unprecedented highly functionalized bicyclo[3.3.0]octane system (<b>17</b>), induced by an intramolecular Michael addition, is presented. This novel framework was found to be similarly active to hyperforin (<b>1</b>), against PC-3 cell lines. A mechanistic study was examined in detail, proposing a number of cascade transformations. Also, reactivity of the Δ^7,10-double bond was examined under several conditions to explain the above results

An Unusual Michael-Induced Skeletal Rearrangement of a Bicyclo[3.3.1]nonane Framework of Phloroglucinols to a Novel Bioactive Bicyclo[3.3.0]octane

A novel skeletal rearrangement of bicyclo[3.3.1]nonane-2,4,9-trione (<b>16</b>) to an unprecedented highly functionalized bicyclo[3.3.0]octane system (<b>17</b>), induced by an intramolecular Michael addition, is presented. This novel framework was found to be similarly active to hyperforin (<b>1</b>), against PC-3 cell lines. A mechanistic study was examined in detail, proposing a number of cascade transformations. Also, reactivity of the Δ^7,10-double bond was examined under several conditions to explain the above results