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Role of constitutive behavior and tumor-host mechanical interactions in the state of stress and growth of solid tumors.

Voutouri C, Mpekris F, Papageorgis P, Odysseos AD, Stylianopoulos T - PLoS ONE (2014)

Bottom Line: 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.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.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.

View Article: PubMed Central - PubMed

Affiliation: Cancer Biophysics laboratory, Department of Mechanical and Manufacturing Engineering, University of Cyprus, Nicosia, Cyprus.

ABSTRACT
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.

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Multiplicative decomposition of the deformation gradient tensor.The stress free state corresponds to an excised tumor having the growth-induced (residual) component of the solid stress released [2], [3]. The load free state corresponds to an excised tumor currying no external loads but holds residual stress, described by Fr. The grown state corresponds to the volumetric growth of the tumor, which is described by Fg and the grown state within the host tissue corresponds to the final configuration of the grown tumor accounting for external stresses (arrows) by the host tissue and described by Fe.
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pone-0104717-g001: Multiplicative decomposition of the deformation gradient tensor.The stress free state corresponds to an excised tumor having the growth-induced (residual) component of the solid stress released [2], [3]. The load free state corresponds to an excised tumor currying no external loads but holds residual stress, described by Fr. The grown state corresponds to the volumetric growth of the tumor, which is described by Fg and the grown state within the host tissue corresponds to the final configuration of the grown tumor accounting for external stresses (arrows) by the host tissue and described by Fe.

Mentions: Solid stress in a tumor has two components: the residual “growth-induced” stress, which accumulates in tumors due to the generation of internal forces among the structural constituents of the tumor and the externally applied stress due to mechanical interactions with the host tissue [3]. To model the growth and mechanical behavior of tumors the multiplicative decomposition of the deformation gradient tensor, F, was used [30], a methodology that has been applied successfully to solid tumors [3], [21], [25], [31]–[33] as well as to other soft tissues [34], [35]. The model considered only the solid phase of the tumor and accounted for i) tumor growth, ii) generation of residual, growth-induced stresses and iii) mechanical interactions between the tumor and the surrounding normal tissue. Therefore, F was divided into three components:(1)where Fe is the elastic component of the deformation gradient tensor and accounts for mechanical interactions with the surrounding normal tissue or with any other external stimulus, Fg is the component that accounts for tumor growth and Fr is the component that accounts for the generation of residual stresses (Figure 1).


Role of constitutive behavior and tumor-host mechanical interactions in the state of stress and growth of solid tumors.

Voutouri C, Mpekris F, Papageorgis P, Odysseos AD, Stylianopoulos T - PLoS ONE (2014)

Multiplicative decomposition of the deformation gradient tensor.The stress free state corresponds to an excised tumor having the growth-induced (residual) component of the solid stress released [2], [3]. The load free state corresponds to an excised tumor currying no external loads but holds residual stress, described by Fr. The grown state corresponds to the volumetric growth of the tumor, which is described by Fg and the grown state within the host tissue corresponds to the final configuration of the grown tumor accounting for external stresses (arrows) by the host tissue and described by Fe.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4128744&req=5

pone-0104717-g001: Multiplicative decomposition of the deformation gradient tensor.The stress free state corresponds to an excised tumor having the growth-induced (residual) component of the solid stress released [2], [3]. The load free state corresponds to an excised tumor currying no external loads but holds residual stress, described by Fr. The grown state corresponds to the volumetric growth of the tumor, which is described by Fg and the grown state within the host tissue corresponds to the final configuration of the grown tumor accounting for external stresses (arrows) by the host tissue and described by Fe.
Mentions: Solid stress in a tumor has two components: the residual “growth-induced” stress, which accumulates in tumors due to the generation of internal forces among the structural constituents of the tumor and the externally applied stress due to mechanical interactions with the host tissue [3]. To model the growth and mechanical behavior of tumors the multiplicative decomposition of the deformation gradient tensor, F, was used [30], a methodology that has been applied successfully to solid tumors [3], [21], [25], [31]–[33] as well as to other soft tissues [34], [35]. The model considered only the solid phase of the tumor and accounted for i) tumor growth, ii) generation of residual, growth-induced stresses and iii) mechanical interactions between the tumor and the surrounding normal tissue. Therefore, F was divided into three components:(1)where Fe is the elastic component of the deformation gradient tensor and accounts for mechanical interactions with the surrounding normal tissue or with any other external stimulus, Fg is the component that accounts for tumor growth and Fr is the component that accounts for the generation of residual stresses (Figure 1).

Bottom Line: 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.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.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.

View Article: PubMed Central - PubMed

Affiliation: Cancer Biophysics laboratory, Department of Mechanical and Manufacturing Engineering, University of Cyprus, Nicosia, Cyprus.

ABSTRACT
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.

Show MeSH
Related in: MedlinePlus