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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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Effect of relative stiffness of the tumor compared to the host tissue on solid stress and tumor growth.Dependence of A) the state of stress and B) tumor volume on the relative stiffness of the tumor compared to the normal tissue, µ*. 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).
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pone-0104717-g007: Effect of relative stiffness of the tumor compared to the host tissue on solid stress and tumor growth.Dependence of A) the state of stress and B) tumor volume on the relative stiffness of the tumor compared to the normal tissue, µ*. 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).

Mentions: Finally, we used the mathematical model to investigate how stiff a tumor should become relative to the host tissue, so that it will be able to grow in size. In vitro studies using cancer cell spheroids grown in a fibrous matrix [5] have shown the existence of a critical value of the relative stiffness of the tumor compared with the host tissue above which tumors can grow, but quantification of this critical stiffness can be estimated only with mathematical modeling. Figure 7 presents the bulk stress and the volume of the tumor as a function of the relative stiffness, µ*. µ* is defined as the ratio of the tumor’s shear modulus over the shear modulus of the normal tissue. We modeled both tissues with the neo-Hookean equation, the value of the shear modulus given in Table 2 for the SW620 cell line was used for the tumor, while the shear modulus of the normal tissue was varied. The results correspond to day 5 of the simulations and two values of the parameter β were used, the one found by fitting the model to the experimental data of Figure 3 and a value of zero, which renders the growth stretch ratio, λg, independent from the stress, and thus, the inhibitory effect of stress on tumor growth diminishes. The compressive solid stress in the tumor interior increases as the shear modulus of the host tissue increases (i.e., µ* becomes smaller), but interestingly it reaches a plateau when the shear modulus of the host tissue is equal to or higher than the modulus of the tumor (Figure 7A). Also, in agreement with the in vitro studies, Figure 7B suggests that the stiffness of the tumor should exceed a critical value compared with the stiffness of the host tissue, so that the tumor will be able to physically displace the tissue and grow in size. The model further predicts that this critical value of relative stiffness should be on the order of 1.5. It is noted, however, that apart from mechanical factors, biological factors that are not accounted for in our analysis, such as the expression of matrix-modifying agents (e.g., matrix metalloproteinases) or the supply of oxygen and nutrients also affect the progression of the tumor.


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)

Effect of relative stiffness of the tumor compared to the host tissue on solid stress and tumor growth.Dependence of A) the state of stress and B) tumor volume on the relative stiffness of the tumor compared to the normal tissue, µ*. 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).
© Copyright Policy
Related In: Results  -  Collection

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

pone-0104717-g007: Effect of relative stiffness of the tumor compared to the host tissue on solid stress and tumor growth.Dependence of A) the state of stress and B) tumor volume on the relative stiffness of the tumor compared to the normal tissue, µ*. 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).
Mentions: Finally, we used the mathematical model to investigate how stiff a tumor should become relative to the host tissue, so that it will be able to grow in size. In vitro studies using cancer cell spheroids grown in a fibrous matrix [5] have shown the existence of a critical value of the relative stiffness of the tumor compared with the host tissue above which tumors can grow, but quantification of this critical stiffness can be estimated only with mathematical modeling. Figure 7 presents the bulk stress and the volume of the tumor as a function of the relative stiffness, µ*. µ* is defined as the ratio of the tumor’s shear modulus over the shear modulus of the normal tissue. We modeled both tissues with the neo-Hookean equation, the value of the shear modulus given in Table 2 for the SW620 cell line was used for the tumor, while the shear modulus of the normal tissue was varied. The results correspond to day 5 of the simulations and two values of the parameter β were used, the one found by fitting the model to the experimental data of Figure 3 and a value of zero, which renders the growth stretch ratio, λg, independent from the stress, and thus, the inhibitory effect of stress on tumor growth diminishes. The compressive solid stress in the tumor interior increases as the shear modulus of the host tissue increases (i.e., µ* becomes smaller), but interestingly it reaches a plateau when the shear modulus of the host tissue is equal to or higher than the modulus of the tumor (Figure 7A). Also, in agreement with the in vitro studies, Figure 7B suggests that the stiffness of the tumor should exceed a critical value compared with the stiffness of the host tissue, so that the tumor will be able to physically displace the tissue and grow in size. The model further predicts that this critical value of relative stiffness should be on the order of 1.5. It is noted, however, that apart from mechanical factors, biological factors that are not accounted for in our analysis, such as the expression of matrix-modifying agents (e.g., matrix metalloproteinases) or the supply of oxygen and nutrients also affect the progression of the tumor.

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