Predicting stress and interstitial fluid pressure in tumors based on biphasic theory

Dwairy, Mutaz; Reddy, J.N.; Righetti, Raffaella

doi:10.1016/j.compbiomed.2023.107651

Cited by 3 publications

(1 citation statement)

References 51 publications

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“…Moreover, Xiang et al [38] developed a Cauchy-Born rule of third order in conjunction with an element-free computational framework to simulate the biomechanical behaviour of microtubules. More recently, Dwairy et al [39] applied the biphasic theory to predict interstitial fluid pressure and stress within solid tumours. They found that mechanical stress in solid tumours highly depends on the nonlinearity and constitutive model of deformation while the interstitial fluid pressure is relatively independent of the fundamental constitutive equation.…”

Section: Introductionmentioning

confidence: 99%

In-Plane Wave Propagation Analysis of Human Breast Lesions Using a Higher-Order Nonlocal Model and Deep Learning

Farajpour,

Ingman

2023

Mathematics

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The wave propagation characteristics of biological tissues are of high importance in improving healthcare technologies and can be used as an early clinical indicator of many diseases. However, the current mathematical models that describe the mechanical properties of biological tissues do not account for the difference in softening and hardening observed at different scales and this limits their utility in biomedical imaging. In this paper, a higher-order nonlocal model is developed to study in-plane wave propagation in healthy, benign, and cancerous breast tissues. To verify the mathematical approach, finite element simulations are conducted. Furthermore, a sequential deep neural network model of feedforward type with multiple hidden layers is developed to understand the intrinsic in-plane wave characteristics of breast tissues. The deep learning algorithm shows potential in accurately extracting the frequencies and phase velocities of breast lesions under in-plane waves even when there is a limited number of clinical samples. Using the higher-order nonlocal model, significant differences between healthy fibroglandular tissue and early breast cancer in the form of ductal carcinoma in situ have been found. The combination of nonlocal and strain gradient parameters allows for the concurrent incorporation of stiffness hardening and softening, solving the rigid-tumour–soft-cell paradox of cancer biomechanics.

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Section: Introductionmentioning

confidence: 99%

In-Plane Wave Propagation Analysis of Human Breast Lesions Using a Higher-Order Nonlocal Model and Deep Learning

Farajpour,

Ingman

2023

Mathematics

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Mechanical models and measurement methods of solid stress in tumors

Bi,

Jin,

Wang

et al. 2024

Appl Microbiol Biotechnol

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In addition to genetic mutations, biomechanical factors also affect the structures and functions of the tumors during tumor growth, including solid stress, interstitial fluid pressure, stiffness, and microarchitecture. Solid stress affects tumors by compressing cancer and stromal cells and deforming blood and lymphatic vessels which reduce supply of oxygen, nutrients and drug delivery, making resistant to treatment. Researchers simulate the stress by creating mechanical models both in vitro and in vivo. Cell models in vitro are divided into two dimensions (2D) and three dimensions (3D). 2D models are simple to operate but exert pressure on apical surface of the cells. 3D models, the multicellular tumor spheres, are more consistent with the actual pathological state in human body. However, the models are more difficult to establish compared with the 2D models. Besides, the procedure of the animal models in vivo is even more complex and tougher to operate. Then, researchers challenged to quantify the solid stress through some measurement methods. We compared the advantages and limitations of these models and methods, which may help to explore new therapeutic targets for normalizing the tumor’s physical microenvironment. Key points •This is the first review to conclude the mechanical models and measurement methods in tumors. •The merit and demerit of these models and methods are compared. •Insights into further models are discussed.

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Parameter estimation in the Montijano-Bergues-Bory-Gompertz stochastic model for unperturbed tumor growth

Bonilla-Capilla,

Bergues Cabrales

2024

Preprint

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Different sources of noises endogenous and exogenous to the cancer are involved in its stochastic growth. The aim of this study is to propose the stochastic version of Montijano-Bergues-Bory-Gompertz equation for the unperturbed tumor growth kinetics. The maximum likelihood estimators for the intrinsic tumor growth rate and the growth decelerating factor, and their respective discrete time approximations were analytically calculated. Different simulations of the deterministic and stochastic of this equation were made for different values of their respective parameters. Limit conditions for the average diffusion coefficient and the growth decelerating factor were established. The tumor volume at the infinite was calculated for several values of parameters of the stochastic Montijano-Bergues-Bory-Gompertz equation. Furthermore, descriptive statistic for the maximum likelihood estimators of the intrinsic tumor growth rate was computed for several parameters of this equation. The results evidenced that solid tumors there are for values of the average diffusion coefficient and the growth decelerating factor less than their respective limit values. The transition between avascular and vascular phases of the unperturbed tumor growth kinetics was revealed in the plot of the discrete time approximation for the maximum likelihood estimator of the growth decelerating factor versus the discrete time approximation for the maximum likelihood estimator of the intrinsic tumor growth rate. These results were connected with different findings in the literature. In conclusion, the stochastic Montijano-Bergues-Bory-Gompertz equation may be applied in the experiment to describe the unperturbed tumor growth kinetics, as previously demonstrated for its deterministic version, in order to estimate the parameters of this equation and their connection with processes involved in the growth, progression and metastasis of unperturbed solid tumors.

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Predicting stress and interstitial fluid pressure in tumors based on biphasic theory

Cited by 3 publications

References 51 publications

In-Plane Wave Propagation Analysis of Human Breast Lesions Using a Higher-Order Nonlocal Model and Deep Learning

In-Plane Wave Propagation Analysis of Human Breast Lesions Using a Higher-Order Nonlocal Model and Deep Learning

Mechanical models and measurement methods of solid stress in tumors

Parameter estimation in the Montijano-Bergues-Bory-Gompertz stochastic model for unperturbed tumor growth

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