Chapter 14 Implications of the “Subquantum Level” in Carcinogenesis and Tumor Progression via Scale Relativity Theory

1. Introduction

2. The biology of cancer

2.1. Cancer, what should be noticed

2.2. Distinguishing traits of cancer

3. Mathematics of cancer

4. A few words about holography

4.1. Early development

4.2. The in-line hologram

4.3. Off-axis holograms

4.4. Recording materials

5. Tumor-associated ECM or tumor microenvironment, nonlinear medium with holographic properties

5.1. Extracellular matrix and tumor microenvironment

5.2. Tumor-associated ECM as a non-differential fractal medium

6. Tumor self-seeding by CTC and hypoxia support the idea of complete holography

6.1. The self-seeding hypothesis of tumor growth

6.2. Hypoxia and cancer

7. Basic model

7.1. The PDE cancer-invasion model

7.2. The PDE cancer-invasion model via scale relativity theory

7.3. Non-dimensionalization and parameterization

7.4. Laser beam in a multiscale diffusion cancer-invasion model

7.4.1. Laser as a lorenz system

7.5. A chaotic multi-scale cancer-invasion model

7.6. Travelling waves in the multiscale diffusion cancer-invasion model

7.7. Nondimensionalization

7.8. Spatially homogeneous system

7.9. Travelling wave analysis

7.10. Stability analysis

8. Conclusions

Author details

References