Spatial Behavior of Temperature Fields at Nanoscale

Abstract

This chapter involves the heating of a single nanoparticle that absorbs the radiation to generate heat, which is then transferred via conduction to the surrounding medium. This entails solving the heat flow equations for both the particle and surrounding fluid, while satisfying the boundary condition at the edge of the nanoparticle. In this chapter, we model 3D thermal fields within and around a plasmonic nanoparticle and cell organelles surrounded by biological medium heated by radiation. This chapter contains material adapted from our publications [2, 3]. A detailed list of references and reviews on a given topic of this chapter can be found in those original papers.

Appendices

Appendix E: Maple Code for Simulating Heat Diffusion Around a Nanoparticle

This appendix contains a Maple code designed for 2D simulations of the temperature distributions (second “dimension” is a temperature) around the nanoparticle (Slide 24.17). The comments within the Maple code should explain the variables, procedures, and functions that are used.

Slide 24.17

Appendix E: Maple Code for simulating heat diffusion around a nanoparticle

Note: This code takes about 10–15 min to complete the integrations. The code comes directly from the Maple file and is therefore formatted to word-wrap according to Maple standard character-per-line limits.

Appendix F: Maple Code for 3D Simulation of Heat Diffusion Around the Nanoparticle

This appendix contains a Maple code designed for 3D simulations of the temperature distributions (third “dimension” is a temperature) around the nanoparticle (Slide 24.18). The comments within the Maple code should explain the variables, procedures, and functions that are used.

Slide 24.18

Appendix F: Maple Code for 3D simulation of heat diffusion around a nanoparticle

Note: This code takes about 10–15 min to complete the integrations. The code comes directly from the Maple file and is therefore formatted to word-wrap according to Maple standard character-per-line limits.

Homework Exercises

8.3.1 Section 8.1: Modeling Heat Diffusion

• 8.1. What is the quasistationary heating approximation?

• 8.2. True or false? In the quasistationary heating approximation, we take into account the time required to reach a maximum temperature by the nanoparticle.

• 8.3. True or false? In the quasistationary heating approximation, the heat diffusion equation gives the space distribution for the maximum temperature of the particle.

• 8.4. What solutions are found from a heat transfer model?

• 8.5. How is the heat source calculated in a heat transfer model?

• 8.6. Describe how radiation is delivered to bone tissue to activate/heat nanoparticles?

• 8.7. What input data are needed for solving a heat transfer model?

• 8.8. Why is the nanoparticle heated to the relatively high temperature of ~600 K?

• 8.9. True or false? The temperature variations within the heated gold nanoparticle are large.

• 8.10. True or false? The temperatures inside the nanoparticle can be considered homogeneous.

• 8.11. What factors define the temperature distribution around the nanoparticle?

• 8.12. How is the thermal damage area of the surrounding tissue around the nanoparticle determined?

• 8.13. By how many times can the thermal necrosis size in bone tissue exceed the diameter of a heated nanoparticle?

• 8.14. True or false? The morphological properties of a nanoparticle can affect the thermal field distribution around the particle.

• 8.15. What energy intensity of the laser pulse can cause thermal necrosis of osteocytes by heated nanoparticles in most cases?

• 8.16. True or false? The energy intensity of the laser pulse for thermal necrosis of osteocytes by heated nanoparticles is greater than the intensity for laser safety requirements.

8.3.2 Section 8.2: Computer Practicum 5: Simulating the Temperature Fields Within and Outside the Nanoparticle

• 8.17. What are the two steps used for simulations of thermal fields around the nanoparticle?

• 8.18. True or false? There is a significant heat loss from the surface of a heated nanoparticle to the surrounding medium.

• 8.19. Using the Maple code in Appendix E, perform spatial simulations of thermal fields distribution inside and around a silver nanoparticle of optimal radius in surrounding cytoplasm, fat, and cell membrane media by employing thermal data from Tables 6.3 and 8.7. Find the optimal radius of the nanoparticle, optimal wavelength of the radiation, absorption efficiency, and energy density of the radiation required to achieve the maximum temperature of the nanoparticle in each surrounding medium. Write a report on your simulation results similar to the practice example 7. Make conclusions about the spatial heating of the nanoparticle and thermal damage area produced by heated nanoparticle in a surrounding biomedia.

• 8.20. Using the Maple code in Appendix E, perform spatial simulations of thermal fields distribution inside and around a fullerene nanoparticle of optimal radius in surrounding cytoplasm, fat, and cell membrane media by employing thermal data from Tables 6.3 and 8.7. Find the optimal radius of the nanoparticle, optimal wavelength of the radiation, absorption efficiency, and energy density of the radiation required to achieve the maximum temperature of the nanoparticle in each surrounding medium. Write a report on your simulation results similar to the practice example 7. Make conclusions about the spatial heating of the nanoparticle and thermal damage area produced by heated nanoparticle in a surrounding biomedia.

• 8.21. Using the Maple code in Appendix E, perform spatial simulations of thermal fields distribution inside and around a polystyrene nanoparticle of optimal radius in surrounding cytoplasm, fat, and cell membrane media by employing thermal data from Tables 6.3 and 8.7. Find the optimal radius of the nanoparticle, optimal wavelength of the radiation, absorption efficiency, and energy density of the radiation required to achieve the maximum temperature of the nanoparticle in each surrounding medium. Write a report on your simulation results similar to the practice example 7. Make conclusions about the spatial heating of the nanoparticle and thermal damage area produced by heated nanoparticle in a surrounding biomedia.

• 8.22. Using the Maple code in Appendix E, perform spatial simulations of thermal fields distribution inside and around a glass nanoparticle of optimal radius in surrounding cytoplasm, fat, and cell membrane media by employing thermal data from Tables 6.3 and 8.7. Find the optimal radius of the nanoparticle, optimal wavelength of the radiation, absorption efficiency, and energy density of the radiation required to achieve the maximum temperature of the nanoparticle in each surrounding medium. Write a report on your simulation results similar to the practice example 7. Make conclusions about the spatial heating of the nanoparticle and thermal damage area produced by heated nanoparticle in a surrounding biomedia.

• 8.23. Using the Maple code in Appendix E, perform spatial simulations of thermal fields distribution inside and around a carbon nanoparticle of optimal radius in surrounding cytoplasm, fat, and cell membrane media by employing thermal data from Tables 6.3 and 8.7. Find the optimal radius of the nanoparticle, optimal wavelength of the radiation, absorption efficiency, and energy density of the radiation required to achieve the maximum temperature of the nanoparticle in each surrounding medium. Write a report on your simulation results similar to the practice example 7. Make conclusions about the spatial heating of the nanoparticle and thermal damage area produced by heated nanoparticle in a surrounding biomedia.

• 8.24. Using the Maple code in Appendix E, perform spatial simulations of thermal fields distribution inside and around an aluminum oxide silver nanoparticle of optimal radius in surrounding cytoplasm, fat, and cell membrane media by employing thermal data from Tables 6.3 and 8.7. Find the optimal radius of the nanoparticle, optimal wavelength of the radiation, absorption efficiency, and energy density of the radiation required to achieve the maximum temperature of the nanoparticle in each surrounding medium. Write a report on your simulation results similar to the practice example 7. Make conclusions about the spatial heating of the nanoparticle and thermal damage area produced by heated nanoparticle in a surrounding biomedia.

• 8.25. Using the Maple code in Appendix E, perform spatial simulations of thermal fields distribution inside and around a magnesium oxide nanoparticle of optimal radius in surrounding cytoplasm, fat, and cell membrane media by employing thermal data from Tables 6.3 and 8.7. Find the optimal radius of the nanoparticle, optimal wavelength of the radiation, absorption efficiency, and energy density of the radiation required to achieve the maximum temperature of the nanoparticle in each surrounding medium. Write a report on your simulation results similar to the practice example 7. Make conclusions about the spatial heating of the nanoparticle and thermal damage area produced by heated nanoparticle in a surrounding biomedia.

• 8.26. Using the Maple code in Appendix E, perform spatial simulations of thermal fields distribution inside and around a nickel oxide nanoparticle of optimal radius in surrounding cytoplasm, fat, and cell membrane media by employing thermal data from Tables 6.3 and 8.7. Find the optimal radius of the nanoparticle, optimal wavelength of the radiation, absorption efficiency, and energy density of the radiation required to achieve the maximum temperature of the nanoparticle in each surrounding medium. Write a report on your simulation results similar to the practice example 7. Make conclusions about the spatial heating of the nanoparticle and thermal damage area produced by heated nanoparticle in a surrounding biomedia.

• 8.27. What is a main purpose of the practice example 8?

• 8.28. True or false? The cell organelle itself may act as an absorbing particle which, on being heated, could destroy the cancer cells without inserting any nanoparticles into the body.

• 8.29. True or false? The cancerous nucleus heats up to a lower temperature than the normal nucleus.

• 8.30. True or false? With the significant increase in temperature of the cancerous nucleus, the cancer cells undergo cell death via thermal ablation of the nucleus.

• 8.31. What causes a significant temperature difference between heating the healthy and cancerous cell organelles?

• 8.32. Using the Maple code in Appendix E, perform spatial simulations of the thermal field distributions around normal and cancerous cell mitochondria in cytoplasm by employing thermal data from Tables 6.5 and 8.7. Find the optimal wavelength of the radiation, absorption efficiency of healthy and cancerous organelles, and energy density of the radiation required to achieve the critical temperature for cancerous cell organelle ablation. Write a report on your simulation results similar to the practice example 8. Make conclusions about the possibility of killing cancer cells by heating the cell organelle.

• 8.33. Using the Maple code in Appendix E, perform spatial simulations of the thermal field distributions around normal and cancerous cell microtubules in cytoplasm by employing thermal data from Tables 6.5 and 8.7. Find the optimal wavelength of the radiation, absorption efficiency of healthy and cancerous organelles, and energy density of the radiation required to achieve the critical temperature for cancerous cell organelle ablation. Write a report on your simulation results similar to the practice example 8. Make conclusions about the possibility of killing cancer cells by heating the cell organelle.

• 8.34. Using the Maple code in Appendix E, perform spatial simulations of the thermal field distributions around normal and cancerous cell ribosomes in cytoplasm by employing thermal data from Tables 6.5 and 8.7. Find the optimal wavelength of the radiation, absorption efficiency of healthy and cancerous organelles, and energy density of the radiation required to achieve the critical temperature for cancerous cell organelle ablation. Write a report on your simulation results similar to the practice example 8. Make conclusions about the possibility of killing cancer cells by heating the cell organelle.

• 8.35. Using the Maple code in Appendix E, perform spatial simulations of the thermal field distributions around normal and cancerous cell cytoskeletons in cytoplasm by employing thermal data from Tables 6.5 and 8.7. Find the optimal wavelength of the radiation, absorption efficiency of healthy and cancerous organelles, and energy density of the radiation required to achieve the critical temperature for cancerous cell organelle ablation. Write a report on your simulation results similar to the practice example 8. Make conclusions about the possibility of killing cancer cells by heating the cell organelle.

• 8.36. Using the Maple code in Appendix E, perform spatial simulations of the thermal field distributions around normal and cancerous cell lysosomes in cytoplasm by employing thermal data from Tables 6.5 and 8.7. Find the optimal wavelength of the radiation, absorption efficiency of healthy and cancerous organelles, and energy density of the radiation required to achieve the critical temperature for cancerous cell organelle ablation. Write a report on your simulation results similar to the practice example 8. Make conclusions about the possibility of killing cancer cells by heating the cell organelle.