Computational Modeling in Medicine 2

Applications in Radiation Therapy

Photo by National Cancer Institute

Part one introduced the transformative potential of computational modelling in medicine, highlighting its role in advancing drug discovery, understanding disease mechanisms, and personalizing patient care. In this instalment, I examine real-world case studies that exhibit how computational models solve complex biomedical challenges and enhance health outcomes.

Computational modelling plays a key role in advancing radiation therapy for cancer treatment. Recent developments permit the simulation of low-energy electrons and water interactions at the molecular level, providing insight into radiation-induced biological damage (Kuncic, 2015).

Photo by National Cancer Institute

With integrative models focusing on tumour growth, cell life cycle, oxygen diffusion, and radiosensitivity, the simulation of the entire radiation treatment protocol enabled, which may lead to improved treatment strategies (Marrero et al., 2017), mathematical modelling contributes to precision medicine by optimising radiation doses based on individual patient radiobiological parameters (Rockne & Frankel, 2017). Furthermore, computational-based patient models combined with Monte Carlo simulations and epidemiological risk models aid in estimating the risk of radiation-induced secondary cancers due to stray or secondary doses in healthy tissues surrounding the tumour (Paganetti, 2009). These advances in computational modelling are enhancing our understanding of the impact of radiation therapy and contributing to the development of more efficacious cancer treatments. Contemporary work in radiation oncology aims to tailor treatment to individual patients, considering tumour shape, site and tissue density. Mathematical modelling has emerged as a promising approach to optimise radiation dose based on radiobiological parameters (Rockne & Frankel, 2017).

Functional imaging techniques provide valuable information on tumour proliferation and cell density, allowing biological optimisation of treatment plans (Dasu, 2008). Increasing the dose in proliferating foci and decreasing the dose in slower-growing areas can improve tumour control while sparing normal tissues (Dasu, 2008). Computed tomography contributes immensely to individual treatment planning by providing density matrices that consider patient-specific heterogeneity (Christ & Breitling, 1978). These advances in radiobiology and imaging techniques provide opportunities to target underlying mechanistic processes and improve radiotherapy outcomes at the individual patient level (Schaue & McBride, 2015). Integrating these approaches may improve tumour management and normal tissue sparing during radiotherapy.

Monte Carlo simulations (MC), are extensively used in radiation therapy for dosimetry planning and analysis. These computational methods accurately predict dose distributions in complex geometries, including CT-based models (Diffenderfer et al., 2013; DeMarco et al., 1998). MC simulations are particularly valuable for pediatric dosimetry, where patient-specific models are essential due to children's high radiosensitivity (Papadimitroulas et al., 2019). Software tools such as Geant4 and MCNP4A facilitate radiation transfer simulations in CT-derived geometries, enabling accurate dose calculations for a variety of applications, including space radiation experiments and clinical radiotherapy (Diffenderfer et al., 2013; DeMarco et al., 1998). Although MC methods excel at modelling physical interactions, challenges remain for radiobiological modelling of treatment outcomes (El Naqa et al., 2012). Ongoing research aims to integrate MC simulations with advanced computational techniques, such as machine learning, to improve the accuracy of tumour control probability (TCP) and normal tissue complication probability (NTCP) estimations, thereby optimising treatment planning and clinical trial design ( Papadimitroulas et al., 2019; El-Naka et al., 2012 ).

Computational models have greatly improved radiation therapy planning and outcomes. Monte Carlo simulations improve dose calculation accuracy, which may reduce radiation exposure to healthy tissues while preserving tumour control (Siantar & Moses, 1998; Paganetti, 2009). These models allow for accurate organ dosimetry and the estimation of secondary cancer risks from scattered radiation (Paganetti, 2009). Bayesian modelling of geometric errors enables personalised planning target volume (PTV) adaptation, which reduces healthy tissue dose by up to 19% while maintaining tumour coverage (Herschtal et al., 2015). Monte Carlo approaches hold potential for enhancing radiobiological modelling by providing more accurate estimates of tumour control probability (TCP) and normal tissue complication probability (NTCP) than classic linear-quadratic models (El Naqa et al., 2012). These advances in computational modeling will help optimize treatment plans, evaluate different treatment modalities, and design clinical trials, ultimately leading to improved patient outcomes in radiation therapy.

Recent research looks into the possibility of merging particle beam therapy, specifically proton therapy, with immunotherapy for cancer treatment. The model-based method is presented as an alternative to randomised controlled trials for determining the efficacy of particle beam therapy (Prayongrat et al., 2018). Proton therapy's distinct physical and biological properties, such as high linear energy transfer and relative biological effectiveness, may improve its immunogenic profile as compared to traditional radiotherapy (Gaikwad et al., 2023). Protons, like photons, have been shown in studies to produce immunogenic modification of irradiated tissue, potentially boosting tumour cell sensitivity to T cell-mediated death (Durante et al. 2016). To improve treatment outcomes, mechanism-based mathematical modelling with quantitative imaging data is proposed for personalising and combining radiotherapy and immunotherapy (Hormuth et al., 2022). These approaches aim to maximize synergy, reduce toxicity, and improve overall treatment efficacy across various cancer types, including brain, lung, and head and neck cancers.

Computational modelling transforms radiation therapy by giving precise, patient-specific information for treatment planning and optimisation. Clinicians may now adapt therapy based on individual tumour features and biological parameters thanks to technological advances such as Monte Carlo simulations, functional imaging, and radiobiological modelling. The combination of computational modelling, real-time imaging, and artificial intelligence paves the way for fully personalised therapy regimens, improving tumour control while preserving healthy tissue. As these technologies advance, they promise to revolutionise the future of medicine by providing more effective and focused care to patients globally.

Examples are for educational purposes only.

1. Monte Carlo Simulation of Photon Transport in Tissues

python

import numpy as np

import matplotlib.pyplot as plt

# Simulation parameters

num_photons = 10000 # Number of photons to simulate

max_steps = 100 # Maximum steps a photon can take

tissue_thickness = 10.0 # Thickness of tissue in cm

scattering_coefficient = 0.8 # Probability of scattering (per cm)

absorption_coefficient = 0.2 # Probability of absorption (per cm)

mean_free_path = 1.0 / (scattering_coefficient + absorption_coefficient)

# Photon tracking

absorbed_photons = 0

escaped_photons = 0

photon_paths = [] # Store photon paths for visualization

# Monte Carlo simulation

for photon in range(num_photons):

x, z = 0.0, 0.0 # Start at the origin

path = [(x, z)] # Track the photon's path

for step in range(max_steps):

# Move the photon a random distance

step_length = -mean_free_path * np.log(np.random.rand())

theta = 2 * np.pi * np.random.rand() # Random direction in 2D

x += step_length * np.cos(theta)

z += step_length * np.sin(theta)

path.append((x, z))

# Check if the photon is absorbed or escapes the tissue

if np.random.rand() < absorption_coefficient / (scattering_coefficient + absorption_coefficient):

absorbed_photons += 1

break # Photon is absorbed

if z > tissue_thickness:

escaped_photons += 1

break # Photon escapes the tissue

photon_paths.append(path)

# Results

print(f"Total photons: {num_photons}")

print(f"Absorbed photons: {absorbed_photons} ({(absorbed_photons / num_photons) * 100:.2f}%)")

print(f"Escaped photons: {escaped_photons} ({(escaped_photons / num_photons) * 100:.2f}%)")

# Visualization of photon paths

plt.figure(figsize=(10, 6))

for path in photon_paths[:100]: # Visualize first 100 photons

path = np.array(path)

plt.plot(path[:, 0], path[:, 1], alpha=0.5)

plt.axhline(y=tissue_thickness, color='r', linestyle='--', label='Tissue Boundary')

plt.title('Monte Carlo Simulation of Photon Transport')

plt.xlabel('Lateral Distance (cm)')

plt.ylabel('Depth (cm)')

plt.legend()

plt.grid(alpha=0.3)

plt.show()

Output

Total photons: 10000
Absorbed photons: 9991 (99.91%)
Escaped photons: 9 (0.09%)

2. Code: Multi-Beam Radiation Dose Distribution with Isodose Curves

python

import numpy as np

import matplotlib.pyplot as plt

from matplotlib.colors import Normalize

# Function to calculate dose from a single radiation source

def calculate_dose(X, Y, center_x, center_y, max_dose, spread):

return max_dose * np.exp(-((X - center_x)**2 + (Y - center_y)**2) / (2 * spread**2))

# Parameters for the grid

x = np.linspace(0, 100, 200) # Higher resolution grid

y = np.linspace(0, 100, 200)

X, Y = np.meshgrid(x, y)

# Define multiple radiation beams (x, y, max dose, spread)

beams = [

{"center_x": 40, "center_y": 50, "max_dose": 80, "spread": 10},

{"center_x": 60, "center_y": 50, "max_dose": 80, "spread": 10},

{"center_x": 50, "center_y": 40, "max_dose": 60, "spread": 15},

{"center_x": 50, "center_y": 60, "max_dose": 60, "spread": 15},

]

# Compute the total dose by summing contributions from all beams

total_dose = np.zeros_like(X)

for beam in beams:

dose = calculate_dose(X, Y, beam["center_x"], beam["center_y"], beam["max_dose"], beam["spread"])

total_dose += dose

# Visualization: Heatmap with Isodose Curves

plt.figure(figsize=(10, 8))

contour = plt.contourf(X, Y, total_dose, levels=30, cmap='hot', norm=Normalize(vmin=0, vmax=np.max(total_dose)))

plt.colorbar(contour, label='Dose (Gy)')

# Add isodose lines at specific dose levels (e.g., 10%, 50%, 90% of max dose)

isodose_levels = [0.1 * np.max(total_dose), 0.5 * np.max(total_dose), 0.9 * np.max(total_dose)]

plt.contour(X, Y, total_dose, levels=isodose_levels, colors=['blue', 'green', 'yellow'], linestyles='--', linewidths=1.5)

plt.clabel(plt.contour(X, Y, total_dose, levels=isodose_levels, colors=['blue', 'green', 'yellow']), fmt='%1.0f Gy')

# Add labels and title

plt.title('Multi-Beam Radiation Dose Distribution with Isodose Lines', fontsize=14)

plt.xlabel('X Coordinate (cm)', fontsize=12)

plt.ylabel('Y Coordinate (cm)', fontsize=12)

plt.grid(alpha=0.3)

plt.show()

Output

References

• Advances in Computational Radiation Biophysics for Cancer Therapy: Simulating Nano-Scale Damage by Low-Energy Electrons Z. Kuncic 2015
  https://doi.org/10.1142/S1793048014500040

• Towards an integrative computational model for simulating tumour growth and response to radiation therapy C. Marrero, V. Aubert, N. Ciferri, Alfredo Hernández, R. Crevoisier, O. Acosta Symposium on Medical Information Processing and Analysis 2017 10.1117/12.2285914

• Mathematical Modeling in Radiation Oncology R. Rockne, P. Frankel 2017

  https://doi.org/10.1007/978-3-319-53235-6_12

• The Use of Computational Patient Models to Assess the Risk of Developing Radiation-Induced Cancers From Radiation Therapy of the Primary Cancer

  H. Paganetti Proceedings of the IEEE 2009 https://doi.org/10.1109/JPROC.2009.2023809

• Mathematical Modeling in Radiation Oncology

  R. Rockne, P. Frankel 2017 https://doi.org/10.1007/978-3-319-53235-6_12

• Opportunities and challenges of radiotherapy for treating cancer

  D. Schaue, W. McBride Nature Reviews Clinical Oncology 2015

  https://doi.org/10.1038/nrclinonc.2015.120

• Treatment planning optimisation based on imaging tumour proliferation and cell density A. Dasu Acta oncologica 2008 https://doi.org/10.1080/02841860802251583

• [The use of computer tomography in individual treatment planning (author's transl)]. G. Christ, G. Breitling RöFo. Fortschritte auf dem Gebiet der Röntgenstrahlen und der bildgebenden Verfahren (Print) 1978

• Monte Carlo modeling in CT-based geometries: dosimetry for biological modeling experiments with particle beam radiation E. Diffenderfer, D. Dolney, Maximilian O. Schaettler, J. Sanzari, J. Mcdonough, K. Cengel Journal of Radiation Research 2013 https://doi.org/10.1093/jrr/rrt118

• A Review on Personalized Pediatric Dosimetry Applications Using Advanced Computational Tools P. Papadimitroulas, Athanasios D. Balomenos, Yiannis Kopsinis, G. Loudos, Christos Alexakos, D. Karnabatidis, G. Kagadis, T. Kostou, Konstantinos P. Chatzipapas, D. Visvikis, Konstantinos A. Mountris, V. Jaouen, K. Katsanos, A. Diamantopoulos, D. Apostolopoulos IEEE Transactions on Radiation and Plasma Medical Sciences 2019 https://doi.org/10.1109/TRPMS.2018.2876562

• The PEREGRINETM program: using physics and computer simulation to improve radiation therapy for cancer C. L. Siantar, E. Moses 1998

• The Use of Computational Patient Models to Assess the Risk of Developing Radiation-Induced Cancers From Radiation Therapy of the Primary Cancer

  H. Paganett Proceedings of the IEEE 2009

• Sparing healthy tissue and increasing tumor dose using bayesian modeling of geometric uncertainties for planning target volume personalization.

  A. Herschtal, L. Te Marvelde, K. Mengersen, F. Foroudi, T. Eade, D. Pham, H. Caine, T. Kron International Journal of Radiation Oncology, Biology, Physics

  2015

• Monte Carlo role in radiobiological modelling of radiotherapy outcomes

  I. E. El Naqa +2 Physics in Medicine and Biology

  2012 ·

• Opportunities for improving brain cancer treatment outcomes through imaging-based mathematical modelling of the delivery of radiotherapy and immunotherapy. D. Hormuth, Maguy Farhat, Chase Christenson, Brandon Curl, C. Chad Quarles, C. Chung, T. Yankeelov Advanced Drug Delivery Reviews 2022

• Combinatorial approach of immuno‐proton therapy in cancer: Rationale and potential impact U. Gaikwad, J. Bajpai, R. Jalali

  Asia-Pacific Journal of Clinical Oncology 2023

• Opportunities for improving brain cancer treatment outcomes through imaging-based mathematical modeling of the delivery of radiotherapy and immunotherapy.D. Hormuth, Maguy Farhat, Chase Christenson, Brandon Curl, C. Chad Quarles, C. Chung, T. Yankeelov Advanced Drug Delivery Reviews

  2022

• Does Heavy Ion Therapy Work Through the Immune System?

  M. Durante, D. Brenner, S. Formenti International Journal of Radiation Oncology, Biology, Physics 2016