Radiation Therapy

Cancer

  • Cancer is the second leading cause of death in the United States, with an estimated 570,000 deaths in 2013

  • Over 1.6 million new cases of cancer will be diagnosed in the United States in 2013

  • In the world, cancer is also a leading cause of death - 8.2 million deaths in 2012

Radiation Therapy

  • Cancer can be treated using radiation therapy (RT)

  • In RT, beams of high energy photons are fired into the patient that are able to kill cancerous cells

  • In the United States, about half of all cancer patients undergo some form of radiation therapy

History of Radiation Therapy

  • X-rays were discovered by Wilhelm Röntgen in 1895 (awarded the first Nobel Prize in Physics in 1901)
    • Shortly after, x-rays started being used to treat skin cancers
  • Radium discovered by Marie and Pierre Curie in 1898 (Nobel Prize in Chemistry in 1911)
    • Begun to used to treat cancer, as well as other diseases

  • First radiation delivery machines (linear accelerators) developed in 1940

  • Computed tomography (CT) invented in 1971

  • Invention of intensity-modulated radiation therapy (IMRT) in early 1980s

IMRT

  • To reach the tumor, radiation passes through healthy issue, and damages both healthy and cancerous tissue

  • Damage to healthy tissue can lead to undesirable side effects that reduce post-treatment quality of life

  • We want the dose to “fit” the tumor as closely as possible, to reduce the dose to healthy tissues

  • In IMRT, the intensity profile of each beam is non-uniform

  • By using non-uniform intensity profiles, the three-dimensional shape of the dose can better fit the tumor

Using Traditional Radiation Therapy

Using IMRT

Designing an IMRT Treatment

  • Fundamental problem:
    • How should the beamlet intensities be selected to deliver a therapeutic dose to the tumor and to minimize damage to healthy tissue

The Data

  • Treatment planning starts from a CT scan
    • A radiation oncologist contours (draws outlines) around the tumor and various critical structures
    • Each structure is discretized into voxels (volume elements) - typically 4 mm x 4 mm x 4 mm
  • From CT scan, can compute how much dose each beamlet delivers to every voxel

Small Example - 9 Voxels, 6 Beamlets

  • Minimize total dose to healthy tissue (spinal + other)

  • Constraints: tumor voxels at least 7Gy (Gray) , spinal cord voxel at most 5Gy

The Model

A Head and Neck Example

  • We will test out this approach on a head-and-neck case
    • Total of 132,878 voxels
    • One target volume (9,777 voxels)
    • Five critical structures: spinal cord, brain, brain stem, parotid glands, mandible (jaw)
    • 5 beams; each beam ~60 beamlets (1cm x 1cm) for a total of 328 beamlets

Treatment Plan Criteria

  • Dose to whole tumor between 70Gy and 77Gy

  • Maximum spinal cord at most 45Gy
    • Significant damage to any voxel will result in loss of function

  • Maximum brain stem dose at 54Gy

  • Maximum mandible dose at most 70Gy

  • Mean parotid gland dose at most 26Gy
    • Parotid gland is a parallel structure: significant damage to any voxel does not jeopardize function of entire organ

The Optimization Problem

Solution

Exploring Different Solutions

  • Mean mandible dose was 11.3Gy - how can we reduce this?

  • one approach: modify objective function
    • Current objective is the sum of the total dose
    \[T_B + T_{BS} + T_{SC} + T_{PG} + T_{M}\]
    • Change objective to
    \[T_B + T_{BS} + T_{SC} + T_{PG} + 10T_{M}\]
    • Set mandible weight from 1 (current solution) to 10

New Solution

Sensitivity

  • Another way to explore tradeoffs is to modify constraints
    • For example: by relaxing the mandible maximum dose constraint, we may improve our total healthy tissue dose
    • How much does the objective change for different constraints?

Shadow Prices

  • Parotid gland and brain stem have shadow prices of zero
    • Modifying these constraints is not beneficial
  • Mandible has highest shadow price
    • If a slight increase in mandible dose is acceptable, total healthy tissue dose can be significantly reduced

IMRT Optimization in Practice

  • Radiation machines are connected to treatment planning software that implements and solves optimization models (linear and other types)
    • Pinnacle by Philips
    • RayStation by RaySearch Labs
    • Eclipse by Varian

Extensions

  • Selection of beam angles
    • Beam angles can be selected jointly with intensity profiles using integer optimization
  • Uncertainty
    • Often quality of IMRT treatments is degraded due to uncertain organ motion (e.g., in lung cancer, patient breathing)
    • Can manage uncertainty using a method known as robust optimization

Efficiency

  • Manually designing an IMRT treatment is inefficient and impractical

  • Linear optimization provides an efficient and systematic way of designing an IMRT treatment
    • Clinical criteria can be modeled using constraints
    • By changing the model, treatment planner can explore tradeoffs

Clinical Benefits

  • Ultimately, IMRT Benefits the patient
    • In head and neck cancers, saliva glands were rarely spared prior to IMRT; optimized IMRT treatments spare saliva glands
    • In prostate cancer, optimized IMRT treatments reduce toxicities and allow for higher tumor doses to be delivered safely
    • In lung cancer, optimized IMRT reduces risk of radiation-induced pneumonia