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A biological optimization method for carbon therapy via iterative Jacobian-based linearization.

Chao Wang1, Ya-Nan Zhu1, Wangyao Li1

  • 1Department of Radiation Oncology, University of Kansas Medical Center, Kansas, KS, United States of America.

Physics in Medicine and Biology
|April 25, 2025
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Summary
This summary is machine-generated.

A new iterative Jacobian-based linearization (IJL) method improves carbon ion radiotherapy (CIRT) planning by accurately and efficiently optimizing biological dose, leading to better tumor control and reduced normal tissue damage.

Keywords:
biological dosecarbon therapyinverse optimizationparticle therapytreatment planning

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Area of Science:

  • Medical Physics
  • Radiation Oncology
  • Computational Biology

Background:

  • Carbon ion radiotherapy (CIRT) offers superior biological effectiveness for radio-resistant tumors compared to photon or proton therapy.
  • Optimizing the biological dose in CIRT is crucial for maximizing tumoricidal effects while minimizing damage to surrounding normal tissues and organs at risk (OAR).
  • Existing biological dose optimization methods for CIRT face mathematical challenges due to nonlinear biological dose models, leading to computational inefficiency and inaccuracy.

Purpose of the Study:

  • To develop an accurate and efficient biological dose optimization method for carbon ion radiotherapy (CIRT).
  • To address the computational challenges posed by nonlinear biological dose models in CIRT.
  • To improve treatment planning by enhancing tumoricidal dose delivery and OAR sparing.

Main Methods:

  • Introduced the iterative Jacobian-based linearization (IJL) method for biological dose optimization in CIRT.
  • Modeled biological dose using the product of physical dose and relative biological effect, based on the linear-quadratic and local effect models.
  • Employed iterative convex relaxation, linearizing the nonlinear biological dose with Jacobian approximations and solving subproblems via the alternating direction method of multipliers (ADMM).
  • Compared IJL against a limited-memory quasi-Newton (QN) method that directly solves the nonlinear optimization problem.

Main Results:

  • IJL demonstrated superior plan accuracy compared to the QN method, evidenced by improved OAR sparing.
  • Biological dose in the planning target volume 1cm (PTV1cm) surrounding the clinical target volume (CTV) was reduced to 89.7% (brain), 95.0% (lung), and 88.3% (abdomen) with IJL.
  • IJL exhibited significantly higher computational efficiency, requiring approximately 1/10 the computational time per iteration compared to QN.
  • IJL showed continuously decreasing objective functions, whereas the QN method stagnated after a certain number of iterations.

Conclusions:

  • The novel iterative Jacobian-based linearization (IJL) algorithm accurately and efficiently solves the biological optimization problem for CIRT.
  • IJL offers significant advantages in plan accuracy and computational efficiency over direct nonlinear optimization methods like QN.
  • This method holds promise for advancing CIRT treatment planning, enabling more precise and effective cancer therapy.