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Meanwhile, compared to PT, CIRT causes more complex and severe DNA damage in tumor cells, which results in a higher relative biological effectiveness (RBE), making it particularly advantageous in treating radioresistant and hypoxia tissues than conventional radiotherapy. However, CIRT's high RBE and the nuclear fragmentation dose tail outside the target presents challenges in sparing organ at risk (OARs). Combining PT and CIRT offers a potential hybrid modality that leverages the biological effectiveness of carbon ions while minimizing normal tissue toxicity with high biological damage.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Purpose<\/jats:title>\n                    <jats:p>Despite the potential of combining PT and CIRT, balancing their respective advantages while mitigating disadvantages remains a significant challenge. This study aims to develop an optimized treatment approach that automatically adjusts the relative contributions of protons and carbon ions, improving target dose conformity while minimizing biological impact on OARs.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Methods<\/jats:title>\n                    <jats:p>We propose a biological optimization framework for multi\u2010modality combining PT and CIRT (CCIPRT). The biological dose is modeled as the product of the physical dose and RBE. Through iterative Jacobian\u2010based linearization, the biological dose of carbon ion is expressed in a linear model, enabling the formulation of a linear least\u2010square objective. The biological dose of proton is formulated as a linear model using the physical dose and dose\u2010averaged linear energy transfer (LET). The joint optimization problem is then solved using iterative convex relaxation and the alternating direction method of multipliers. For comparison, single\u2010modality PT and CIRT were also implemented.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Results<\/jats:title>\n                    <jats:p>When the target dose of CCIPRT is prescribed in terms of the physical dose, compared to PT, CCIPRT increased the mean biological dose in the target by 37.7%, 29.6%, and 31.1% for brain, lung, and abdomen, respectively; compared to CIRT, CCIPRT reduced the biological dose in CTV1cm (ring surrounding CTV with 1\u00a0cm width) by 47.2%, 32.3%, and 40.4% for brain, lung, and abdomen, respectively. When the target dose of CCIPRT is prescribed in terms of the biological dose, compared to PT, CCIPRT achieved higher conformity index (CCIPRT: 0.96 and 0.97; PT: 0.93 and 0.96 for brain and liver cases, respectively) and reduced the dose in CTV1cm by 9.5% and 7.0% for brain and liver cases, respectively; compared to CIRT, CCIPRT enhanced healthy tissue sparing, reducing the dose to the body by 7.5% and 9.2% for brain and liver cases, respectively.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Conclusions<\/jats:title>\n                    <jats:p>A novel multi\u2010modality CCIPRT treatment planning is developed with demonstrated superior performance over single\u2010modality PT or CIRT, with enhanced biological effectiveness and dose conformity compared to PT and reduced OAR dose compared to CIRT.<\/jats:p>\n                  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