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1. Spatiotemporal fractionation schemes for stereotactic radiosurgery of multiple brain metastases

   https://doi.org/10.1002/mp.16457  

   Torelli, Nathan ; Papp, Dávid ; Unkelbach, Jan ( June 2023 , Medical Physics)

   Stereotactic radiosurgery (SRS) is an established treatment for patients with brain metastases (BMs). However, damage to the healthy brain may limit the tumor dose for patients with multiple lesions.

   In this study, we investigate the potential of spatiotemporal fractionation schemes to reduce the biological dose received by the healthy brain in SRS of multiple BMs, and also demonstrate a novel concept of spatiotemporal fractionation for polymetastatic cancer patients that faces less hurdles for clinical implementation.

   Spatiotemporal fractionation (STF) schemes aim at partial hypofractionation in the metastases along with more uniform fractionation in the healthy brain. This is achieved by delivering distinct dose distributions in different fractions, which are designed based on their cumulative biologically effective dose () such that each fraction contributes with high doses to complementary parts of the target volume, while similar dose baths are delivered to the normal tissue. For patients with multiple brain metastases, a novel constrained approach to spatiotemporal fractionation (cSTF) is proposed, which is more robust against setup and biological uncertainties. The approach aims at irradiating entire metastases with possibly different doses, but spatially similar dose distributions in every fraction, where the optimal dose contribution of every fraction to each metastasis is determined using a new planning objective to be added to the BED‐based treatment plan optimization problem. The benefits of spatiotemporal fractionation schemes are evaluated for three patients, each with >25 BMs.

   For the same tumor BED₁₀and the same brain volume exposed to high doses in all plans, the mean brain BED₂can be reduced compared to uniformly fractionated plans by 9%–12% with the cSTF plans and by 13%–19% with the STF plans. In contrast to the STF plans, the cSTF plans avoid partial irradiation of the individual metastases and are less sensitive to misalignments of the fractional dose distributions when setup errors occur.

   Spatiotemporal fractionation schemes represent an approach to lower the biological dose to the healthy brain in SRS‐based treatments of multiple BMs. Although cSTF cannot achieve the full BED reduction of STF, it improves on uniform fractionation and is more robust against both setup errors and biological uncertainties related to partial tumor irradiation.

    

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2. A novel stochastic optimization method for handling misalignments of proton and photon doses in combined treatments

   https://doi.org/10.1088/1361-6560/ac858f  

   Fabiano, Silvia ; Torelli, Nathan ; Papp, Dávid ; Unkelbach, Jan ( September 2022 , Physics in Medicine & Biology)

   Objective.Combined proton–photon treatments, where most fractions are delivered with photons and only a few are delivered with protons, may represent a practical approach to optimally use limited proton resources. It has been shown that, when organs at risk (OARs) are located within or near the tumor, the optimal multi-modality treatment uses protons to hypofractionate parts of the target volume and photons to achieve near-uniform fractionation in dose-limiting healthy tissues, thus exploiting the fractionation effect. These plans may be sensitive to range and setup errors, especially misalignments between proton and photon doses. Thus, we developed a novel stochastic optimization method to directly incorporate these uncertainties into the biologically effective dose (BED)-based simultaneous optimization of proton and photon plans.Approach.The method considers the expected value$E\left(b\right)$and standard deviation$\sigma \left(b\right)$of the cumulative BED$b$in every voxel of a structure. For the target, a piecewise quadratic penalty function of the form${\left[b^{\min }-\left(E\left(b\right)-2\sigma \left(b\right)\right)\right]}_{+}^2$is minimized, aiming for plans in which the expected BED minus two times the standard deviation exceeds the prescribed BED$b^{\min }.$Analogously,${\left[\left(E\left(b\right)+2\sigma \left(b\right)\right)-b^{\max }\right]}_{+}^2$is considered for OARs.Main results.Using a spinal metastasis case and a liver cancer patient, it is demonstrated that the novel stochastic optimization method yields robust combined treatment plans. Tumor coverage and a good sparing of the main OARs are maintained despite range and setup errors, and especially misalignments between proton and photon doses. This is achieved without explicitly considering all combinations of proton and photon error scenarios.Significance.Concerns about range and setup errors for safe clinical implementation of optimized proton–photon radiotherapy can be addressed through an appropriate stochastic planning method.

    

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3. Dose kernel decomposition for spot‐based radiotherapy treatment planning

   https://doi.org/10.1002/mp.15415  

   Chen, Mingli ; Yang, Zi ; Wardak, Zabi ; Stojadinovic, Strahinja ; Gu, Xuejun ; Lu, Weiguo ( December 2021 , Medical Physics)

   Pre‐calculation of accurate dose deposition kernels for treatment planning of spot‐based radiotherapies, such as Gamma Knife (GK) and Gamma Pod (GP), can be very time‐consuming and may require large data storage with an enormous number of possible spots. We proposed a novel kernel decomposition (KD) model to address accurate and fast (real‐time) dose calculation with reduced data storage requirements for spot‐based treatment planning. The application of the KD model was demonstrated for clinical GK and GP radiotherapy platforms.

   The dose deposition kernel at each spot (shot position) is modeled as the product of a shift‐invariant kernel based on a reference kernel and spatially variant scale factor. The reference kernel, one for each collimator, is defined at the center of the commissioning phantom for GK and at the center of the treatment target for GP and calculated using the Monte Carlo (MC) method. The spatially variant scale factor is defined as the ratio of the mean tissue maximum ratio (TMR) at the candidate shot position to that at the reference kernel position, and the mean TMR map is calculated within the entire volume through parallel beam ray tracing on the density image followed by averaging over all source directions. The proposed KD dose calculations were compared with the MC method and with the GK and GP treatment planning system (TPS) computations for various shot positions and collimator sizes utilizing a phantom and 14 and 12 clinical plans for GK and GP, respectively.

   For the phantom study, the KD Gamma index (3%/1 mm) passing rates were greater than 99% (median 100%) relative to the MC doses, except for the shots close to the boundary. The passing rates dropped below 90% for 8 mm (16 mm) shots positioned within ∼1 cm (∼2 cm) of the boundary. For the clinical GK plans, the KD Gamma passing rates were greater than 99% (median 100%) compared to the MC and greater than 92% (median 99%) compared to the TPS. For the clinical GP plans, the KD Gamma passing rates were greater than 95% (median 98%) compared to the MC and greater than 91% (median 97%) compared to the TPS. The scale factors were calculated in sub‐seconds with GPU implementation and only need to be calculated once before treatment plan optimization. The calculation of the dose kernel was also within sub‐seconds without requiring beam‐by‐beam calculation commonly done in the TPS.

   The proposed model can provide an accurate dose and enables real‐time dose and derivative calculations by kernel shifting and scaling without pre‐calculating or requiring large data storage for GK and GP dose deposition kernels during treatment planning. This model could be useful for spot‐based radiotherapy treatment planning by allowing an efficient global fine search for optimal spots.

    

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4. Algorithm-hardware co-optimization of the memristor-based framework for solving SOCP and homogeneous QCQP problems

   https://doi.org/10.1109/ASPDAC.2017.7858420  

   Ren, Ao ; Liu, Sijia ; Cai, Ruizhe ; Wen, Wujie ; Varshney, Pramod K. ; Wang, Yanzhi ( January 2017 , 2017 22nd Asia and South Pacific Design Automation Conference (ASP-DAC))

   A memristor crossbar, which is constructed with memristor devices, has the unique ability to change and memorize the state of each of its memristor elements. It also has other highly desirable features such as high density, low power operation and excellent scalability. Hence the memristor crossbar technology can potentially be utilized for developing low-complexity and high-scalability solution frameworks for solving a large class of convex optimization problems, which involve extensive matrix operations and have critical applications in multiple disciplines. This paper, as the first attempt towards this direction, proposes a novel memristor crossbar-based framework for solving two important convex optimization problems, i.e., second-order cone programming (SOCP) and homogeneous quadratically constrained quadratic programming (QCQP) problems. In this paper, the alternating direction method of multipliers (ADMM) is adopted. It splits the SOCP and homogeneous QCQP problems into sub-problems that involve the solution of linear systems, which could be effectively solved using the memristor crossbar in O(1) time complexity. The proposed algorithm is an iterative procedure that iterates a constant number of times. Therefore, algorithms to solve SOCP and homogeneous QCQP problems have pseudo-O(N) complexity, which is a significant reduction compared to the state-of-the-art software solvers (O(N3.5)-O(N4)). 

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5. Objective Selection for Cancer Treatment: An Inverse Optimization Approach

   https://doi.org/10.1287/opre.2021.2192  

   Ajayi, Temitayo ; Lee, Taewoo ; Schaefer, Andrew J. ( May 2022 , Operations Research)

   In radiation therapy treatment plan optimization, selecting a set of clinical objectives that are tractable and parsimonious yet effective is a challenging task. In clinical practice, this is typically done by trial and error based on the treatment planner’s subjective assessment, which often makes the planning process inefficient and inconsistent. We develop the objective selection problem that infers a sparse set of objectives for prostate cancer treatment planning based on historical treatment data. We formulate the problem as a nonconvex bilevel mixed-integer program using inverse optimization and highlight its connection with feature selection to propose multiple solution approaches, including greedy heuristics and regularized problems and application-specific methods that use anatomical information of the patients. Our results show that the proposed heuristics find objectives that are near optimal. Via curve analysis on dose-volume histograms, we show that the learned objectives closely represent latent clinical preferences. 

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