We consider the problem of designing a feedback controller for a multivariable linear time-invariant system, which regulates a system output to the solution of an equality-constrained convex optimization problem despite unknown constant exogenous disturbances; we term this the linear-convex optimal steady-state (OSS) control problem. We introduce the notion of an optimality model, and show that the existence of an optimality model is sufficient to reduce the OSS control problem to a stabilization problem. This yields a design framework for OSS control that unifies and extends existing design methods in the literature. We illustrate the approach via an application to optimal frequency control of power networks, where our methodology recovers centralized and distributed controllers reported in the recent literature.

To describe the implementation and initial results of using Chemical Exchange Saturation Transfer (CEST) for monitoring patients with central nervous system (CNS) tumours treated using a 1.5 tesla MR-guided radiotherapy system. CNS patients were treated with up to 30 fractions (total dose up to 60 Gy) using a 1.5 T Elekta Unity MR-Linac. CEST scans were obtained in 54 subjects at one or more time points during treatment. CEST metrics, including the amide magnetization transfer ratio (MTRAmide), nuclear Overhauser effect (NOE) MTR (MTRNOE) and asymmetry, were quantified in phantoms and CNS patients. The signal was investigated between tumour and white matter, across time, and across disease categories including high- and low-grade tumours. The gross tumour volume (GTV) exhibited lower MTRAmide and MTRNOE and higher asymmetry compared to contralateral normal appearing white matter. Signal changes in the GTV during fractionated radiotherapy were observed. There were differences between high- and low-grade tumours, with higher CEST asymmetry associated with higher grade disease. CEST MRI using a 1.5 T MR-Linac was demonstrated to be feasible for in vivo imaging of CNS tumours. CEST images showed tumour/white-matter contrast, temporal CEST signal changes, and associations with tumour grade. These results show promise for the eventual goal of using metabolic imaging to inform the design of adaptive radiotherapy protocols.

Background/Objectives: Radiotherapy for tumors of the central nervous system (CNS) could be improved by incorporating advanced imaging techniques into treatment planning and response assessment. The objective of this narrative review is to highlight the recent developments in magnetic resonance imaging (MRI) and positron emission tomography (PET) for applications in CNS radiotherapy. Methods: Recent articles were selected for discussion, covering the following topics: advanced imaging on MRI-linear accelerators for early response assessment in glioma; PET for guiding treatment planning and response assessment in glioma; and contrast-enhanced imaging and metabolic imaging for differentiating tumor progression and radiation necrosis for brain metastasis treatment. Where necessary, searches of scholarly databases (e.g., Google Scholar, PubMed) were used to find papers for each topic. The topics were chosen based on the perception of promise in advancing specific applications of CNS radiotherapy and not covered in detail elsewhere. This review is not intended to be comprehensive. Results: Advanced MRI sequences and PET could have a substantial impact on CNS radiotherapy. For gliomas, the tumor response to therapy could be assessed much earlier than using the conventional technique of measuring changes in tumor size. Using advanced imaging on combined imaging/therapy devices like MR-Linacs would enable response monitoring throughout radiotherapy. For brain metastases, radiation necrosis and tumor progression might be reliably differentiated with imaging techniques sensitive to perfusion or metabolism. However, the lack of level 1 evidence supporting specific uses for each imaging technique is an impediment to widespread use. Conclusions: Advanced MRI and PET have great promise to change the standard of care for CNS radiotherapy, but clinical trials validating specific applications are needed.

Background: Direct three‐dimensional imaging of radiation beams could enable more accurate radiation dosimetry. It has been previously reported that changes in T ₁ ‐weighted magnetic resonance imaging (MRI) intensity could be observed during radiation due to radiochemical oxygen depletion. Quantitative T ₁ mapping could increase sensitivity for dosimetry applications. Purpose: We use an MRI linear accelerator (MR‐Linac) to visualize radiation delivery through the real‐time effects of dose on the spin‐lattice magnetic relaxation time ( T ₁ ) of water. We quantify the relationships between dose, spin‐lattice relaxation rates ( R ₁ ) and dissolved oxygen concentration to further investigate the mechanisms of T ₁ change. Methods: An ultrapure water phantom and a 1% agarose gel phantom were irradiated and imaged on a 1.5 T Elekta Unity MR‐Linac. Radiation plans were created using the Monaco treatment planning system. Images were acquired before, during and after radiation. A dual‐echo Look‐Locker inversion recovery pulse sequence was used for simultaneous dynamic T ₁ / B ₀ mapping. The change in R ₁ with respect to dose (∆ R ₁ /∆Dose) and the radiochemical oxygen depletion (ROD = ∆O ₂ /∆Dose) were measured. The relaxivity of oxygen ( r _1,O2 = ∆ R ₁ /∆O ₂ ) in water was also measured in a separate experiment with samples of various dissolved oxygen concentrations. The minimum measurable dose over a 20‐min period was estimated using a single‐tailed 99th quantile Student's t ‐distribution. Results: Changes to R ₁ were found to be spatiotemporally correlated to the predicted delivered radiation dose and persisted for at least 1 h after radiation. A complex dose plan could be imaged in the 1% agarose gel phantom, as the gel limits diffusion and convective mixing. In water, the ∆ R ₁ /∆Dose was found to be −1.0 × 10 ⁻⁴ s ⁻¹ /Gy, the r _1,O2 was found to be 5.4 × 10 ⁻³ s ⁻¹ /(mg/L), and the ROD was found to be −0.010 (mg/L)/Gy. Both r _1,O2 and ROD agree with published values. However, combining these two values yields a predicted ∆ R ₁ /∆Dose of −5.4 × 10 ⁻⁵ s ⁻¹ /Gy, indicating that radiochemical oxygen depletion alone under‐predicts the MRI effect. The detection limit of R ₁ was 1.1 × 10 ⁻³ s ⁻¹ which corresponded to a single‐voxel minimum detectable dose of 11.1 Gy for this specific sequence. Conclusion: Quantitative T ₁ mapping was used to image radiation dose patterns in real‐time in water and agarose gel. Radiochemical oxygen depletion only partially explains the T ₁ changes measured. Agarose gel could be used as a simple system for three‐dimensional patient‐specific quality assurance. Future applications may include in vivo dosimetry for FLASH radiotherapy, though improvements in acquisition methods and hardware are likely needed.