Dr.Lewei Zhao is medical physics resident in Department of Radiation Oncology, Stanford University. He graduated from Wuhan University, China, 2014 with a BS in Pure Mathematics. He got his PhD from Wayne State University, 2019 in Computational Mathematics. He was a postdoc in Beaumont Proton Therapy Center, Michigan from 2019 to 2023. During his postdoc, he took a medical physics certificate program from Wayne State University 2021-2022. His research interest is mathematical application s in medical physics.

Clinical Focus

  • Fellow
  • radiation therapy
  • Physics
  • Mathematical Computing
  • Mathematical Model

Professional Education

  • BS, School of Mathematics and Statistics, Wuhan University, Pure Mathematics (2014)
  • PhD, Department of Mathematics, Wayne State University, Applied and Computational Mathematics (2019)
  • CAMPEP Certificate, Department of Radiation Oncology, Wayne State University, Medical Physics (2022)

Research Interests

  • Data Sciences

Current Research and Scholarly Interests

Mathematical applications in medical physics

All Publications

  • A novel fast robust optimization algorithm for intensity-modulated proton therapy with minimum monitor unit constraint. Medical physics Fan, Q., Zhao, L., Li, X., Hu, J., Lu, X., Yang, Z., Zhang, S., Yang, K., Ding, X., Liu, G., Dai, S. 2024


    Intensity-modulated proton therapy (IMPT) optimizes spot intensities and position, providing better conformability. However, the successful application of IMPT is dependent upon addressing the challenges posed by range and setup uncertainties. In order to address the uncertainties in IMPT, robust optimization is essential.This study aims to develop a novel fast algorithm for robust optimization of IMPT with minimum monitor unit (MU) constraint.The study formulates a robust optimization problem and proposes a novel, fast algorithm based on the alternating direction method of multipliers (ADMM) framework. This algorithm enables distributed computation and parallel processing. Ten clinical cases were used as test scenarios to evaluate the performance of the proposed approach. The robust optimization method (RBO-NEW) was compared with plans that only consider nominal optimization using CTV (NMO-CTV) without handling uncertainties and PTV (NMO-PTV) to handle the uncertainties, as well as with conventional robust-optimized plans (RBO-CONV). Dosimetric metrics, including D95, homogeneity index, and Dmean, were used to evaluate the dose distribution quality. The area under the root-mean-square dose (RMSD)-volume histogram curves (AUC) and dose-volume histogram (DVH) bands were used to evaluate the robustness of the treatment plan. Optimization time cost was also assessed to measure computational efficiency.The results demonstrated that the RBO plans exhibited better plan quality and robustness than the NMO plans, with RBO-NEW showing superior computational efficiency and plan quality compared to RBO-CONV. Specifically, statistical analysis results indicated that RBO-NEW was able to reduce the computational time from 389.70 ± 207.40 $389.70\pm 207.40$ to 228.60 ± 123.67 $228.60\pm 123.67$ s ( p < 0.01 $p<0.01$ ) and reduce the mean organ-at-risk (OAR) dose from 9.38 ± 12.80 $9.38\pm 12.80$ % of the prescription dose to 9.07 ± 12.39 $9.07\pm 12.39$ % of the prescription dose ( p < 0.05 $p<0.05$ ) compared to RBO-CONV.This study introduces a novel fast robust optimization algorithm for IMPT treatment planning with minimum MU constraint. Such an algorithm is not only able to enhance the plan's robustness and computational efficiency without compromising OAR sparing but also able to improve treatment plan quality and reliability.

    View details for DOI 10.1002/mp.17285

    View details for PubMedID 38967477

  • The first investigation of the dosimetric perturbations from the spot position errors in spot-scanning arc therapy (SPArc). Physics in medicine and biology Liu, P., Zhao, L., Liu, G., Cong, X., Li, X., Ding, X. 2024


    To quantitatively investigate the impact of spot position error (PE) on the dose distribution in (Spot-scanning arc therapy) SPArc plans compared to Intensity-Modulated Proton Therapy (IMPT). Approach: Four representative disease sites, including brain, lung, liver, and prostate cancers, were retrospectively selected. Spot PEs were simulated during dynamic SPArc treatment delivery. Two types of errors were generated, including random error and systematic error. Two different probability distributions of random errors were used (1) Gaussian distribution (PEran-GS) (2) uniform distribution (PEran-UN). In PEran-UN, four sub-scenarios were considered: 25%, 50%, 75%, and 100% spots were randomly selected to in various directions in the scale of 0-1 mm or 0-2mm of PE. Additionally, systematic error was simulated by shifting all the spot uniformly by 1 or 2mm in various directions (PEsys). Gamma Passing Rate (GPR) is applied to assess the dosimetric perturbation. Main results: For PEran-GS in 1mm scenario, both SPArc and IMPT are comparable with a GPR exceeding 95%. However, for PEran-GS in 2mm scenario, SPArc could provide better GPR. As PEran-UN of 2mm, SPArc plans have a much better GPR compared to IMPT plans: SPArc's GPR is 99.40±0.74%, 93.66±4.75% and 61.53±10.30% for 3mm/3%, 2mm/2% and 1mm/1% criteria compared to IMPT with 98.18±2.11%, 86.12±5.58% and 39.74±7.71%. Besides, SPArc has shown its advantage in dosimetric sparing and robustness in the Organ-at-risks. For example, the brain case of 2mm PEsys, SPArc significantly reduced the dosimetric perturbation in the maximum dose to the brainstem (109cGy) and the mean dose to the left cochlea (32cGy) compared to IMPT (296cGy, 146cGy). Significance: Compared to IMPT, SPArc shows better dosimetric robustness in spot PEs. This study presents the first simulation results and the methodology that serves as a reference to guide future investigations into the accuracy and quality assurance of SPArc treatment delivery .

    View details for DOI 10.1088/1361-6560/ad5827

    View details for PubMedID 38870996

  • First direct machine-specific parameters incorporated in Spot-scanning Proton Arc (SPArc) optimization algorithm. Medical physics Liu, G., Fan, Q., Zhao, L., Liu, P., Cong, X., Yan, D., Li, X., Ding, X. 2024


    Spot-scanning Proton Arc (SPArc) has been of significant interest in recent years because of its superior plan quality. Currently, the primary focus of research and development is on deliverability and treatment efficiency.To address the challenges in generating a deliverable and efficient SPArc plan for a proton therapy system with a massive gantry, we developed a novel SPArc optimization algorithm (SPArcDMPO ) by directly incorporating the machine-specific parameters such as gantry mechanical constraints and proton delivery sequence.SPArc delivery sequence model (DSMarc ) was built based on the machine-specific parameters of the prototype arc delivery system, IBA ProteusONE®, including mechanical constraint (maximum gantry speed, acceleration, and deceleration) and proton delivery sequence (energy and spot delivery sequence, and irradiation time). SPArcDMPO resamples and adjusts each control point's delivery speed based on the DSMarc calculation through the iterative approach. In SPArcDMPO, users could set a reasonable arc delivery time during the plan optimization, which aims to minimize the gantry momentum changes and improve the delivery efficiency. Ten cases were selected to test SPArcDMPO . Two kinds of SPArc plans were generated using the same planning objective functions: (1) original SPArc plan (SPArcoriginal ); (2) SPArcDMPO plan with a user-pre-defined delivery time. Additionally, arc delivery sequence was simulated based on the DSMarc and was compared. Treatment delivery time was compared between SPArcoriginal and SPArcDMPO . Dynamic arc delivery time, the static irradiation time, and its corresponding time differential (time differential = dynamic arc delivery time-static irradiation time) were analyzed, respectively. The total gantry velocity change was accumulated throughout the treatment delivery.With a similar plan quality, objective value, number of energy layers, and spots, both SPArcoriginal and SPArcDMPO plans could be delivered continuously within the ± 1 degree tolerance window. However, compared to the SPArcoriginal , the strategy of SPArcDMPO is able to reduce the time differential from 30.55 ± 11.42%(90 ± 32 s) to 14.67 ± 6.97%(42 ± 20 s), p < 0.01. Furthermore, the corresponding total variations of gantry velocity during dynamic arc delivery are mitigated (SPArcoriginal vs. SPArcDMPO ) from 14.73 ± 9.14 degree/s to 4.28 ± 2.42 degree/s, p < 0.01. Consequently, the SPArcDMPO plans could minimize the gantry momentum change based on the clinical user's input compared to the SPArcoriginal plans, which could help relieve the mechanical challenge of accelerating or decelerating the massive proton gantry.For the first time, clinical users not only could generate a SPArc plan meeting the mechanical constraint of their proton system but also directly control the arc treatment speed and momentum changes of the gantry during the plan optimization process. This work paved the way for the routine clinical implementation of proton arc therapy in the treatment planning system.

    View details for DOI 10.1002/mp.16985

    View details for PubMedID 38340368

  • Development of a standalone delivery sequence model for proton arc therapy. Medical physics Liu, G., Zhao, L., Liu, P., Yan, D., Deraniyagala, R., Stevens, C., Li, X., Ding, X. 2023


    Spot-scanning proton arc (SPArc) has been drawing significant interests in recent years because of its capability of continuous proton irradiation during the gantry rotation. Previous studies demonstrated SPArc plans were delivered on a prototype of the DynamicARC solution, IBA ProteusONE.We built a novel delivery sequence model through an independent experimental approach: the first SPArc delivery sequence model (DSMSPArc ). Based on the model, we investigated SPArc treatment efficiency improvement in the routine proton clinical operation.SPArc test plans were generated and delivered on a prototype of the DynamicARC solution, IBA ProteusONE. An independent gantry inclinometer and the machine logfiles were used to derive the DSMSPArc. Seventeen SPArc plans were used to validate the model's accuracy independently. Two random clinical operation dates (6th January and 22nd March, 2021) from a single-room proton therapy center (PTC) were selected to quantitatively assess the improvement of treatment efficiency compared to the IMPT.The difference between the logfile and DSMSPArc is about 3.2 ± 4.8%. SPArc reduced 58.1% of the average treatment delivery time per patient compared to IMPT (p < 0.01). Daily treatment throughput could be increased by 30% using SPArc using a single-room proton therapy system.The first model of dynamic arc therapy is established in this study through an independent experimental approach using logfiles and measurements which allows clinical users and investigators to simulate the dynamic treatment delivery and assess the daily treatment throughput improvement.

    View details for DOI 10.1002/mp.16879

    View details for PubMedID 38064634

  • The first investigation of spot-scanning proton arc (SPArc) delivery time and accuracy with different delivery tolerance window settings. Physics in medicine and biology Liu, G., Zhao, L., Liu, P., Dao, R., Qian, Y., Cong, X., Janssens, G., Li, X., Ding, X. 2023; 68 (21)


    Objective. To investigate the impact of various delivery tolerance window settings on the treatment delivery time and dosimetric accuracy of spot-scanning proton arc (SPArc) therapy.Approach. SPArc plans were generated for three representative disease sites (brain, lung, and liver cancer) with an angle sampling frequency of 2.5°. An in-house dynamic arc controller was used to simulate the arc treatment delivery with various tolerance windows (±0.25, ±0.5, ±1, and ±1.25°). The controller generates virtual logfiles during the arc delivery simulation, such as gantry speed, acceleration and deceleration, spot position, and delivery sequence, similar to machine logfiles. The virtual logfile was then imported to the treatment planning system to reconstruct the delivered dose distribution and compare it to the initial SPArc nominal plan. A three-dimensional gamma index was used to quantitatively assess delivery accuracy. Total treatment delivery time and relative lost time (dynamic arc delivery time-fix beam delivery time)/fix beam delivery time) were reported.Main Results. The 3D gamma passing rate (GPR) was greater than 99% for all cases when using 3%/3 mm and 2%/2 mm criteria and the GPR (1%/1 mm criteria) degraded as the tolerance window opens. The total delivery time for dynamic arc delivery increased with the decreasing delivery tolerance window length. The average delivery time and the relative lost time (%) were 630 ± 212 s (253% ± 68%), 322 ± 101 s (81% ± 31%), 225 ± 60 s (27% ± 16%), 196 ± 41 s (11% ± 6%), 187 ± 29 s (6% ± 1%) for tolerance windows ±0.25, ±0.5, ±1, and ±1.25° respectively.Significance. The study quantitatively analyzed the dynamic SPArc delivery time and accuracy with different delivery tolerance window settings, which offer a critical reference in the future SPArc plan optimization and delivery controller design.

    View details for DOI 10.1088/1361-6560/acfec5

    View details for PubMedID 37774715

  • Introduce a rotational robust optimization framework for spot-scanning proton arc (SPArc) therapy PHYSICS IN MEDICINE AND BIOLOGY Chang, S., Liu, G., Zhao, L., Zheng, W., Yan, D., Chen, P., Li, X., Deraniyagala, R., Stevens, C., Grills, I., Chinnaiyan, P., Li, X., Ding, X. 2023; 68 (1)


    Objective. Proton dosimetric uncertainties resulting from the patient's daily setup errors in rotational directions exist even with advanced image-guided radiotherapy techniques. Thus, we developed a new rotational robust optimization SPArc algorithm (SPArcrot) to mitigate the dosimetric impact of the rotational setup error in Raystation ver. 6.02 (RaySearch Laboratory AB, Stockholm, Sweden).Approach.The initial planning CT was rotated ±5° simulating the worst-case setup error in the roll direction. The SPArcrotuses a multi-CT robust optimization framework by taking into account of such rotational setup errors. Five cases representing different disease sites were evaluated. Both SPArcoriginaland SPArcrotplans were generated using the same translational robust optimized parameters. To quantitatively investigate the mitigation effect from the rotational setup errors, all plans were recalculated using a series of pseudo-CT with rotational setup error (±1°/±2°/±3°/±5°). Dosimetric metrics such as D98% of CTV, and 3D gamma analysis were used to assess the dose distribution changes in the target and OARs.Main results.The magnitudes of dosimetric changes in the targets due to rotational setup error were significantly reduced by the SPArcrotcompared to SPArc in all cases. The uncertainties of the max dose to the OARs, such as brainstem, spinal cord and esophagus were significantly reduced using SPArcrot. The uncertainties of the mean dose to the OARs such as liver and oral cavity, parotid were comparable between the two planning techniques. The gamma passing rate (3%/3 mm) was significantly improved for CTV of all tumor sites through SPArcrot.Significance.Rotational setup error is one of the major issues which could lead to significant dose perturbations. SPArcrotplanning approach can consider such rotational error from patient setup or gantry rotation error by effectively mitigating the dose uncertainties to the target and in the adjunct series OARs.

    View details for DOI 10.1088/1361-6560/aca874

    View details for Web of Science ID 000902410500001

    View details for PubMedID 36546347

  • Bi-criteria Pareto optimization to balance irradiation time and dosimetric objectives in proton arc therapy PHYSICS IN MEDICINE AND BIOLOGY Wuyckens, S., Zhao, L., Saint-Guillain, M., Janssens, G., Sterpin, E., Souris, K., Ding, X., Lee, J. A. 2022; 67 (24)


    Objective. Proton arc therapy (PAT) is a new delivery technique that exploits the continuous rotation of the gantry to distribute the therapeutic dose over many angular windows instead of using a few static fields, as in conventional (intensity-modulated) proton therapy. Although coming along with many potential clinical and dosimetric benefits, PAT has also raised a new optimization challenge. In addition to the dosimetric goals, the beam delivery time (BDT) needs to be considered in the objective function. Considering this bi-objective formulation, the task of finding a good compromise with appropriate weighting factors can turn out to be cumbersome.Approach. We have computed Pareto-optimal plans for three disease sites: a brain, a lung, and a liver, following a method of iteratively choosing weight vectors to approximate the Pareto front with few points. Mixed-integer programming (MIP) was selected to state the bi-criteria PAT problem and to find Pareto optimal points with a suited solver.Main results. The trade-offs between plan quality and beam irradiation time (staticBDT) are investigated by inspecting three plans from the Pareto front. The latter are carefully picked to demonstrate significant differences in dose distribution and delivery time depending on their location on the frontier. The results were benchmarked against IMPT and SPArc plans showing the strength of degrees of freedom coming along with MIP optimization.Significance. This paper presents for the first time the application of bi-criteria optimization to the PAT problem, which eventually permits the planners to select the best treatment strategy according to the patient conditions and clinical resources available.

    View details for DOI 10.1088/1361-6560/aca5e9

    View details for Web of Science ID 000897929700001

    View details for PubMedID 36541505