# A Dual Quaternion Based Method for Estimating PTV Margins in Intensity-Modulated Radiotherapy

> **NIH NIH R03** · STATE UNIVERSITY NEW YORK STONY BROOK · 2020 · $94,375

## Abstract

This project aims to produce a better definition of the target space for image guided therapy. In order to cover
the tumor as it is displaced during treatment, the clinical target must be expanded to cover the region through
which it might move. In radiation therapy, the expanded target is known as the Planning Target Volume. The
International Commission on Radiation Units and Measurements notes that available planning systems allow
only Cartesian expansions that account for the three translational components of motion. The rotational
components of displacements are neglected, producing planning target volumes that either miss the true target
motion or are larger than needed to cover the target path. As the head rotates in an arc about the long axis of
the spine,eg, the planning target volume does not follow the true path of the target that tangents the
prevertebral pharyngeal constrictors but juts into these structures to form a box that encloses the curve. The
overlap produces higher constrictor doses, a known predictor for late head and neck radiotherapy
complications including aspirations which carry mortality risk and necessitate long term feeding tube
dependence. Statistical sampling has been examined, mainly in Europe, to draw positions based on observed
shifts needed to register planning and treatment images. These methods breakdown because the non
commutativity of rotations means that positons can’t be recovered from a uniform sampling of the displacement
components. The computational burdens of a six dimensional sampling permuting the rotations is forbidding
and rotations away from the target center are neglected This proposal aims to use the projective geometry of
displacements expressed as dual quaternions to form the convex hull of the positions swept out by the target
as it shifts within its range of translations, rotational angles and rotational axes. Computational experiments
will be performed using head and neck cases, to demonstrate generation of planning target volumes within an
acceptable time frame (0.25hr). The planning target volume size, coverage, and overlap with the pharyngeal
constrictors produced by forming the convex hull of displacements generated by off axis rotations and
translations will be compared to simple Cartesian expansions. The long term goal is to reduce treatment
morbidity and improve target coverage. The reduction in morbidity, such as aspiration risk, from substituting
the new method for target volume creation for conventional simple isotropic expansion is testable in future
clinical trials.

## Key facts

- **NIH application ID:** 9968526
- **Project number:** 1R03CA249545-01
- **Recipient organization:** STATE UNIVERSITY NEW YORK STONY BROOK
- **Principal Investigator:** Qiaode Jefffrey Ge
- **Activity code:** R03 (R01, R21, SBIR, etc.)
- **Funding institute:** NIH
- **Fiscal year:** 2020
- **Award amount:** $94,375
- **Award type:** 1
- **Project period:** 2020-05-07 → 2022-04-30

## Primary source

NIH RePORTER: https://reporter.nih.gov/project-details/9968526

## Citation

> US National Institutes of Health, RePORTER application 9968526, A Dual Quaternion Based Method for Estimating PTV Margins in Intensity-Modulated Radiotherapy (1R03CA249545-01). Retrieved via AI Analytics 2026-05-27 from https://api.ai-analytics.org/grant/nih/9968526. Licensed CC0.

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