A mathematical deconvolution formulation for superficial dose distribution measurement by Cerenkov light dosimetry

Estimation of diffuse Cherenkov optical emission from external beam radiation build-up in tissue

SIGNIFICANCE

Optical imaging of Cherenkov emission during radiation therapy could be used to verify dose delivery in real-time if a more comprehensive quantitative understanding of the factors affecting emission intensity could be developed.

AIM

This study aims to explore the change in diffuse Cherenkov emission intensity with x-ray beam energy from irradiated tissue, both theoretically and experimentally.

APPROACH

Derivation of the emitted Cherenkov signal was achieved using diffusion theory, and experimental studies with 6 to 18 MV energy x-rays were performed in tissue phantoms to confirm the model predictions as related to the radiation build-up factor with depth into tissue.

RESULTS

Irradiation at lower x-ray energies results in a greater surface dose and higher build-up slope, which results in a ∼46  %   greater diffusely emitted Cherenkov signal per unit dose at 6 MV relative to 18 MV x-rays. However, this phenomenon competes with a decrease in signal from less Cherenkov photons being generated at lower energies, a ∼44  %   reduction at 6 versus 18 MV. The result is an emitted Cherenkov signal that is nearly constant with beam energy.

CONCLUSIONS

This study explains why the observed Cherenkov emission from tissue is not a strong function of beam energy, despite the known strong correlation between Cherenkov intensity and particle energy in the absence of build-up and scattering effects.

Analysis of corrected Cerenkov emission during electron radiotherapy by Monte Carlo method

Cerenkov emission during electron radiotherapy had been emerging as a new dose assessment approach for clinical radiotherapy and could be imaged through a standard commercial camera. The purpose of this work aimed to study the accuracy of corrected Cerenkov emission method during electron radiotherapy by Monte Carlo (MC) method. GAMOS MC software was used to model the physics of electron therapy and calculated dose and Cerenkov photon distribution in water phantom. Compared to ionization chamber and diode measurement, MC simulated dose discrepancy was less than 1% in percentage depth dose (PDD) curves and less than. 2% in crossline profile curves, which was acceptable for clinical criterion. Compared to ionization chamber dose measurement, MC simulated Cerenkov discrepancy was less than 2% in crossline profile distribution, which was acceptable for clinical criterion. However, the Cerenkov PDD curves tended to overestimate the dose at the build-up region and underestimate the dose at the remaining attenuation region. After increasing the Cerenkov distribution depth to 2-3 mm, the discrepancy became well within 1% at the remaining attenuation region, which was acceptable for clinical criterion. Therefore, corrected Cerenkov emission could be used to assess PDD accuracy and crossline profile accuracy during electron radiotherapy.

Review of in vivo optical molecular imaging and sensing from x-ray excitation

SIGNIFICANCE

Deep-tissue penetration by x-rays to induce optical responses of specific molecular reporters is a new way to sense and image features of tissue function in vivo. Advances in this field are emerging, as biocompatible probes are invented along with innovations in how to optimally utilize x-ray sources.

AIM

A comprehensive review is provided of the many tools and techniques developed for x-ray-induced optical molecular sensing, covering topics ranging from foundations of x-ray fluorescence imaging and x-ray tomography to the adaptation of these methods for sensing and imaging in vivo.

APPROACH

The ways in which x-rays can interact with molecules and lead to their optical luminescence are reviewed, including temporal methods based on gated acquisition and multipoint scanning for improved lateral or axial resolution.

RESULTS

While some known probes can generate light upon x-ray scintillation, there has been an emergent recognition that excitation of molecular probes by x-ray-induced Cherenkov light is also possible. Emission of Cherenkov radiation requires a threshold energy of x-rays in the high kV or MV range, but has the advantage of being able to excite a broad range of optical molecular probes. In comparison, most scintillating agents are more readily activated by lower keV x-ray energies but are composed of crystalline inorganic constituents, although some organic biocompatible agents have been designed as well. Methods to create high-resolution structured x-ray-optical images are now available, based upon unique scanning approaches and/or a priori knowledge of the scanned x-ray beam geometry. Further improvements in spatial resolution can be achieved by careful system design and algorithm optimization. Current applications of these hybrid x-ray-optical approaches include imaging of tissue oxygenation and pH as well as of certain fluorescent proteins.

CONCLUSIONS

Discovery of x-ray-excited reporters combined with optimized x-ray scan sequences can improve imaging resolution and sensitivity.

Technical note: Generation of a Cerenkov scatter function convolution kernel for a primary proton beam

Purpose

To generate a Cerenkov scatter function (CSF) for a primary proton beam and to study the dependence of the CSF on the irradiated medium.

Materials and Methods

The MCNP 6.2 code was used to generate the CSF. The CSF was calculated for light‐pigmented, medium‐pigmented, and dark‐pigmented stratified skin, as well as for a homogeneous optical phantom, which mimics the optical properties of human tissue. CSFs were generated by binning all of the Cerenkov photons which escape the back end (end opposite beam incidence) of a 20 × 20 × 20 cm phantom. A 4 × 4 cm, 500 × 500 bin grid was used to create a histogram of the Cerenkov photon flux on the simulated medium’s back surface (surface opposite beam incidence). A triple Gaussian was then used to fit the data.

Results

From the triple Gaussian fit, the coefficients of the CSF for the four phantom materials was generated. The individual CSF fit coefficient errors, with respect to the Gaussian representation, were found to be between 0.92% and 4.11%. The R² value for the fit was calculated to be 0.99. The phantom material was found to have a significant effect (63% difference between materials) on the CSF amplitude and full width at half maximum (195% difference between materials). The difference in these parameters for the three skin pigments was found to be small.

Conclusions

The CSF was obtained for a proton beam using the MCNP 6.2 code for a phantom constructed of light, medium, and dark stratified human skin, as well as for an optical phantom. The CSFs were then fit with a triple‐Gaussian function. The coefficients can be used to generate a radially symmetric CSF, which can then be used to deconvolve a measured Cerenkov image to obtain the dose distribution.

Theoretical lateral and axial sensitivity limits and choices of molecular reporters for Cherenkov-excited luminescence in tissue during x-ray beam scanning

PURPOSE

Unlike fluorescence imaging utilizing an external excitation source, Cherenkov emissions and Cherenkov-excited luminescence occur within a medium when irradiated with high-energy x-rays. Methods to improve the understanding of the lateral spread and axial depth distribution of these emissions are needed as an initial step to improve the overall system resolution.

METHODS

Monte Carlo simulations were developed to investigate the lateral spread of thin sheets of high-energy sources and compared to experimental measurements of similar sources in water. Additional simulations of a multilayer skin model were used to investigate the limits of detection using both 6- and 18-MV x-ray sources with fluorescence excitation for inclusion depths up to 1 cm.

RESULTS

Simulations comparing the lateral spread of high-energy sources show approximately 100  ×   higher optical yield from electrons than photons, although electrons showed a larger penumbra in both the simulations and experimental measurements. Cherenkov excitation has a roughly inverse wavelength squared dependence in intensity but is largely redshifted in excitation through any distance of tissue. The calculated emission spectra in tissue were convolved with a database of luminescent compounds to produce a computational ranking of potential Cherenkov-excited luminescence molecular contrast agents.

CONCLUSIONS

Models of thin x-ray and electron sources were compared with experimental measurements, showing similar trends in energy and source type. Surface detection of Cherenkov-excited luminescence appears to be limited by the mean free path of the luminescence emission, where for the given simulation only 2% of the inclusion emissions reached the surface from a depth of 7 mm in a multilayer tissue model.

Cherenkov imaging for total skin electron therapy (TSET)

BACKGROUND

Total skin electron therapy (TSET) utilizes high-energy electrons to treat malignancies on the entire body surface. The otherwise invisible radiation beam can be observed via the optical Cherenkov photons emitted from interactions between the high-energy electron beam and tissue.

METHODS AND MATERIALS

With a time-gated intensified camera system, the Cherenkov emission can be used to evaluate the dose uniformity on the surface of the patient in real time. Fifteen patients undergoing TSET in various conditions (whole body and half body) were imaged and analyzed. Each patient was monitored during TSET via in vivo detectors (IVD) in nine locations. For accurate Cherenkov imaging, a comparison between IVD and Cherenkov profiles was conducted using a polyvinyl chloride board to establish the perspective corrections.

RESULTS AND DISCUSSION

With proper corrections developed in this study including the perspective and inverse square corrections, the Cherenkov imaging provided two-dimensional maps proportional to dose and projected on patient skin. The results of ratio between chest and umbilicus points were in good agreement with in vivo point dose measurements, with a standard deviation of 2.4% compared to OSLD measurements.

CONCLUSIONS

Cherenkov imaging is a viable tool for validating patient-specific dose distributions during TSET.

Space-variant deconvolution of Cerenkov light images acquired from a curved surface

PURPOSE

Cerenkov photons are generated by high-energy radiation used in external beam radiation therapy (EBRT). This study expands upon the Cerenkov light dosimetry formula previously developed to relate an image of Cerenkov photons to the primary beam fluence. Extension of this formulation allows for deconvolution to be performed on images acquired from curved geometries.

METHODS

The integral equation, which represented the formation of Cerenkov photon image from an incident high-energy photon beam, was expanded to allow for space-variance of the convolution kernel called as the Cerenkov scatter function (CSF). The GAMOS (Geant4-based Architecture for Medicine-Oriented Simulations) Monte Carlo (MC) particle simulation software was used to obtain the CSF for different incident beam angles. The image of a curved surface was first projected to a flat plane by using a perspective correction method. Then, the planar image was partitioned into small segments (or blocks), where a CSF corresponding to a specific beam incident angle was applied for deconvolution. The block size and the margin around the block were optimized by studying the effects of those parameters on the deconvolution accuracy for a test image. We evaluated three deconvolution techniques: Richardson-Lucy, Blind, and Total Variation minimization (TV/L2) algorithms, to select the most accurate method for the current applications.

RESULTS

Analysis of deconvolution algorithms showed that the TV/L2 method provided the most accurate solution to the deconvolution problem for Cerenkov imaging. Optimization of space-variant deconvolution parameters showed that including a margin that is at least 42.9% of the image width provided the most accurate product image. There was no optimal size for the deconvolution area and should be chosen based on the presence of unique CSF kernels within an image. Space-variant deconvolution improved measured field size in Cerenkov photon images by 7.37%, as compared with 1.74% by space-invariant deconvolution. Space-variant deconvolution improved measured penumbra by 99.3%, as compared with 76.7% by space-invariant deconvolution. Space-variant deconvolution introduced artifacts in flat regions of the beam. Artifacts were avoided through selective space-variant deconvolution in only the penumbra region.

CONCLUSIONS

Primary photon fluence distributions of a curved surface can be obtained by using space-variant deconvolution methods in Cerenkov light dosimetry. The TV/L2 algorithm is the best method for deconvolution of Cerenkov photon images from an open-field beam derived from either a flat or curved surface. The partition size chosen for space-variant deconvolution should be at least six times the full width at half maximum (FWHM) of the corresponding scatter kernel used in deconvolution. Space-variant deconvolution is necessary if the incident beam angle difference is larger than 6 ∘ between regions of an image.