Quantitative modeling of Cerenkov light production efficiency from medical radionuclides

Abstract

There has been recent and growing interest in applying Cerenkov radiation (CR) for biological applications. Knowledge of the production efficiency and other characteristics of the CR produced by various radionuclides would help in accessing the feasibility of proposed applications and guide the choice of radionuclides. To generate this information we developed models of CR production efficiency based on the Frank-Tamm equation and models of CR distribution based on Monte-Carlo simulations of photon and β particle transport. All models were validated against direct measurements using multiple radionuclides and then applied to a number of radionuclides commonly used in biomedical applications. We show that two radionuclides, Ac-225 and In-111, which have been reported to produce CR in water, do not in fact produce CR directly. We also propose a simple means of using this information to calibrate high sensitivity luminescence imaging systems and show evidence suggesting that this calibration may be more accurate than methods in routine current use.

Figure 1. Evaluation and Correction of Luminescence Imaging System for CR.

A) The CR efficiency measured as a function of one over the photon wavelength squared using calibrations provided by the manufacturer. These plots should be linear. B) Test of the linearity of the photon flux measurements. C) The diagram depicts the lens of the luminescence imager (gray ellipse) and defines the parameters used in expression (4). Plot on right shows the measured camera sensitivity as a function of the height of the imaged object (dark circles) along with a fit of expression (3) to determine the value for parameter H (which was otherwise difficult to measure directly). D) Same data as in (A) but now after calibrations based on our model and the spectral measurements for Ga-68. All measured spectral data are now very close to linear.

Figure 2. CR Efficiency Contributions From Three Sources; Modeled and Experimental Readings.

A) The experimental setup is shown for a representative acquisition. The radionuclide was diluted in a defined medium and CR efficiency was measured and the background is subsequently subtracted. B) CR efficiency contributions from three sources, β-particles, conversion electrons and secondary electrons, as determined by our models along with comparisons to measured efficiencies. C) Contributions to CR production by Ac-225 and its daughters in deionized water as predicted by our model. D) Modeled and measured CR production efficiency for In-111 plus an assumed 0.05% impurity of In-114. All efficiencies shown are for the production of photons having wavelengths between 650 and 670 nanometers. The results are from experiments using deionized water and a 25% by weight sodium chloride and water solution (“salt”). Note - Ac-225+ denotes Ac-225 plus its daughters in transient equilibrium.

Figure 3. CR from β's Point Spread Functions.

A) Simulated β⁺ tracks (blue) from an F-18 point source. Red tracks are from δ particles. B) A representative acquisition of the PSF experimental setup. This shows the channel in the acrylic block filled with a mixture of activity, surfactant and India ink. C) Integrated F-18 and D) Ga-68 measured radiance profiles shown as diamonds. Solid lines are modeled shapes with fitted amplitudes assuming β-particle source of CR.

Figure 4. Volume Dependence of CR Production.

A) Projected point spread function for F-18 drop placed on acrylic plastic. Measured radiance shown as diamonds. Solid line is modeled shape with fitted amplitude assuming secondary electron source of CR. B) CR efficiency of Zr-89 as a function of the dimensions of the deionized water medium. Measured values made using the 560 nanometer bandpass filter are shown as diamonds. Solid line is the modeled efficiency.

Figure 5. Modeled Cerenkov production efficiencies as a function of refractive index.

Curves are the modeled efficiencies for β-particle produced CR as a function of refractive index assuming β cross-section properties and density of water. Efficiencies are in photons within the 550 to 570 nm range per disintegration. The X's used the β cross section properties of biological tissue. (A) and (B) list different radionuclides. Note - Ac-225+ denotes Ac-225 plus its daughters in transient equilibrium.