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Supporting Information

Optical imaging as an expansion of nuclear medicine:Cerenkov-based luminescence vs. fluorescence-based luminescence.

Patrick T. K. Chin,1 Mick M. Welling,1 Stefan C. J. Meskers,2 Renato A. Valdes Olmos,1,3 Hans Tanke,4 Fijs W. B. van Leeuwen1*

  1. Interventional Molecular Imaging Laboratory, Department of Radiology, Leiden University Medical Center, P.O.Box 9600, 2300 RC Leiden, the Netherlands
  2. Molecular Materials and Nanosystems, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
  3. Department of Nuclear Medicine, Netherlands Cancer Institute-Antoni van Leeuwenhoek Hospital, Plesmanlaan 121, 1066 CX Amsterdam, The Netherlands
  4. Department of Molecular Cell Biology, Leiden University Medical Center, P.O.Box 9600, 2300 RC Leiden, the Netherlands

* corresponding author:

S1. A quantitative comparison between CLI and fluorescence

S1.1 Cerenkov emission based luminescence

The number of Cerenkov photons emitted depends on the velocity and therefore the energy of the traveling -particle and the refractive index (n) of the medium, which is expressed by the Frank-Tamm formula.[1],[2]

(1)

Where d2N is the increment in the number of produced photons per the infinitesimal distance (dx) travelled by the emitted particle and per infinitesimal wavelength interval (d).  is the fine-structure constant (≈1/137). The number of photons produced in a certain wavelength interval from 1 to 2 is obtained from the integral .

Mitchell et al.1 predicted that a single 18F isotope (positron end point energy; (633 keV) will produce 1.4 Cerenkov photons per β-decay in water. Assuming - for simplicity - that a single 18F isotope decays within its half life (1/2) it then corresponds to a photon flux of 1.4/(109.7 min·60 s)= 2.1·10-4photons·s-1 per 18F isotope (1/2=109.7 min.).[3]

As stated in the article the Cerenkov emission intensity is also dependent on the half-life of the isotopes. The signal intensity suffers from a logarithmic decrease over time, which is identical to the common formula for radioactive decay.

(2)

Herein A(t) the amount of activity at time (t), and A0 the initial activity at t=0.For example; the prediction by Liu et al. that during surgery on a 70 kg patient 2.1 GBq of 18F-FDG would be required, suggests that when the tracer is administered 4 hours prior surgery to an initial dose 18F-FDG of ≈ 9.7 GBq would be required.

S1.2 Fluorescence-based luminescence

The total expected photon flux (Ie) from a singleICG molecule is calculated using the excitationintensity (I0):

(3)

With P the “realistic clinical” excitation power of 1 mW/cm2, h Planck constant, c (m/s) the speed of light in vacuum,  the excitation wavelength (780 nm), This results in an excitation intensity(I0)of 3.92·1015 photons·s-1·cm-2.By multiplying the excitation intensity (I0) with the optical cross section of a molecule, therate constantof absorption (ka) for a single ICG moleculecan be calculated.

(4)

The optical cross section () can be calculated from the extinction coefficient, a measure for the absorption of excitation light (for ICG: = 1.1379105 L·mol-1·cm-1;at 780 nm)[4]using the following formula with Avogadro number (Na= 6.022∙1023 molecules/mol).

(5)

Resulting in optical cross-section () of 4.35·10-16 cm2/molecule. Formula 4 and 5 combined this resultin a rate constant for absorption (ka) of 1.7052 s-1.The rate constant (kf) for relaxation, meaning the depopulation rate of the excited singlet state to the ground is related to the fluorescence lifetime(1/2). For ICG this1/2 = 0.97 ns.[5]

(6)

This calculation yields a rate constant (kf) of 1.03·109 s-1.From both rate constants (ka and kf) one can determine the fraction of molecules in the excited state (x) using:

(7)

This shows that at a 1 mW/cm2 excitation intensity, only a very small fraction of the molecules is in the excited state, namely x = 1.66·10-7 %.As stated in the article an increase of the excitation power(P) will result in an increase of ka, which will increase the outcome of this calculation.

When all these factors are combined with the fluorescence quantum yield a measure for the conversion of excitation light into a luminescence (f; for ICG = 0.027)[6]using the formula below (8), this corresponds to an expected average photon flux per ICG molecule ofIe=4.6·10-2 photons·s-1.

(8)

In the calculation we have neglected the tissue attenuation by scattering but thisfactorisdiscussed below.

S2Influence of scattering

Above we calculated the photon flux of both of a single 18F Cerenkov isotope and a single ICG molecule, but we did not compensate forattenuation due to wavelength dependent tissue scattering.[7]Scattering reduces the detectible emission intensity following an exponential dependence along its path length in the direction (z), resulting in a by scattering reduced emission intensity (Iz)following:

(9)

The reduced scattering coefficient ('s) is wavelength dependent following i) -0.37 for “larger” sized scattering objects like cells and organelles and ii) -4 (often referred to as Rayleigh scattering) for the “small” scattering objects like proteins.7 Between human and animal soft tissue are similar trends for 's observed.[8],[9],[10]

To exemplify this effect we have determined the reduction of the detectible photon flux through 1 mm (z) of tissue using the wavelength dependent 'sobtained from a mouse tumor model.10With 's ≈ 1.5mm-1(= 350 nm)10 for the 18F CL and 's ≈ 0.5mm-1(=800 nm)10 for ICG, the reduced signal intensities are: Iz 18F= 4.7·10-5photons·s-1·cm-2 per isotope and Iz ICG= 2.7·10-2photons·s-1·cm-2 per molecule. A comparison of expected photon fluxes of two typical Cerenkov isotopes and 3 clinical fluorophores is shown in table 1 (main text).

References

[1]Mitchell GS, Gill RK, Boucher DL, Li C, Cherry SR: In vivo Cerenkov luminescence imaging: a new tool for molecular imaging. Phil Trans A Math Phys Eng Sci 2011, 369: 4605-4619

[2]Frank IM, Tamm IE: Coherent visible radiation of fast electrons passing through

matter, Dokl. Akad. Nauk SSSR 1937, 14: 109-114

[3]Pfennig G, Klewe-Nebenius H, Seelmann-Eggebert W: Karlsruher Nuklidkarte, Haberbeck Gmbh, Germany 1998, 6 th edn.

[4]Landsman MLJ, Kwant G, Mook GA, Zijlstra WG: Light-absorbing properties, stability, and spectral stabilization of indocyanine green J Appl Physiol 1976, 40: 575-583

[5]Berezin MY, Achilefu S: Fluorescence lifetime measurements and biological imaging Chem Rev 2010, 110: 2641-2684

[6]Russin TJ, Altinoglu EI, Eklund PC: Measuring the fluorescent quantum efficiency of indocyanine green encapsulated in nanocomposite particulates. J Phys: Condens Matter 2010, 22: 334217

[7]Mourant JR, Fuselier T, Boyer J, Johnson TM, Bigio IJ: Predictions and measurements of scattering and absorption over broad wavelength ranges in tissue phantoms. Appl Optics 1997, 36: 949-957

[8]Marquez G, Wang LV, Lin S-P, Schwartz JA, Thomsen SL: Anisotropy in the absorption and scattering spectra of chicken breast tissue Appl Optics 1998, 37: 798-804

[9]Tuchin VV: Light scattering study of tissues. Phys Usp 1997, 40: 495-514

[10]Honda N, Ishii K, Terada T, Nanjo T, Awazu K: Determination of the tumor tissue optical properties and after photodynamic therapy using inverse Monte Carlo method and double integrating sphere between 350 and 1000 nm J BioMed Opt 2011,16: 058003-1-7