There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

We describe the development of multifunctional nanoparticle probes based on semiconductor quantum dots (QDs) for cancer targeting and imaging in living animals. The structural design involves encapsulating luminescent QDs with an ABC triblock copolymer and linking this amphiphilic polymer to tumor-targeting ligands and drug-delivery functionalities. In vivo targeting studies of human prostate cancer growing in nude mice indicate that the QD probes accumulate at tumors both by the enhanced permeability and retention of tumor sites and by antibody binding to cancer-specific cell surface biomarkers. Using both subcutaneous injection of QD-tagged cancer cells and systemic injection of multifunctional QD probes, we have achieved sensitive and multicolor fluorescence imaging of cancer cells under in vivo conditions. We have also integrated a whole-body macro-illumination system with wavelength-resolved spectral imaging for efficient background removal and precise delineation of weak spectral signatures. These results raise new possibilities for ultrasensitive and multiplexed imaging of molecular targets in vivo.

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In vivo cancer targeting and imaging with semiconductor quantum dots

A review of reported tissue optical properties summarizes the wavelength-dependent behavior of scattering and absorption. Formulae are presented for generating the optical properties of a generic tissue with variable amounts of absorbing chromophores (blood, water, melanin, fat, yellow pigments) and a variable balance between small-scale scatterers and large-scale scatterers in the ultrastructures of cells and tissues.

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Optical properties of biological tissues: a review.

A Monte Carlo model of steady-state light transport in multi-layered tissues (MCML) has been coded in ANSI Standard C; therefore, the program can be used on various computers. Dynamic data allocation is used for MCML, hence the number of tissue layers and grid elements of the grid system can be varied by users at run time. The coordinates of the simulated data for each grid element in the radial and angular directions are optimized. Some of the MCML computational results have been verified with those of other theories or other investigators. The program, including the source code, has been in the public domain since 1992.

MCML-Monte Carlo modeling of light transport in multi-layered tissues

The known optical properties (absorption, scattering, total attenuation, effective attenuation, and/or anisotropy coefficients) of various biological tissues at a variety of wavelengths are reviewed. The theoretical foundations for most experimental approaches are outlined. Relations between Kubelka-Munk parameters and transport coefficients are listed. The optical properties of aorta, liver, and muscle at 633 nm are discussed in detail. An extensive bibliography is provided. >

A review of the optical properties of biological tissues

The absorption, scattering, and anisotropy coefficients of the fat emulsion lntralipid-10% have been measured at 457.9, 514.5, 632.8, and 1064 nm. The size and shape distributions of the scattering particles in lntralipid-10% were determined by transmission electron microscopy. Mie theory calculations performed by using the particle size distribution yielded values for the scattering and anisotropy coefficients from 400 to 1100 nm. The agreement with experimental values is better than 6%.

Light scattering in Intralipid-10% in the wavelength range of 400-1100 nm.

A method is described for finding the optical properties (scattering, absorption, and scattering anisotropy) of a slab of turbid material by using total reflection, unscattered transmission, and total transmission measurements. This method is applicable to homogeneous turbid slabs with any optical thickness, albedo, or phase function. The slab may have a different index of refraction from its surroundings and may or may not be bounded by glass. The optical properties are obtained by iterating an adding–doubling solution of the radiative transport equation until the calculated values of the reflection and transmission match the measured ones. Exhaustive numerical tests show that the intrinsic error in the method is <3% when four quadrature points are used.

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Determining the optical properties of turbid media by using the adding–doubling method

The Monte Carlo method is rapidly becoming the model of choice for simulating light transport in tissue. This paper provides all the details necessary for implementation of a Monte Carlo program. Variance reduction schemes that improve the eciency of the Monte Carlo method are discussed. Analytic expressions facilitating convolution calculations for finite flat and Gaussian beams are included. Useful validation benchmarks are presented.

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A Monte Carlo model of light propagation in tissue

A system is described and evaluated for the simultaneous measurement of the intrinsic optical properties of tissue: the scattering coefficient, the absorption coefficient, and the anisotropy factor. This system synthesizes the theory of two integrating spheres and an intervening scattering sample with the inverse adding–doubling algorithm, which employs the adding–doubling solution of the radiative transfer equation to determine the optical properties from the measurement of the light flux within each sphere and of the unscattered transmission. The optical properties may be determined simultaneously, which allows for measurements to be made while the sample undergoes heating, chemical change, or some other external stimulus. An experimental validation of the system with tissue phantoms resulted in the determination of the optical properties with a <5% deviation when the optical density was between 1 and 10 and the albedo was between 0.4 and 0.95.

Scott A. Prahl

Papers

A review of the optical properties of biological tissues

Light scattering in Intralipid-10% in the wavelength range of 400-1100 nm.

Determining the optical properties of turbid media by using the adding–doubling method

A Monte Carlo model of light propagation in tissue

Double-integrating-sphere system for measuring the optical properties of tissue