This article is a tutorial describing an introduction to gold nanorods (GNRs) based diffusion reflection (DR) measurements (DR-GNRs) for cancer and atherosclerosis (AS) detection purposes. The DR-GNRs method is now 6 years old, and opportunities for its applications increase with time. We present a summary of the DR-GNRs method and its current status.
This tutorial is divided into three main sections: Section 2 discusses the theory of light transport within the tissue, mainly focusing on the solutions for the radiative transfer equation (RTE) that has been used in our research. Section 3 introduces the unique optical properties of gold nanoparticles (GNPs) that make it highly useful for diagnosis purposes, focusing on their absorption properties that were used in the DR method. Section 4 presents in vivo measurements performed by the DR-GNRs methods, for the detection of cancer and AS. The goal of this work is to provide an introduction to the unique use of GNRs as absorption contrast agents in DR measurements which act as a simple, noninvasive, and highly sensitive diagnostic tool.
2 Diffusion reflection–theory
Most of the optical-physiological diagnoses are based on the illumination of light, with known parameters, onto a tested tissue, followed by the measurement of the reflected or transmitted light. Changes in the optical properties of this light such as its spectrum, polarization and intensity, compared to the injected light, result due to the interactions of the irradiated light with the tissue’s components , and hence is used for diagnostic purposes. Due to the important information which can be inferred from the changes in the re-emitted or transmitted light, photon migration in the irradiated tissue was, and still is, intensively investigated , , .
The basis for the development of optical-based diagnosis methods lies in the theory of light transfer in biological tissues. The optical regime is highly desired for biomedical applications as it is a nonionizing radiation, abundantly available, and inexpensive. Several approaches have been developed in order to best describe the photon transfer in biological tissues. The main equation used for the description of the photon movement is the radiative transport equation (RTE) , :(1)
c is the speed of light, L is the radiance, P is the phase function, representing the probability of light to be scattered toward the k direction, is the source function , and μa and μs are the absorption and scattering coefficients of the tissue, respectively.
Equation (1) has two main different solving approaches, the numerical and the analytical approaches. In the numerical field, the Monte Carlo (MC) simulation is the most popular and provides accurate results that best correlate between the optical properties of the tissue and the reflected or transmitted photons . This method simulates random trajectories for the photons within the tissue, in which each photon can be randomly absorbed or scattered in different directions, and determined according to the optical properties of the tissue:(3)(4)
r n is the photon location in the tissue in the nth step, s is the step length of the photon, ε is a computational random number, and is the vector location of the photon in step n:(5)
where θ and φ are randomly determined, based on the scattering properties of the tissue.
The MC simulations usually result in the collection of the diffuse transmitted and reflected light (Td and Rd, respectively). In this article, we focus on the simulations and measurements of the light reflected from the tissue, measured at the tissue’s surface. Rd can be schematically described as shown in Figure 1, which illustrates the symmetry in the diffusion measurements, resulting in the same intensity values and shape for a given radius ρ (light source-detector separation). Therefore, it is common to describe the diffusive reflectance by circles around the light injecting point (Figure 1B). In the MC simulation, the collected Rd(ρ) is normalized by these circles area .
The MC method was, and still is, successfully applied for biomedical imaging purposes , , , , such as for brain activity , , cardiovascular investigation , , X-ray imaging , oxygen saturation measurements , etc. , . In the DR-GNRs method, the MC simulation was used to adjust between the tissue’s optical properties and the DR profile, as will be further described in this review.
The main approach studied for solving the RTE is the analytical, diffusion approach , . By this approach, the spherical harmonics ,  describe the radiance propagation in the tissue according to the following expressions:(6)
where Pn,m (cosθ) is the Legendre polynomial, given by:(7)
The spherical harmonics enables to represent a radiance, which does not depend on the spatial angles φ and θ, by the arithmetic progression:(8)
where L is the radiance penetrating the tissue.
Using this solution, one arrives at the RTE which depends only on the radial distance r and the time t:(9)
Equation (9) is called the optical diffusion equation . It has several optional solutions, depending on the given boundary conditions. In this review, we will focus on the DR-GNRs method developed in our lab, presenting boundary conditions of semi-infinite turbid medium and a continuous laser source (resulting with a time independent equation) placed on a single point on the tissue surface. Thus, the result for ∅(r) under these conditions is (using a point spread function or the Green’s function ):(12)
According to Fick’s first law, the DR from the semi-infinite scattering medium is, approximately, the current density reflected onto the surface normal, given by:(13)
Thus, by inserting Eq. (13) into Eq. (12), we get:(14)
Here, α′ is the transport albedo, z′ is equal to and ρ1 and ρ2 are the distances between the observation point (r, 0, 0) and the light source injection point (0, 0, lt′) and between the observation point and the image source point (0, 0, −lt′+4D), respectively (see in Ref. ). μs′ is the reduced scattering coefficient, as described by:(15)
Patterson et al.  have presented a slightly different result for Rd, under the condition of and an image source point at :(16)
The equation given suggests that Rd(ρ) depends on ρ2, rather than on ρ. Under restricted ranges of ρ, Farrell et al. have simplified the Rd(ρ) expression from Eq. (16) into a simple term , which enables the simple extraction of the tissue’s optical properties from the DR profile:(17)
This simplified equation highly depends on the distance from the light source, as well as on the optical aperture of the setup. C1 is a constant, depending on the optical properties of the medium and the sizes of the source and detector apertures. μ is the effective attenuation coefficient given by:(18)
2.1 Calculating the tissue’s optical properties
As mentioned earlier, the DR model enables to calculate the absorption coefficient (μa) and the reduced scattering coefficient (μs′) from Rd(ρ) of the measured tissue, as long as the power m in the diffusion equation is known. Therefore, determining the power m was the first required step in order to establish a quantitative approach for our DR measurements. The DR computerized MC simulations and experimental data analyses were performed, as described in our article written in 2012 , in order to find the model that gives the best agreement between Rd(ρ) and the measured optical properties. Results indicated that m=2, suggesting that the best correlation between the DR profile and the tissue’s optical properties is achieved when the DR profile is presented in the logarithmic form ln(ρ2R(ρ)). This result is consistent with Eq. (17) for Rd(ρ), which was developed for turbid medium presenting μa≪μs′, as simulated and measured using our DR experiments . In addition, in order to provide a mathematical base for our experiments, we have experimentally tested whether measurements were performed in the diffusive regime. The DR measurements presented in this article were performed in relatively small values of ρ (1<ρ<6 mm), and also a low value of scattering coefficient (~1.6 mm−1). Thus, the diffusive regime, which is determined by the mean free path: was ~0.6 mm, resulting in low optical path lengths and small light source-detector separations .
In the case of m=2, the reflectance profile is highly sensitive to the optical properties of the tissue and, as a result, better distinguishes between absorption coefficients that only slightly differ from each other. By inserting m=2 into Eq. (17), it can be rewritten as:(19)
Equation (19) presents a simple, linear correlation between ln(ρ2R(ρ)) and μ. The square slope of the linear curve depends on the product of the absorption and the reduced scattering coefficients of the tissue. This equation was the basis for the analyses of the DR measurements presented in this article.
3 Gold nanoparticles in the diagnostic field
Gold nanoparticles are part of the metal nanoparticles family. Once an electromagnetic field irradiates a metal nanoparticle, it generates enhanced electromagnetic field that affects its local environment. The ability to enhance the surface electric field of the metal nanoparticles, such as by their irradiation with light, enables the development of many applications. While light in resonance with the surface plasmon oscillation of a metal nanoparticle is irradiated on it, a standing oscillation is generated by the free electrons in the conduction band. These oscillations result with intense scattering light, while the scattering light intensity is extremely sensitive to the size and aggregation state of the particles . The resonance condition was found to depend also on the shape and dielectric constants of both the metal and the surrounding material , ,  which presents a basis for surrounding-sensitive diagnosis methods, such as pH sensitive , temperature dependent , or Ca+2 release indicators .
Due to their unique optical properties, the development of imaging methods based GNPs as contrast agents has gained intensive attention, resulting in an increased use of GNPs for bioimaging. Thus, for example, X-ray , computed tomography (CT) , surface-enhanced Raman scattering , photoacoustic tomography (PAT) , and photothermal imaging  have added GNPs as contrast agents. X-ray and CT have proven to be useful in imaging bodily structure, providing a relatively high spatial resolution, but they do so using ionizing radiation with its associated patient risk , . Surface-enhanced Raman scattering, as well as PAT and photothermal imaging, have been used for detecting GNP under in vivo conditions . Copland et al.  used PAT to image gold nanostructures to a depth of 6 cm in phantom experiments using near-infrared (NIR) light. However, high-power laser intensity (~15 mJ/cm2) is being used in PAT and photothermal imaging, which might cause some thermal effects to the surrounding tissue. Photoacoustic imaging was also used for tumor detection, based on the red-shift in the aggregated GNPs spectrum , .
These methods are powerful and suggest a real improvement in the imaging world, but they are also sophisticated and expensive. In addition, all of the above-mentioned methods are based on the detection of the scattered light from the GNPs. It is well known that the scattering properties of a tissue are very dominant, and it is not a simple task to overcome it, especially using optical methods (rather than X-ray or IR irradiations). The DR-GNRs method suggests overcoming the natural scattering disruptions of the tissue by focusing on the absorption properties of these particles.
3.1 Light interaction with gold nanoparticles
The interaction between the electromagnetic field of light and a GNP is commonly described by the Lorentz model for light interaction with a molecule . With this model, following the interaction between the electromagnetic field and the molecule, a dipole is being generated in the electron cloud, which can be described by the following equation:(20)
where Ne is the electron density, me is the electron mass, ω and ω0 are the frequency and resonance frequency, respectively, and f is the friction coefficient.
This theory performs the basis for the calculation of the scattering and absorption coefficients of nanoparticles. Following light interaction with the nanoparticle, the last is described as a group of dipoles, with a scattered light described by the Mie theory . Based on these theories, the extinction coefficient γ of randomly oriented particles in the dipole approximation is :(21)
where N is the number of particles per unit volume, V the volume of each particle, εm the dielectric constant of the surrounding medium, λ the wavelength of the interacting light, and ε1 and ε2 are the real and imaginary parts of the material dielectric function, respectively. Specifically for light interaction with a rod nanoparticle, Pj is the depolarization factor for the three axes A, B, C of the rod with A>B=C . These calculations provided an adequate theory that correlates between the GNR aspect ratio (A/B) and the resulting absorption peak.
The DR-GNRs method used gold nanorods (GNRs); as among the GNPs family (gold nanospheres, gold nanorods, and gold nanoshells) they present the highest absorption properties in the visible-NIR optical region. While the absorption properties of the GNRs are mostly used for their therapeutic application, such as photothermal therapy , , the DR-GNRs method uses the GNRs absorption properties for diagnosis purposes, based on the tissue’s absorption properties changes (see Figure 2). This absorption-dependent diagnosis DR-GNRs method gains the ability to easily overcome the high scattering distributions caused by the scattering properties of the tissue, by establishing a novel GNRs absorption-based diagnosis method. Due to the relatively low absorption of the tissue, the GNRs serve as strong contrast agents for noninvasive detection.
4 Diffusion reflection in clinical applications
The development of medical diagnostic methods is under intensive care, since a key factor for a good healing treatment is the malady early detection. Different techniques were developed for biomedical applications in the optical range, such as surface-enhanced Raman scattering , photoacoustic tomography (PAT) , photothermal imaging and more.
The DR method, which is mostly based on the simple extraction of the tissue’s optical properties, provides an easy-to-use, safe, optical method. The DR-based methods are in use for diagnostic purposes and clinical applications , , . The ability of the light to penetrate tissues was first exploited by Bright in 1831 , who noted that light could be transmitted through the head of a child with hydrocephalus . Ever since, additional clinical applications based on DR measurements have been developed. Thus, for example, Jöbsis’ technique came to be known as NIR spectroscopy , , . It is a valuable technique that has been used to investigate brain function and pathology in both neonates and adults . Johansson et al.  have presented a real-time light dosimetry software tool for interstitial photodynamic therapy of the human prostate. The DR in the frequency domain was also investigated, as a multi-wavelength; high bandwidth (1 GHz) frequency domain photon migration instrument has been developed for quantitative and noninvasive measurements of tissue’s optical and physiological properties . Lin et al.  introduced a spatial frequency domain imaging (SFDI) method for quantitative in vivo optical imaging of brain tissue composition and physiology, such as tissue hemoglobin, oxygen saturation, and water. SFDI was used to generate optical absorption and scattering maps at different wavelengths in the NIR region (650–1000 nm), wherein tissue absorption that is relatively low and light can penetrate deep volumes of tissue (up to several centimeters). The SFDI method is in routine clinical use for breast cancer detection in the Beckman Laser Institute, Prof. Tromberg’s laboratories , .
In this section, we review the unique use of contrast agents-based DR method. The combination of the unique optical properties of the GNRs and the simple sensitivity of DR-based diagnostic method has established a completely new, interesting diagnostic field, with a high potential for a routine use in clinics. The subsequent paragraphs introduce the DR-GNRs successful achievements, presenting in vivo measurements of tumor-bearing mice and atherosclerotic rats.
4.1 DR-GNRs in cancer detection
4.1.1 Head and neck cancer detection
The basis for the DR-GNRs method to detect tumor is the accumulation of the GNRs in the tumor, which causes major change in its optical properties. In order to do so, the GNRs were bio-conjugated to anti-epidermal growth factor receptors (anti-EGFR). The EGFR is a cell-surface receptor, belonging to the ErbB family of tyrosine kinase, which plays a vital role in the regulation of cell proliferation. This receptor is associated with the development of variety of tumors , such as head and neck cancer (HNC), oral, breast, bladder, ovarian, renal, colon cancer and more , expressing over 10-fold EGFRs than normal cells . Overexpression of EGFR is associated with worse prognosis, and great efforts have been made in the last decades to design therapeutic and diagnostic agents for EGFR targeting , . GNPs conjugated to anti-EGFR are commonly used to detect tumor cells which possess EGFR. In most of the diagnosis methods based on these GNPs-EGFR, the basis for the tumor cells detection is the scattered light from the GNPs , . The DR-GNRs method detects the absorption properties of the GNRs-EGFR attached to the tumor.
The GNRs were conjugated to anti-EGFR antibodies, which home specifically to squamous cell carcinoma HNC . Figure 3 shows the Rd(ρ) results of HNC detection in tumor bearing mice. The GNRs conjugated to anti-EGFR were intravenously injected to the mice in order to specifically target the HNC tumor cells. The DR measurements were performed before injection, and 10 h post-injection in both normal and tumor sites. The DR measurements resulted in Rd(ρ)profiles which are correlated with the tissue’s optical properties. Thus, it was well observed that the slope of the reflectance curve in the tumor site is much sharper than the slopes of the normal sites, indicating enhanced absorption of the tumor region compared to the healthy tissue, due to the GNRs accumulation in this site.
The DR curves of the tumor were further investigated in order to evaluate the GNRs concentration within the tissue. As mentioned in the first paragraph, from the DR profile Rd(ρ)the tissue’s optical properties can be extracted [Eqs. (14) and (16)]. Therefore, the increase in the DR slope can be translated into the increase in the absorption coefficient of the tumor, from which the GNRs concentration can be directly calculated . As the GNRs were bio-conjugated to anti-EGFR, their concentration is an indicator of the EGFR amount, a signature for the tumor severity. Calculation procedure and results were presented in our article published in the Journal of Biophotonics , while the main equation that enabled to correlate between the DR slope and the absorption coefficient change was:(22)
C 1 and C2 are constants determined from experimental measurements of phantoms with increased absorption coefficients. Main results for the GNRs concentration in the tumor, according to Eq. (22), are presented in Table 1.
4.2 DR-GNRs method enables the detection of tumor margins in oral cancer
The DR-GNRs method was also used in oral cancer detection. The oral cancer cells overexpress the EGFR, therefore, the GNRs-EGFR can also accumulate in these cells. Oral carcinoma is among the 10 most common cancers worldwide with an estimated 400,000 new cases annually , . A major challenge exists in identifying the tumor within its margins, as up to 22% of surgical margins were found to test positive , . In the routine procedures performed in clinics, only microscopic examination of frozen sections is a routine practice in assessing the margins of HNC resections . However, freezing the tissue often disrupts morphology, making the interpretation difficult.
The DR measurements of cancerous oral tissue sections that were incubated with GNRs-EGFR enabled the detection of oral tumor in vitro, with specificity and sensitivity of 97% and 87.5%, respectively . The GNRs-EGFR attached the oral cancer cells, resulting with an enhancement in the cells absorption and an increase in the DR slope . Yet, a major challenge was to find the tumor margins using the DR-GNRs method. That was achieved with the help of the air Scanning Electron Microscopy (AirSEM) . This unique microscopy method enables the actual visualization of GNRs on tissue, without early preparations. Results, presented in Ref. , provided the EGFR spreading on the tissue. In the tumor site, a great amount of the GNRs was detected and in the healthy site only few nanoparticles were observed (Figure 4). The surprising result was an in-between site (named as “Border”), in which an intermediate amount of GNRs was observed. This border site determined a 1 mm distance between the healthy and tumor site. This result, suggesting that an optical resolution higher than 1 mm is not required, is of high importance for all optical methods that desire to determine the tumor margins.
Once the border site was revealed, the DR profiles of the same oral cancer tissue were investigated in a resolution of 1 mm, meaning that the slope of each 1 mm in the DR profile was extracted (see Figure 5). Results are presented in Table 2, and suggest a clear decrease in the slope values between 3 and 4 mm. It means that the healthy site in the cancerous tissue starts at 4 mm from the light source injecting point, and the border is 3–4 mm from the same point. These results suggest the DR method to be able to find tumor margins, in real time .
4.3 DR-GNRs in atherosclerosis detection
Arteriosclerotic vascular disease (ASVD), a leading cause of premature morbidity and mortality, is a condition in which an artery wall thickens as a result of the accumulation of plaque that is made of fatty substances such as cholesterol and leukocytes, especially infiltrating monocytes and tissue macrophages , , . ASVD is considered as a chronic disease that remains asymptomatic for years . ASVD plaques are divided into two broad categories: stable and unstable/vulnerable plaques. Stable AS plaques tend to be rich in extracellular matrices and smooth muscle cells, while unstable plaques are rich in certain macrophage subsets, foam cells and inflammatory cells, and usually have a weak fibrous cap . Therefore, unstable plaques are prone to rupture into the circulation, inducing thrombus formation in the lumen . One of the most common and fatal complications of ASVD is ruptured unstable plaque followed by thrombotic occlusion, causing myocardial infarction. Another potentially fatal complication is ischemic stroke, generally caused by embolization of athero-thrombotic material from a ruptured plaque in the carotid arteries, for instance, to a small artery in the brain. Therefore, real challenge exists in the early detection of the unstable plaques and major efforts are performed in this field , , .
The DR-GNRs method was successfully applied for the detection of the unstable plaques . The detection was based on the known facts that the unstable plaques are rich in macrophages, and these macrophages uptake GNPs , . As a result, once GNRs are injected in vivo, they accumulate in the unstable plaque thus, similar to the GNRs-EGFR accumulation in the tumor, they change their absorption properties. Hyperspectral images of GNPs uptake by the macrophages, as well as the DR profile of rat injured artery before and after the GNRs injection, are presented in Figure 6.
In this review, we introduce a novel optical imaging method which combines contrast agents with the traditional DR measurements. Contrast agents have a major importance in biomolecular imaging, as they can be attached to specific antigens for the detection of an abnormal site in the tissue. Thus, the combination of the DR method, which is in general use for tissue characterization, and contrast agents, which are mostly used for molecular imaging, proposes a unique diagnostic tool for the diagnosis of inner tissue maladies.
In this work, the proposed contrast agents are the GNRs. These GNPs have unique optical properties that enable their identification within a specific tissue site. As mentioned earlier, the specialty of their combination with the DR method is to focus on their absorption properties, rather than on their scattering properties. It is well known that the challenge in optical imaging is to overcome the natural scattering of the tissue, which causes a real obstacle that decreases the SNR. As the DR method desires to be simple and use safe irradiation, to overcome the natural scattering of the tissue is very difficult. Therefore, the addition of GNRs that changes the tissue absorption is a real innovation. In this way, the DR-GNRs method ignores the tissue scattering and focuses on its absorption properties, that by natural it is low and each slight change can be easily detected. This new look at the GNRs as absorption contrast agents paves the way for the development of other absorption-based diagnosis methods.
For further investigation, the DR-GNR method should be used for the detection of additional types of cancer, such as breast, bladder and colon cancer, which also present overexpression of the EGFR . Moreover, the DR method might be improved in different perspectives, such as to create a spatial image of the tissue surface and to provide high penetration depth, deeper than 1 cm , .
In summary, the DR-GNRs method presents the DR measurements as a new, molecular-based diagnostic method, with high sensitivity and specificity for diagnosis of tissue abnormalities.
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