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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
 
Phys Med Biol. Author manuscript; available in PMC 2016 July 21.
Published in final edited form as:
PMCID: PMC4522156
NIHMSID: NIHMS705969

Quantitative in vivo cell-surface receptor imaging in oncology: kinetic modeling & paired-agent principles from nuclear medicine and optical imaging

Abstract

The development of methods to accurately quantify cell-surface receptors in living tissues would have a seminal impact in oncology. For example, accurate measures of receptor density in vivo could enhance early detection or surgical resection of tumors via protein-based contrast, allowing removal of cancer with high phenotype specificity. Alternatively, accurate receptor expression estimation could be used as a biomarker to guide patient-specific clinical oncology targeting of the same molecular pathway. Unfortunately, conventional molecular contrast-based imaging approaches are not well adapted to accurately estimating the nanomolar-level cell-surface receptor concentrations in tumors, as most images are dominated by nonspecific sources of contrast such as high vascular permeability and lymphatic inhibition. This article reviews approaches for overcoming these limitations based upon tracer kinetic modeling and the use of emerging protocols to estimate binding potential and the related receptor concentration. Methods such as using single time point imaging or a reference-tissue approach tend to have low accuracy in tumors, whereas paired-agent methods or advanced kinetic analyses are more promising to eliminate the dominance of interstitial space in the signals. Nuclear medicine and optical molecular imaging are the primary modalities used, as they have the nanomolar level sensitivity needed to quantify cell-surface receptor concentrations present in tissue, although each likely has a different clinical niche.

1. Introduction

Cell-surface receptors that are specific to, or overexpressed by, cancer cells have been a critical target of interest in oncological research for decades (Gambhir, 2002; Weissleder, 2006). The overexpression, mutation, and selective expression of cell-surface receptors in cancer compared to healthy tissue were first observed through serological tests of cancer in the 1960s (Rettig and Old, 1989; van den Eynde and Scott, 1998). Since then, the identification of these receptors through medical imaging technologies (i.e. “molecular imaging”) has been proposed as a means of significantly improving many aspects of cancer management, including (1) enabling more sensitive and early detection of cancer at the molecular level (Massoud and Gambhir, 2003; Schottelius and Wester, 2009; Yang et al., 2006), (2) improving the delineation of tumor from healthy tissue during cancer surgery (Liu et al., 2014; Vahrmeijer et al., 2013), and (3) revealing accessible molecular targets for cancer-specific pharmaceuticals (Brannon-Peppas and Blanchette, 2012; de Wiele et al., 2008). The utility of molecular imaging with respect to cancer diagnosis and image-guided surgery (example 1 and 2 above) is obvious. In targeted-drug applications (example 3), biopsies are often obtained to analyze the molecular status of a patient’s cancer in order to guide and personalize a therapeutic regimen (Baloch et al., 2008; DeMarzo et al., 2003; Rouzier et al., 2005). However, recent studies have observed significant intra-tumor spatial heterogeneity in molecular biomarker expression, as well as variations in expression patterns over time, suggesting that a regional biopsy at a fixed time point may not be representative of the complete disease (van den Eynde and Scott, 1998; Fidler, 1978; Gerlinger et al., 2012; Longo, 2012). In response, in vivo molecular imaging approaches have been proposed to comprehensively examine the molecular profile of entire tumors (including satellite sites), potentially over time, to better guide personalized treatments (Weissleder and Pittet, 2008).

Significant advances have been achieved over the years with respect to imaging and identifying receptors in tissues, with the vast majority of these studies being carried out using nuclear medicine or optical imaging modalities since conventional magnetic resonance imaging and x-ray computed tomography are typically unable to offer the level of molecular sensitivity required to detect protein receptors (Fig. 1). With respect to nuclear medicine and optical imaging, there are vast differences in depth sensitivity, instrumentation, and image reconstruction; however, there are substantial similarities as well. Since both provide the ability to detect nanomolar concentrations of imaging agents, all of the image-analysis and kinetic-modeling methods discussed in this review article generally apply to both modalities.

Figure 1
Comparison of dominant medical imaging modalities with respect to molecular sensitivity (lowest concentration of an imaging reporter that can be accurately detected in a medium) and spatial resolution. Note that while optical imaging is capable of cellular ...

In cancer diagnosis, after initial studies of antibody-based cell-surface receptor imaging in the 1970s (Goldenberg et al., 1978; Mach et al., 1974), the imaging of glucose metabolism with 18F-fluorodeoxyglucose (18F-FDG) positron emission tomography (PET) took over as the standard molecular-imaging approach (Fletcher et al., 2008). Though effective in many cases, 18F-FDG PET has its limitations: (1) increased glucose metabolism is not obvious in all cancer types, with some tumors demonstrating heightened metabolism without contrast on 18F-FDG-PET (Hicks, 2004); (2) increased glucose metabolism is typically confined to aggressive late-stage cancers and may not be as effective as an early indicator of disease (Hicks, 2004); and (3) certain benign lesions are also known to present with heightened glucose metabolism resulting in false-positives (Strauss, 1996). In light of these limitations and the known distinctiveness of cell-surface receptor phenotypes for cancer cells vs. healthy cells (Rettig and Old, 1989), recent developments in molecular imaging have sparked a revival of cell-surface-antigen-targeted imaging for diagnosing cancer (Boerman and Oyen, 2011). For example, in molecular-imaging-guided surgery, a folate-receptor-targeted fluorescent imaging agent was imaged in a landmark study in the Netherlands to improve the identification of ovarian cancer during resection (van Dam et al., 2011). Similarly, for guiding personalized therapy, recent studies in patients with metastatic breast cancer have explored the relationship between pre-therapy expression levels of human epidermal growth factor receptor 2 (HER2) and the response of patients to a HER2-targeted therapy (Mortimer et al., 2014).

Despite recent advances in molecular imaging, there remain many obstacles to realizing the full potential of receptor identification in cancer management. Currently, 18F-FDG PET continues to be the only clinical molecular imaging approach that is widely used for cancer diagnosis/screening (James and Gambhir, 2012), and there has only been one molecular imaging-guided cancer surgery study in humans to date (van Dam et al., 2011). Furthermore, the failure rate for clinical trials of new drugs remains astronomically high, ~95% (DiMasi et al., 2003), even for targeted therapeutics with apriori molecular-imaging guidance (Scott et al., 2012). While the reasons for these apparent shortcomings are debatable and multifaceted, there is a growing recognition that a major problem is the quantitative limitations of conventional imaging approaches often employed for molecular diagnosis and for guiding cancer therapy (Tomasi et al., 2012).

The features that characterize the ideal molecular imaging approach will vary based on each application. For cancer diagnosis and surgical guidance, it may be sufficient to simply delineate between cancerous and healthy tissues, whereas for guiding targeted therapeutics, it may be advantageous to quantify the concentration of drug-targetable receptors. In either case, the signals displayed in a molecular image should ideally be proportional to the concentration of cell-surface receptors. This is challenging considering various nonspecific (non-molecular) factors that can alter the distribution of an exogenous contrast agent, including high physiological variability within and amongst tumors in terms of vascularity, vascular permeability, interstitial pressure, blood flow, etc (Jain, 1990a, b, 2001). In this review article, the history of quantitative cell-surface-receptor molecular imaging is presented, with a particular focus on the quantitative limitations of conventional approaches and potential solutions to mitigate some of these shortcomings, including kinetic modeling and “paired-agent” techniques.

2. Limitations of conventional receptor imaging

The most common approach for imaging cell-surface receptor distribution in vivo is the “inject, wait, and image” approach. Here a targeted imaging agent is injected systemically and yields an image of the agent’s retention in the patient after sufficient time has elapsed for unbound concentrations of the agent to be “washed out” of the tissues, ideally leaving only specifically bound agent (Weissleder and Mahmood, 2001). Studies that have employed this approach for imaging cell-surface receptor concentrations in preclinical models and clinical cancer cases now number in the thousands, dating back to the 1970s (Goldenberg et al., 1978; Mach et al., 1974), and have been surveyed in several review articles (Schottelius and Wester, 2009; Yang et al., 2006; Weissleder, 2006; Gambhir, 2002; Van Den Bossche and Van de Wiele, 2004; Ntziachristos et al., 2005; Weissleder, 2002; Leblond et al., 2010; Kaur et al., 2012). With over four decades of studies showcasing the potential benefits of receptor imaging for early diagnosis, for surgical guidance, and for guiding cancer therapies, a critical question to ponder is: why has receptor imaging not been adopted to a greater extent by oncologists?

Certainly, the onerous and expensive path for diagnostic agents to become approved for human use is a significant impediment for the clinical adoption of receptor imaging (Choi and Frangioni, 2010; Gioux et al., 2010; Sevick-Muraca, 2012; Sevick-Muraca et al., 2013; Weissleder, 2006). However, there are more fundamental problems associated with the imaging of cancer-related cell-surface receptors. Most importantly, perhaps, is the high risk of discordance between the measured uptake of an imaging agent and the true concentration of cell-surface receptors. In other words, there are a number of physiological and technological factors that significantly obfuscate the relationship between the signal measured from a targeted imaging agent and its true level of binding to a targeted receptor (Prabhakar et al., 2013). In the case of systemically administered imaging agents – i.e., agents injected into the blood stream – these obfuscating factors can include, but are not limited to, blood flow (Fang et al., 2011), vascular permeability (Jain, 2013; Maeda et al., 2000), extent of vascularization [hypovascular or hypervascular] (Allen and Cullis, 2004), efficacy of lymphatic drainage (Seymour, 1992), cellular internalization of the agent (Bartlett et al., 2007), metabolism of the imaging agent and therefore the potential (at least in nuclear medicine) for metabolites to preferentially accumulate in tumors that exhibit enhanced permeability and retention (Lammertsma, 2002; Maeda, 2001), nonspecific chemical binding (Mintun et al., 1988), spatial diffusion (Wilks et al., 2014), binding-site barriers (Thurber et al., 2008), blood/interstitial pressure (Jain, 1990a, b), and the pharmacokinetics of the agent in the blood [e.g., excretion rate] (Wu and Yazaki, 2000). Many of these factors can be amplified in cancers, and worse, physiological heterogeneities within and amongst tumors can lead to substantial variability in these factors, making the imaging of cell-surface receptors in tumors particularly problematic (Brown and Giaccia, 1998; Brown et al., 2001; Heneweer et al., 2011). In particular, the heightened uptake of “foreign substances” in many tumors compared to normal tissue, now coined the “enhanced permeability and retention (EPR)” effect (Maeda et al., 2000), was originally observed back in the 1930s (Duran-Reynolds, 1939), and is now leveraged in many chemotherapies (Maeda, 2001). For example, increased/preferential uptake of indocyanine green (an untargeted fluorescent agent) was observed in tumors compared to healthy tissue at up to 24 h after injection [Fig. 2] (Kosaka et al., 2011), despite relatively rapid plasma clearance (Krieger et al., 2011). While this result may be leveraged for certain applications such as identifying tumors for surgery, it is a significant problem if one aims to relate the uptake of the targeted imaging agent to the true abundance of the receptor for applications such as image-guided drug therapy. This nonspecific uptake and retention is often overlooked, yet it can become the dominant factor for larger imaging agents such as nanoparticle-based agents where both specific and nonspecific binding/retention can be effectively irreversible and binding rates can far exceed rates of efflux back into the blood (Wittrup et al., 2012). In this scenario, irreversible nonspecific uptake and trapping of large imaging agents may be a dominant effect such that molecular targeting is not likely to enhance their retention; however, many nanoparticle developers continue to functionalize their particles with antibodies and other targeting moieties. In some cases a benefit may be achieved, but proper control studies should be carried out to prove the effect is significant.

Figure 2
Variability of imaging-agent delivery and non-specific retention in tumors. (a) Example of an untargeted fluorescent imaging agent, indocyanine green (ICG), exhibiting preferential uptake and retention in an orthotopic mouse model of ovarian cancer. Obvious ...

It should be noted that additional factors other than delivery and retention can affect the measured uptake of a targeted imaging agent, such as the accuracy and reproducibility of the imaging modality/system used. In response to this challenge, great efforts have been made to quantify signals from more advanced nuclear medicine molecular imaging modalities [PET and SPECT] (Hutton et al., 2011; Kinahan et al., 1998); however, quantification in fluorescence imaging can be particularly challenging owing to the heterogeneous optical properties of biological tissues, which can greatly affect detected signal levels (Jacques, 2013; Ntziachristos et al., 2005; Hilderbrand and Weissleder, 2010; Sevick-Muraca, 2012). In addition, owing to the limited penetration depth of optical radiation, the geometry of the detection device with respect to a tissue surface (e.g., angle of detection, working distance, etc.) can also affect signal levels.

In light of the significant effects that tumor physiology can have on the uptake and retention of imaging agents in tissue, there are two straightforward, non-exclusive approaches for quantifying receptor concentrations: 1) develop tracers that are less affected by these effects, and 2) develop imaging analysis approaches that can account for these effects and thereby extract receptor concentrations. Extensive efforts have been devoted to developing imaging agents that are less susceptible to nonspecific uptake and delivery effects and there are a number of excellent review articles providing surveys of state-of-the-art agents for targeting cell surface receptors (James and Gambhir, 2012, 2010; Gao et al., 2004; Bai and Bornhop, 2012; Kobayashi and Choyke, 2011; Luo et al., 2011; Tolmachev et al., 2010a; Wu and Senter, 2005; Wu and Yazaki, 2000; Lee et al., 2010). While a discussion of imaging-agent development is outside the scope of this review article, it is important to understand that even the most advanced agents cannot completely circumvent the problems of nonspecific accumulation and delivery variability. The following sections will focus primarily on imaging methodologies and analyses, based on tracer-kinetic and pharmacokinetic modeling, which provide a direct means of quantifying cell-surface receptors (Fig. 3).

Figure 3
Summary of methods to quantify cell-surface receptor concentrations in vivo using molecular imaging. Row A presents the dominant method in cancer imaging, the “wait and image” approach where a targeted imaging agent is injected and imaging ...

3. Quantitative kinetic modeling

The field of quantitative kinetic modeling in cancer molecular imaging stems predominantly from brain PET studies. For a thorough overview of the subject, the reader is referred to a recent comprehensive review article (Gunn et al., 2015). However, owing to the importance of these concepts in this review, a history of in vivo kinetic modeling and its progression to cancer imaging is still presented here. The vast majority of kinetic models used in molecular imaging analyses are based on so-called “compartment modeling,” where the problem is simplified by assuming the imaging agent can only be in a set number of physical or chemical “compartments” within a tissue volume. In the early 1980s, landmark papers were published (Mintun et al., 1984; Patlak et al., 1983) presenting simple compartment models that assumed the imaging agent could only be in three compartments: in the blood plasma (Cp), freely associated in the extravascular extracellular (interstitial) space (Cf), or bound specifically to the receptor of interest (Cb) (Fig. 4 & 5a). To model distribution of the imaging agent amongst the compartments in time, first order rate equations were assumed with 4 rate constants, K1, k2, k3, and k4; where the rate of extravasation of the agent (Cp to Cf) is proportional to the concentration in Cp multiplied by the rate constant K1, the rate of washout of the agent (Cf to Cp) is proportional to the concentration in Cf multiplied by the rate constant k2, the rate of specific binding of the agent to the receptor (Cf to Cb) is proportional to the concentration in Cf multiplied by the rate constant k3, and the rate of dissociation of the agent from (Cp to Cf) is proportional to the concentration in Cb multiplied by the rate constant k4 (Fig 5a).

Figure 4
Distribution of a molecular targeted imaging agent in tissue. At any time, the concentration of an injected agent in tissue is in a dynamic balance between at least three “compartments:” the blood (specifically the blood plasma volume), ...
Figure 5
Basic principles of kinetic compartment modeling of imaging agents that (a) reversibly target cell-surface receptors in tumors or (b) are used as untargeted controls. These form the basis for all kinetic modeling used to estimate or quantify cell-surface ...

Two subtle points of the naming convention are worth mentioning: 1) K1 is the only rate constant that is capitalized to indicate that it is defined as a proportionality associated with the blood plasma concentration of the imaging agent, while all other rate constants are typically defined as proportionalities associated with the voxel concentration of the agent; 2) the “blood” concentration is typically defined as the “blood plasma” concentration. The major components of blood being red blood cells and plasma, the imaging agent is only available to extravasate into the tissue if it is freely associated in the blood plasma and not associated with the red blood cells, and so studies that incorporate a blood draw to analyze the blood concentration of imaging agent typically report on the plasma concentration, Cp. However, if the concentration of agent bound to red blood cells is significant, it should also be measured as it will contribute to the signal measured in the region-of-interest (ROI) or voxel in the image, where ROI(t)=ηiviCi(t) with the scaling factor, η, representing the proportionality between the measured signal of an imaging agent (ROI) and the true concentration of the imaging agent in the ROI, Ci(t) representing the concentration of the imaging agent in the ith compartment (e.g. bound concentration, Cb), and vi being the weighting factors to correct for the fractional volume of the ith compartment in the ROI. While the early works on compartment modeling of cell-surface receptor targeted imaging agents focused on the analysis of brain tissue and not cancer, they represent the first imaging approaches capable of estimating cell-surface receptor concentrations in vivo, and provide an excellent lead-in to the imaging of receptor concentrations in cancer, which is a far less mature field. In both the Mintun et al. and Patlak et al. papers, the authors recognized the confounding impact that blood flow, nonspecific binding, and vascular permeability – amongst other factors summarized in Section 2 – could have on the accurate prediction of receptor concentrations when measuring the uptake of targeted agents at a single time point. The majority of subsequent kinetic modeling methods have been built upon the compartment models proposed in these early works, which assumed three possible environments for the imaging agent: two physical environments (blood and tissue) and one chemical environment (specific binding to tissue receptors). The imaging agent is assumed to be “free” in the tissue compartment prior to association with, or upon dissociation from (for reversible binding), the bound compartment. This assumes that the receptors of interest are located on cells within the tissue compartment and are therefore not directly accessible to agents in the blood.

These early models represent variations of the “arterial input function” imaging methodology represented in Fig. 3B. The model developed by Mintun et al. allows for the possibility of reversible binding (k4), whereas the model developed by Patlak et al. assumes that binding is irreversible. The method proposed by Patlak et al., while requiring arterial blood sampling, is relatively straightforward and is widely used today for imaging agents that are assumed to exhibit irreversible binding. However, agents that target cell-surface receptors often exhibit reversible binding characteristics. Patlak and Blasberg followed up their irreversible-binding paper with a more general derivation allowing for reversible binding (Patlak and Blasberg, 1985); yet, even with this new model it is not possible to decouple binding-related parameters (k3 and k4) from the blood-tissue rate constants (K1 and k2) (a particular problem in cancer imaging as discussed below), nor does the model have the flexibility to correct for the intravascular contribution to the signal. However these models are insensitive to slow kinetic non-specific compartments. On the other hand, the model proposed by Mintun et al. was capable of isolating binding parameters from other kinetic parameters. Unfortunately, the approach was far too complicated to be applied on a wide scale, requiring: (1) arterial blood sampling as an input function, (2) uptake in an ideal “reference tissue” devoid of specific binding to estimate vascular permeability and the non-displaceable fraction of the imaging agent, and (3) subsequent or prior imaging of both blood flow and blood volume using separate radioactive imaging agents, 15O-water (Raichle et al., 1983) and 15O-carbon monoxide (Grubb et al., 1978), respectively. In response to the complexity of the Mintun model, a number of groups have since worked out more simplified approaches to approximate BP (see Section 3.3 for more discussion on the importance of the binding potential parameter), predominantly for neurotransmitter imaging applications (Lammertsma et al., 1996). Some important simplifications that have greatly increased the use of kinetic modeling in molecular imaging include the realization that the arterial input function, which is invasive to measure in nuclear medicine studies, could be derived from serial imaging of the heart or aorta owing to the large blood pool in these regions (Germano et al., 1992), or could be mathematically replaced by the “reference tissue” input function described by Mintun et al. that was originally used to estimate vascular permeability (Hume et al., 1992).

3.1 Reference tissue modeling

“Reference tissue” models (Fig. 3C) turn out to be poorly suited for cancer imaging; nevertheless, they warrant some discussion as all of the mathematical models that have been developed for reference-tissue approaches are directly translatable to the “paired-agent” approaches (Fig. 3E), which are described in Section 4 and are ideal for quantifying receptor concentrations in cancer. Reference-tissue models essentially stemmed from the recognition that if the temporal uptake of an imaging agent in any region of interest is dependent on the following parameters:

  1. arterial input function
  2. blood-tissue transfer kinetics (K1 and k2)
  3. specific binding and dissociation (k3 and k4)

and the uptake of the same imaging agent in a tissue region devoid of targeted receptor (reference tissue) is dependent on only i. and ii., then the reference-tissue uptake may be used to account for i. and ii. in any other tissue region. This, in turn, would allow for an extraction of the binding potential (k3/k4) of that region. In other words, the uptake of the imaging agent in a tissue devoid of receptor (reference tissue) can be used as a surrogate of the plasma input function in all other tissues, as long as the ratio of the delivery kinetics (K1/k2) of the imaging agent are similar in all tissues (the validity of this assumption will be discussed in the context of tumor imaging below). Hume et al. published the original presentation of this approach in 1992 (Hume et al., 1992), but the implications of the approach were not fully appreciated until Lammertsma and Hume (Lammertsma and Hume, 1996) and Logan et al. (Logan et al., 1996) published their “simplified” and “graphical” reference tissue models, respectively, which are regularly employed in brain neurotransmitter PET imaging today. Many modifications of the original reference-tissue model have been explored, with each model requiring its own set of assumptions; however, one assumption that is central to all reference-tissue models is that the dynamics of imaging agent delivery and retention be equivalent between the reference tissue and any other region of interest under analysis (Lammertsma and Hume, 1996). Note that agent delivery and retention are represented by the ratio of rate constants, K1/k2, which in turn are dependent on blood flow, vascular permeability, interstitial pressure, and other factors. As discussed in a recent review on quantitative PET imaging in oncology (Tomasi et al., 2012), this assumption has only been validated in brain-tissue imaging, and it is known that the factors that influence K1 and k2 can be highly abnormal in tumors (Jain, 2001). There are a few studies that have employed reference tissue models for cancer imaging (Ardeshirpour et al., 2014; Chernomordik et al., 2010; Hassan et al., 2012; Zielinski et al., 2012; Guo et al., 2012; Zhang et al., 2006; Zhu et al., 2012); however, a recent study from our group demonstrates that tumors can have variable and odd K1/k2 ratios that can make it difficult to identify a suitable reference tissue from any healthy tissue (Tichauer et al., 2012a).

3.2 Temporal kinetic analyses

With suitable reference tissue regions being difficult to identify for cancerous tissue (owing to the significant difference between tumor and normal tissues in almost every possible way), most single-imaging-agent receptor-concentration imaging efforts have employed complex kinetic models with numerous fitting parameters similar to the Mintun approach (Mintun et al., 1984). The Mintun approach, in turn, is based on other early two-tissue compartment PET neurotransmitter imaging models that require arterial input functions (Fig. 3B) (Farde et al., 1989; Lammertsma et al., 1996; Sawle et al., 1993; Volkow et al., 1993). A list of kinetic-modeling studies for the imaging of cancer receptors is presented in Table 1. In general, the goal in kinetic modeling is to find a solution with as few parameters as possible while accurately describing as much of the biological behavior as possible. By fitting imaging agent temporal uptake curves, which are relatively featureless, with models that include four or more parameters through nonlinear curve-fitting algorithms, significant parameter covariance can be encountered. Here, covariance refers to models in which changes in two or more parameters can result in similar changes to the model’s output (i.e. imaging agent-uptake curve shape), thereby reducing the uniqueness of a solution. In addition, models with large numbers of parameters often result in longer computational times, and require relatively accurate initial parameter “guesses” to prevent convergence to local minima, all of which can significantly reduce the accuracy and precision of the model. Software packages for compartment-model fitting often seek to reduce the instability of nonlinear fitting routines (Barrett et al., 1998; Mikolajczyk et al., 1998; Muzic and Cornelius, 2001; Gambhir et al., 1996), and the use of artificial network nodes has been employed with some success to improve convergence to global minima and to speed up computation times (Gambhir et al., 1998). Simplified reference-tissue models (a subcategory of Fig. 3C), introduced by Lammertsma et al. (Lammertsma and Hume, 1996), improve conditioning of nonlinear fitting further by reducing the model to three parameters, while linearized and constrained versions of this model have been explored to enhance the noise stability and computational efficiency (Gunn et al., 1997; Hume et al., 1998; Ichise et al., 2003). Graphical models, such as the Patlak (Patlak and Blasberg, 1985) [Fig. 3B model]s and Logan models (Logan et al., 1996; Logan et al., 1990) [Fig. 3C models], simplify the fitting process further, and as a result, are used in a large number of neurotransmitter imaging studies.

Table 1
List of publications from independent groups that have employed kinetic modeling to estimate cell-surface receptor concentrations in vivo in tumors (multiple instances are presented from the same group for unique kinetic models). Under the Approach column: ...

Unfortunately, all of the simplified models in their current form are not readily adaptable to tumor imaging. As mentioned in Section 3.1, reference tissue models are problematic since it is difficult to find an ideal “reference tissue” for all tumors, and the estimates of receptor concentration provided by the Patlak and Logan graphical models are dependent on the dynamics of imaging agent delivery and retention, which often vary substantially within and amongst different tumors (Tichauer et al., 2012a). Moreover, some tumors exhibit substantial nonspecific uptake of foreign substances, which could require addition of a “nonspecific compartment” in the models, thereby increasing the number of fitting parameters depending on whether or not there is rapid equilibrium between free imaging agents and the nonspecific concentrations. In the case of rapid equilibrium, nonspecific retention is often addressed by solving for the “non-displaceable” binding potential, BPND, which is the product of the true BP and fND, the fraction of imaging agent in the “free” space that is not associated with the nonspecific compartment [see Section 4 for further discussion] (Innis et al., 2007).

As a result of these complications, less than 40 articles have been published in the last 25 years that have employed kinetic modeling to estimate cell-surface receptor concentrations in tumors using a single targeted imaging agent, the majority of which are listed in Table 1. This number pales in comparison to the quantity of PET neurotransmitter studies carried out in non-cancerous brain tissue that have been published in the same time period, which number in the thousands. Clearly, a more robust means of imaging receptor concentration in tumors is required in order to achieve acceptance by the wider cancer molecular imaging community, the majority of which continues to rely on the standard “inject-wait-image” protocols that are discussed in Fig. 3A and Section 2. Section 4 reviews the growing field of “paired-agent” imaging that may hold the key for more quantitative imaging of tumor receptors.

3.3 Binding potential

With much of the cancer-imaging world likely being unfamiliar with the kinetic parameter, BP (binding potential), a summary of the parameter is provided here; however, a more detailed discussion of the utility and limitations of BP are presented in a consensus paper (Innis et al., 2007), and in a recent review article (Gunn et al., 2015). In a general sense, the binding potential (BP) can be written as:

BPk3k4=Bavail·KA,
(1)

where Bavail represents the concentration of targeted cell-surface receptors available for binding and KA represents the “affinity” of the imaging agent for the receptor [where KA = kon/koff in the reaction-kinetics literature] (Innis et al., 2007).

In many cases it is possible to approximate KA from in vitro analyses (Annis et al., 2007), and therefore solve Eq. (1) for Bavail, yet the majority of articles employing kinetic modeling to estimate receptor concentrations prefer to report BP rather than the Bavail. As of August 2014, a PubMed.gov search for the phrase “binding potential” brought up a list of over 1700 publications in the last 20 years, with a relatively consistent increase in the rate of appearance since the early 1990s. There are a number of reasons why BP is considered a preferable parameter to Bavail, and why the measurement of BP is proposed for cancer imaging in this review. First, there is evidence that suggests discordance between in vitro and in vivo measurements of KA at least in neurotransmitter receptor imaging studies (Laruelle et al., 1994; Robertson et al., 1991), which would suggest that environmental factors can influence the affinity of an imaging agent for its targeted receptor. Since tumor environments tend to be particularly abnormal and variable, the in vitro and in vivo affinities of a given imaging agent should be compared in extensive studies by varying the occupancy of the receptor with the imaging agent (Laruelle et al., 1993) before attempting to convert in vivo images of BP to maps of receptor concentration. A second, more important reason for reporting BP is that it may be more informative for studies of natural ligands or drug binding than the more-difficult-to-quantify receptor concentration. For instance, if BP is measured using an imaging agent analog of a targeted therapeutic or natural ligand, then, as a unitless parameter, that BP could be used directly to estimate the proportion of drug/ligand that will bind to target receptors given a known drug dose or ligand concentration. More specifically, if the concentration of a drug in a tissue is represented by C (C = Cf + Cb), which is measurable by conventional molecular imaging if signal can be converted to imaging-agent concentration and the blood concentration of the agent is negligible, then the amount of bound drug could be estimated by the product: CBP/(1+BP) (Mintun et al., 1984).

As a final note, there are many competing approaches for estimating BP that tend to result in one of three different in vivo manifestations of the parameter – a non- displaceable BP (BPND), a “free” BP (BPF), and a plasma BP (BPP) – each of which is only proportional to in vitro BP (subscript free). A full discussion of the specifics of each BP definition can be found elsewhere (Innis et al., 2007; Gunn et al., 2015). Here, the important definition is BPND, which results from reference-tissue and paired-agent kinetic analyses and is proportional to the in vitro BP multiplied by favail and fND, where fND is the fraction of free imaging agent in the non-displaceable compartment and favail is the fraction of receptors available for binding in vivo compared to in vitro.

4. Paired-imaging-agent approaches

Instead of employing complex kinetic models to account for the variable delivery and retention of imaging agents in tumors (Section 3), in the 1950s, the group of David Pressman at Roswell Park Memorial Institute took a much more direct approach. Realizing that antibody uptake in tumors could be skewed by significant nonspecific background (Duran-Reynolds, 1939), the group proposed the use of a second, untargeted imaging agent to be administered alongside the targeted antibody. The uptake of the untargeted agent could then be used as an estimate of the extent of nonspecific uptake. The group coined this ingenious approach of estimating specific binding in tumors as paired-labeling (Pressman et al., 1957), which has since been referred to as ratiometric (Liu et al., 2009; Wang et al., 2012; Wang et al., 2014b) or dual-probe/reporter/tracer (Baeten et al., 2009; Pogue et al., 2010; Tichauer et al., 2012c) imaging. In this review article, we propose the use of paired-agent imaging to represent all approaches that employ an untargeted imaging agent to account for nonspecific (non-molecular) aspects of a targeted imaging agent’s delivery and retention. As an example of the utility of such an approach, one can imagine a scenario where a targeted imaging agent is preferentially retained in a tumor compared to healthy tissue. Conventionally, such a finding would be taken to mean that the targeted agent was binding to the specific cancer receptor it was targeted to. However, using the paired-agent approach, if the untargeted agent is also preferentially retained in the tumor compared to healthy tissue, one could infer that the preferential tumor uptake of the “targeted” agent is due, at least in part, to nonspecific (non-molecular) mechanisms, and that the extent of specific binding to cancer receptors is ambiguous. Paired-agent approaches have the power to identify imaging-agent retention attributable to specific vs. nonspecific binding by the extent to which targeted agent retention is higher than untargeted agent retention in any tissue (Fig. 5 & 6).

Figure 6
Paired-agent imaging applications. (a) Three-dimensional microscopy of a human epidermal growth factor receptor 2 (HER2)-targeted fluorescent contrast agent used to stain HER2-positive tumor cells suspended in a 3D matrix (Liu et al., 2009). The left ...

The original paired-agent approach was rather involved, entailing the injection of 131I-labeled antiserum antibody and 133I-labeled normal serum antibody with subsequent perfusion of dissected tissues in 1-gram sections for placement in a scintillator well. Since the mean gamma radiation emission energies of the two iodine isotopes were significantly different (360 keV and 530 keV, respectively), signal emissions from each could be separated by a two-channel scintillation spectrometer. Crosstalk between channels was problematic and required a form of normalization to scintillation measurements on fractions of the injected solution prior to injection and at the time of tissue imaging (Pressman et al., 1957). In the years following its initial proposal, paired-agent approaches were adapted for in vivo autoradiography (Blau et al., 1958), highlighted in Nature in 1962 to quantify chemical differences between antibody fragments (Roholt et al., 1962), and later applied to tissue sections and cell smears (Tanigaki et al., 1967). In the late 1960s and early 1970s, the approach was picked up by the group of Dr. Frank J. Dixon at the Scripps Clinic and Research Foundation to quantify immunogenic activity of antigens (McConahey et al., 1968; McPhaul and Dixon, 1970; Wilson and Dixon, 1971; Wilson et al., 1971); yet only a few groups other than Pressman’s applied the approach to cancer receptor analyses (Boone et al., 1973a; Boone et al., 1973b; Duthu and de Vaux Saint-Cyr, 1975; Sears and Wilson, 1981; Chatal et al., 1983; Buchegger et al., 1983; Kurth et al., 1993; Behnke et al., 1988; Matzku et al., 1987). It was not until the mid-1980s that the approach was adopted as regular practice for tumor-receptor imaging by the labs of Dr. Darrel D. Bigner and then Dr. Michael R. Zalutsky at Duke University who have conducted the vast majority of paired-agent studies up to the present, producing more than 60 publications using the method, a selection of which are cited here (Bourdon et al., 1984; Wikstrand et al., 1986; Blasberg et al., 1987; Zalutsky and Narula, 1987; Garg et al., 1992; Reist et al., 1995; Reist et al., 1997; Wikstrand et al., 1997; Foulon et al., 2000; Pruszynski et al., 2014). Outside of the substantial work carried out at Duke University with paired-agent approaches, few other groups have picked up on the methodology for nuclear medicine tumor imaging (Demignot et al., 1990; Sung et al., 1990; Gadina et al., 1991; Khawli et al., 1996; Repetto-Llamazares et al., 2014; Shockley et al., 1992; Stein et al., 2001; Stein et al., 2003; Tolmachev et al., 2010b; Yokota et al., 1993; Terwisscha van Scheltinga et al., 2014). Almost certainly, the limited use of paired-agent approaches is attributable to complexities in carrying out the methodology. First, it involves higher radiation dose because administration of an untargeted radioactive agent in addition to the targeted radioactive agent is required. Second, it can be difficult to accurately resolve signal from targeted and untargeted agents even with advanced gamma cameras owing to crosstalk between gamma emission energy distributions (El Fakhri et al., 2001). Third, it is not possible to resolve signal from more than one species of agent using the more advanced nuclear medicine modality, PET, restricting in vivo paired-agent receptor imaging to SPECT systems.

In order to mitigate problems associated with signal crosstalk, a number of groups have preferred to compare targeted-agent uptake in one set of tumor-bearing animals with untargeted-agent uptake in a second, independent set of tumor-bearing animals (Chattopadhyay et al., 2012; Goldenberg et al., 1974; Green et al., 2014; McLarty et al., 2009; Nagengast et al., 2007; Otsuji et al., 1992). While this approach is not adaptable to the clinic, it demonstrates specific uptake for the testing of new drugs or imaging agents. McLarty et al. have demonstrated that the ratio of targeted to untargeted agent uptake correlates relatively well with differences in receptor concentration in various tumor lines (McLarty et al., 2009). However, by not injecting both agents into the same animal, the untargeted agent cannot be used to correct for tissue heterogeneity and inter-subject variability and subtle differences in blood plasma kinetics between targeted agents may be less obvious owing to animal-to-animal variability.

As an aside, the use of antibodies by McLarty et al. warrants further discussion as antibodies are often considered to be irreversible binding agents since they internalize and become trapped inside cells upon binding to cell-surface receptors at rates that exceed dissociation (Mattes et al., 1994). Under such conditions, there is modeling and data to support the hypothesis that if the tissue concentration of the antibody-based imaging agent is at sub-receptor-saturation levels, all agent taken up by the tissue should be internalized regardless of receptor density (Thurber and Weissleder, 2011b, a). It follows from this hypothesis that receptor density would not be estimable under such conditions even with normalization by an untargeted control imaging agent; however, if a saturating dose is used (McLarty et al. 2009; Thurber and Weissleder, 2011b, a), then the signal can correspond to receptor concentration since excess unbound antibody is able to wash out of the tissue. While the hypothesis that antibody binding is irreversible works well to explain the underestimation of high-receptor-expressing tumor lines in McLarty et al., it is based on the assumption that k3 is much larger than k2. If this were not the case, then kinetic normalization of a targeted imaging agent by an untargeted agent would still allow one to estimate receptor concentration in sub-saturation doses, as long as the model accounts for the fact that antibody binding is irreversible. Interestingly, recent results exploring EGFR concentration with smaller, reversible binding peptide-based imaging agents demonstrated very similar apparent underestimations for A431 xenografts (Tichauer et al., 2012c) as observed by McLarty et al. This suggests that these measurements may not be underestimations in EGFR, but rather accurate estimates of the “available” EGFR in an in vivo environment. To support this alternative hypothesis, it was recently determined that the proportion of EGFR available for binding in vivo for A431 is significantly lower than the measurement of EGFR in vitro (Samkoe et al., 2014), by the same factor observed in McLarty et al. Further studies are needed to fully characterize binding conditions of antibodies and whether they can be used effectively in paired-agent imaging.

A more recent approach to minimize signal crosstalk and radioactive dose in paired-agent methods has been to employ the approach with the optical imaging modality. For certain applications, optical imaging is ideally suited for paired-agent approaches: it avoids the use of ionizing radiation and can allow for fast and sensitive measures of the uptake of multiple imaging agents in biological tissue, as long as the light emission wavelengths and/or absorption spectra of each imaging agent are significantly different. However, with the relatively recent development of more advanced optical imaging agents and imaging systems, paired-agent approaches were not adopted in the biomedical optics field until the late 2000s when three groups unearthed the approach for various applications, almost simultaneously (Baeten et al., 2009; Liu et al., 2009; Pogue et al., 2010) [Fig. 6]. Baeten et al. observed that activatable protease-sensing fluorescent imaging agents only correlated with expected levels of protease if delivery variability was accounted for by normalizing activatable imaging-agent signals by an internal blood-pool (nonspecific) imaging agent (Baeten et al., 2009). In the context of 3D optical-sectioning microscopy, Liu et al. demonstrated that nonspecific background signals, from unbound concentrations of a topically administered targeted imaging agent, could be mitigated through normalization with an untargeted agent (Liu et al., 2009). Finally, Pogue et al. introduced a kinetic model that was employed to estimate the binding rate k3 for an epidermal growth factor (EGF)-targeted imaging agent in a mouse xenograft model (Pogue et al., 2010). This compartment model based approach with two paired imaging agents provides the needed reference to accurately fit data with model-based methods for the molecular binding parameters.

4.1 Paired-agent kinetic modeling

Paired-agent kinetic models had been developed for brain imaging in the late 1980s by Blasberg et al. (Blasberg et al., 1987) and Huang et al. (Huang et al., 1989); however, neither of these early methods caught on, likely owing to their complexity. Both techniques required plasma input function measurements of the targeted and untargeted imaging agents, and the Huang et al. approach involved injection of a high-affinity binding agent in succession with a low-affinity binding agent (since this study was carried out with PET instrumentation, signal from different imaging agents could not be resolved at the same time). It wasn’t until recently that it was realized that the highly developed reference tissue models developed for neurotransmitter studies in PET (Section 3.1) could be translated to paired-agent studies in tumors – to directly measure BP as a marker of receptor concentration – if the plasma-input functions of a targeted and untargeted pair of agents could be assumed to be identical (Tichauer et al., 2012c). With the availability of robust commercial fluorescence imaging systems that have been optimized to image signals from at least two fluorescent markers in rapid succession (Keereweer et al., 2012; Nakayama et al., 2011), it is straightforward to quantify targeted receptor concentrations in tumors with a paired-agent approach. Already, such quantitative molecular imaging approaches have been utilized for various applications such as measuring intravascular marker concentrations (Tichauer et al., 2014a), for imaging of orthotopic tumors via MRI-guided fluorescence tomography (Davis et al., 2013), for surgical guidance (Sinha et al., 2015), and for estimating the extent of metastatic burden in lymph nodes [Fig. 6d] (Tichauer et al., 2014c). Validation in multiple tumor lines is an essential part of validating these methods, and Samkoe et al. (Samkoe et al., 2014) have shown that this is possible.

Advancing this field is still complex, because it requires careful selection and or synthesis of optimal targeted/untargeted imaging agent pairs. As mentioned, targeted and untargeted agents need to have similar plasma input functions for the reference tissue-based models to work. This needs to be validated with blood studies, estimated by image-based means (Elliott et al., 2014), or with pulse-dye-densitometry studies (Elliott et al., 2012). Alternatively, it is also possible to account for differences in plasma input function by directly measuring both input functions through blood sampling or image-derived means, or by using a correction based on agent kinetics in tissues devoid of targeted receptor (a deconvolution approach described recently) without actually measuring the plasma kinetics (Tichauer et al., 2014b). A second characteristic of an ideal targeted/untargeted agent pair is that the efficiency of agent delivery and retention (quantified by the ratio K1/k2) must be nearly equivalent between the agents within the same tissues (Lammertsma and Hume, 1996). Furthermore, K1 and k2 must be substantial enough to provide ample uptake and washout of both targeted and untargeted imaging agents so that differences in binding between the two can be observed. Since these parameters rely on blood flow, vascular permeability, and interstitial pressure; as long as the targeted and untargeted agents are of similar size, geometry, and chemistry (e.g. polarity), such an assumption should hold (Tichauer et al., 2014b), though it should be noted that the FDA-approved untargeted optical imaging agents, fluorescein and indocyanine green, bind readily to proteins in the blood plasma, predominantly albumin, which significantly alters their effective molecular characteristics in vivo. Two additional assumptions apply specifically to fluorescence-based paired-agent imaging: 1) There is negligible photobleaching observed over the course of an imaging protocol, or if photobleaching is unavoidable, that the magnitude of bleaching is roughly the same for both the targeted and untargeted agents. 2) The absorption/scattering characteristics, and the average trajectory of the excitation and emission photons, are similar when imaging both the targeted and untargeted agents. Monte Carlo simulations have established that this is an adequate assumption for IRDye-800CW and IRDye-700DX imaged on a LI-COR Pearl System (Kanick et al., 2014); however, such simulations should be repeated for different imaging systems and fluorophore combinations. Finally, recent studies have utilized multiplexed surface enhanced Raman scattering (SERS) nanoparticles that do not photobleach. More importantly, these agents can all be excited at a single illumination wavelength, and all emit within a similar wavelength band (Wang et al., 2014a; Wang et al., 2014b; Zavaleta et al., 2013). The two assumptions mentioned above are therefore both true for this new class of optical imaging agents. Furthermore, these glass-encapsulated gold-core nanoparticles (~120 nm in diameter) are largely identical in terms of size and surface chemistry, and therefore should exhibit similar delivery and retention characteristics in tissue. Recent studies with topically applied SERS NPs conjugated to targeted monoclonal antibodies and isotype-control antibodies (untargeted) have shown that the nonspecific behavior of these targeted and untargeted NPs is virtually identical (Wang et al., 2014a; Wang et al., 2014b). The unique spectral “fingerprint” of SERS NPs offer exquisite signal-to-background properties (Kircher et al., 2012) and the potential to simultaneously image a large multiplexed panel of biomarker targets with laser illumination at a single wavelength (Zavaleta et al., 2008; Zavaleta et al., 2013; Zavaleta et al., 2009), which will be advantageous for identifying and stratifying tumors with greater accuracy in light of the known variability in molecular phenotypes between tumors and even within a single tumor over space and time (Gerlinger et al., 2012). It should be noted, that while these SERS NP imaging agents have demonstrated utility for tissue staining, even paired-agent kinetic modeling may not be sufficient for these and many other targeted/untargeted large imaging-agent pairs owing to high specific and nonspecific tissue uptake coupled with low k2 rates (tissue release of the imaging agents) (Wittrup et al., 2012). Thus, for systemically delivered imaging agents, paired-agent kinetic modeling will likely only be effective for smaller protein, peptide, and small molecule based agents (rather than nanoparticles) that exhibit appreciable k2 washout.

Another key point in paired-agent kinetic modeling is the relationship between imaging-agent concentration and the measured signal from the agent. In dual-isotope SPECT, great efforts have been made to quantify respective concentrations of at least two isotopes in biological tissue; however, in optical imaging, the quantification of imaging-agent concentrations is considerably more difficult owing to high levels of light scattering in tissue and the effect of heterogeneous optical properties (Ntziachristos et al., 2003; Frangioni, 2003; Leblond et al., 2010). It is important to note, however, that paired-agent imaging strategies do not require absolute quantification of imaging agent concentrations since the signal from the untargeted agent acts to normalize the signal from the targeted agent. For example, in the ratiometric imaging approach, it is assumed that the signal ratio between targeted and untargeted agents is largely independent of many of the nonspecific effects that are common to all imaging agents and imaging channels (Wang et al., 2012; Wang et al., 2014a; Wang et al., 2014b; Liu et al., 2009).

Note that the measured signal of any one fluorophore is reliant on a number of properties specific to that particular fluorophore, including fluorophore quantum efficiency, optical properties of the tissue, and the detection efficiency of the imaging system at the fluorophore’s emission wavelength. A tissue-specific means of normalizing targeted and untargeted imaging agent signals is necessary in certain cases. Such approaches have included a “reference tissue” normalization approach (assuming concentrations of both agents in a tissue devoid of binding should be equivalent) (Tichauer et al., 2012c), a pixel-based normalization approach (assuming concentration of both agents are equivalent at very early time points after injection in all tissues) (Kanick et al., 2014), and spectral imaging approaches to directly account for tissue optical property heterogeneities (Valdes et al., 2012). It should be noted that autofluorescence background, if significant, must be removed from images prior to the use of any normalization approach. In kinetic modeling, it may be possible to simply subtract off a pre-injection background-fluorescence image for both agent-imaging channels; however, spectral decomposition approaches also offer an accurate means of autofluorescence removal, and do not require pre-injection imaging (Davis et al., 2008). Further to the point, spectral removal of autofluorescence is particularly enhanced with the emergence of new SERS NP contrast agents that have distinct spectral signatures that can easily be separated from autofluorescence (Kircher et al., 2012; Zavaleta et al., 2008).

Section 5: Conclusions

With the recent application of robust kinetic-modeling techniques and paired-agent methods, in addition to optimized multiple-imaging-agent imaging technologies in both optics and nuclear medicine, preclinical and clinical methods are finally available to accurately quantify cell-surface receptor concentrations in cancerous lesions through noninvasive and relatively straightforward means. The methods are now available to exploit these assays to, for example, guide personalized medicine or optimize surgical resection procedures in human therapy, or to assist in the development and discovery of new drugs in pre-clinical work. Customization of imaging tools to display BP or receptor concentration values directly may be the next technological advance that will help translate these methods into wider practice.

Acknowledgments

This work was sponsored by the US National Institutes of Health research grants R21 EB015016, R01 CA109558, and R01 CA167413.

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