Clinical and Translational Imaging

, Volume 2, Issue 4, pp 305–320 | Cite as

The role of quantitative PET in predicting cancer treatment outcomes

Review Article

Abstract

Recent years have witnessed increasing use of positron emission tomography (PET) in cancer staging and monitoring. In particular, 18F-fluoro-2-deoxy-d-glucose (FDG) has frequently been used in clinical practice for tumor detection, staging, and gross tumor volume definition in different cancer sites. More recently, there has been accumulating evidence that pre- and intra-treatment FDG uptake could be used as a prognostic factor for predicting cancer treatment outcomes. Typically, quantitative analysis of FDG uptake is based on observed changes in the standardized uptake value (SUV). However, SUV descriptors themselves might be influenced by the initial FDG uptake intensity, radiotracer distribution, and changes in tumor volume. These factors and others might make this approach prone to significant intra- and inter-observer variability. Alternatively, more recent efforts have been directed toward the use of advanced image feature analysis techniques as part of the emerging field of radiomics. In this work, we review recent advances and discuss current challenges regarding the use of PET imaging for predicting cancer outcomes. We discuss issues related to image feature extraction, statistical modeling, tracer type, and combination with other imaging modalities for the purpose of developing robust PET-based models of treatment outcomes. We provide examples based on our experience, and that of others, of PET imaging used alone or with other complementary modalities for predicting outcomes in radiotherapy and their application in personalizing treatment through dose painting. We also highlight the potential opportunities in this field for personalizing cancer treatment and improving clinical decision making.

Keywords

PET Cancer Treatment outcomes Prediction Multimodality Radiomics 

Introduction

Positron emission tomography (PET) imaging is increasingly used in oncology in general, and in radiation oncology in particular, for the purposes of diagnosis, grading, staging and assessment of treatment response. For instance, PET imaging with 18F-fluoro-2-deoxy-d-glucose (FDG), a glucose metabolism analog, has been applied for the diagnosis, staging and treatment planning of lung cancer [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], head and neck cancer [11, 12], prostate cancer [13], cervical cancer [14, 15], colorectal cancer [16], lymphoma [17, 18], melanoma [19] and breast cancer [20, 21, 22]. Moreover, there is accumulating evidence that pre-treatment or post-treatment FDG PET uptake could be used as a prognostic factor for predicting outcomes [23, 24, 25, 26, 27]. This suggestion was motivated by the fact that tumor uptake is dependent on the characteristics of its microenvironment, which may influence treatment response. For instance, in a pre-clinical study, FDG uptake appeared to be positively correlated with hypoxia and negatively correlated with proliferation and perfusion [28]. Besides FDG, other PET tracers have been shown to be useful biomarkers for interrogating tumor properties that could affect response to therapy such as blood flow, investigated using 15O-water; hypoxia using 18F-fluoromisonidazole (FMISO) or 64Cu-diacetyl-bis(N(4)-methylthiosemicarbazone) (Cu-ATSM); and DNA synthesis and cell proliferation using 18F-fluorothymidine (FLT) and 18F-1-(2′-deoxy-2′-fluoro-β-d-arabinofuranosyl)-thymine (FMAU) [29]. Tumor oxygenation could be evaluated using Cu-ATSM [30] or FMISO [31], both of which have been shown to correlate with treatment failure. Cellular proliferation may be measured with radiolabeled nucleosides, such as FLT. In an experimental model, changes in FLT uptake post-irradiation were shown to be more pronounced than changes in FDG uptake and to correlate well with the proliferative activity of transplanted tumors [32]. In a pilot study, it was shown that FLT can be used to monitor changes in cellular proliferation in lung cancer patients during radical chemoradiotherapy [33].

The extraction of quantitative information from imaging modalities and the relating of this extracted information to biological and clinical endpoints is the subject of a new emerging field referred to as ‘radiomics’ [34, 35]. Traditionally, quantitative analysis of uptake of FDG or of other PET tracers is based on observed changes in the standardized uptake value (SUV). For instance, decreased SUVs post-irradiation have been associated with better outcomes in lung cancer [36, 37]. However, SUV measurements themselves are potentially prone to errors due to the initial FDG uptake kinetics and radiotracer distribution, which are dependent on the initial radiotracer injected activity and the time elapsing between the tracer injection and the image acquisition. In addition, some commonly reported SUV measurements might be sensitive to changes in tumor volume definition (e.g., mean SUV). These factors and others might make such an approach subject to significant intra- and inter-observer variability [25, 27, 38].

Several approaches have been proposed in the literature to overcome the limitations of simple SUV descriptors. A visual assessment method was used by Kalff et al. [25] to evaluate heterogeneity in FDG images from patients with locally advanced rectal carcinoma. Hicks et al. [27] applied a simple pattern recognition technique to FDG images of lung cancer and found that inflammatory changes correlated with tumor response suggesting that tumor radioresponsiveness and normal tissue radiosensitivity may be linked. However, more recent approaches have focused on the application of more advanced image-based features to distinguish responders from non-responders to therapy. Moreover, the extraction of relevant image features to a particular clinical endpoint remains a challenging task. This is an emerging area in outcomes research that innovative approaches developed in the field of radiomics aim to investigate. The problem of radiomics could be posed as an engineering pattern recognition problem [38, 39, 40], which requires an understanding of the observed clinical endpoint and the underlying characteristics of the imaging modality considered. Image-derived features can generally be divided, according to their nature, into spatial (static) and temporal (dynamic) features or combinations of the two. Static image features would include intensity histogram analysis, shape and morphology, and texture/roughness. These image-based features can provide better spatial characterization of uptake heterogeneity than the simple SUV descriptors currently employed [38] and might therefore result in improved ability to predict treatment outcomes [41]. Dynamic features are extracted from time-varying acquisition protocols such as dynamic PET or MR. These features are based on kinetic analysis using, for example, tissue compartment models and parameters related to tracer transport and binding rates, and they can provide radiomics modelers with valuable temporal information about tracer uptake variability [42].

In addition to the valuable physiological information (tumor metabolism, proliferation, necrosis, hypoxic regions, etc.) that can be collected from PET, additional knowledge can be gained from incorporating other imaging modalities that provide anatomical information, thereby making it possible to improve treatment planning, monitoring and prognosis in different cancer sites. For instance, changes in tumor volume captured on CT may be predictive of local tumor control in lung cancer patients [43, 44]. Interestingly, recent studies show that rectum status (full/empty) or the presence of bowel gas at the time of treatment planning may predict treatment failure [45] and the risk of rectal bleeding [46], probably due to a shift of the irradiation field compared to anatomy upon delivery. The complementary nature of different imaging modalities has led to direct efforts toward combining the physical and biological information they provide to achieve better treatment outcomes. For example, PET/CT has been utilized for staging, planning and assessment of response to radiation therapy in different cancer sites including lung, gynecological, and colorectal cancers [47]. Denecke et al. [48] compared CT, MRI and FDG PET in the prediction of outcome of neoadjuvant radiochemotherapy in patients with locally advanced primary rectal cancer, demonstrating sensitivities of 100 % for FDG PET, 54 % for CT, and 71 % for MRI, and specificities of 60 % for FDG PET, 80 % for CT, 67 % for MRI. Benz et al. [49] showed that combined assessment of metabolic and volumetric changes predicts tumor response in patients with soft-tissue sarcomas. Similarly, Yang et al. [50] showed that the combined evaluation of contrast-enhanced CT and FDG PET/CT predicts clinical outcomes in patients with aggressive non-Hodgkin’s lymphoma.

In this review, we will describe different imaging features used for characterizing tumor behavior. We will provide a review of the statistical modeling techniques that could be applied to integrate these different features for the purpose of developing robust PET-based models of treatment outcomes and discuss their application in personalizing treatment using techniques such as dose painting. We also discuss current issues and challenges and highlight the potential opportunities in this field for personalizing cancer treatment and improving clinical decision making in oncology.

PET image-based features

The features extracted from PET images (radiomics) can be divided into static (time-invariant) and dynamic (time-varying) features according to the acquisition protocol at the time of scanning and into pre- or intra-treatment features according to the scanning time point. Examples of static and dynamic features used in the literature are described below and summarized in Table 1.
Table 1

Summary of variables commonly extracted from PET images for outcome modeling in oncology

Category

Data

Comments

SUV descriptive measurements

Maximum

The highest single value within the region of interest (ROI)

Peak

Derived from a circular ROI of 0.75–1.5 cm in diameter centered on the maximum-value pixel; the mean SUV within this ROI is evaluated

Total lesion glycolysis

Mean SUV by tumor volume

Other statistics

Mean, minimum, standard deviation, coefficient of variation

Intensity–volume metrics

V x (5–100 in steps of 5 as percentage of the SUV uptake)

Percentage volume having x% intensity

I x (5–100 in steps of 5)

Minimum intensity to x% volume

Heterogeneity metrics

Difference between I x and V x measures

Texture-based features

GLCM

2nd order histogram features (energy, entropy, contrast and homogeneity)

NGTDM

Higher order histogram features (coarseness, contrast, busyness, and complexity)

RLM

Regional features

GLSZM

Regional features

Shape-based features

Eccentricity

Geometric and topological characteristics

Euler number

Solidity

Extent

Kinetic parameters

K 1, k 2, k 3, and k 4

Compartment modeling parameters (cf. Fig. 2)

Metabolic uptake rate (K-FDG)

FDG compartment analysis

Static PET features

  1. (a)
    SUV descriptors: SUV measurement is a standard method in quantitative analysis of PET images [51]. In this case, raw intensity values are converted into SUVs and statistical descriptors such as maximum, minimum, mean, standard deviation (SD), and coefficient of variation (CV) are extracted. An example is shown in Fig. 1, which shows PET-based nomograms for predicting cervical cancer treatment response [52].
    Fig. 1

    FDG PET-based prognostic nomograms using PET lymph node involvement, cervical tumor SUVmax, and PET tumor volume for recurrence-free survival (reproduced with permission from Ref. [52])

     
  2. (b)

    Total lesion glycolysis (TLG): This is defined as the product of tumor volume and mean SUV [5, 49, 53].

     
  3. (c)

    Intensity–volume histogram (IVH): This is analogous to the dose–volume histogram widely used in radiotherapy treatment planning to reduce complicated 3D data to a single curve that is easier to interpret. Each point on the IVH defines the absolute or relative volume of the structure (tumor or normal tissue) that exceeds a variable intensity threshold as a percentage of the maximum intensity [38]. This method allows the extraction of several metrics from PET images for outcome analysis, such as I x (minimum intensity to x% highest intensity volume), V x (percentage volume having at least x% intensity value), in addition to descriptive statistics (mean, minimum, maximum, SD, etc.). We have previously reported examples of the use of the IVH approach for predicting local control in lung cancer from PET/CT images [54].

     
  4. (d)

    Morphological features: These are generally geometrical shape attributes such as eccentricity (a measure of non-circularity), which is useful for describing tumor growth directionality; Euler number (the number of connected objects in a region minus the number of holes), which is useful for describing tumors with necrotic regions; and solidity (this is a measurement of convexity), which may be a characteristic of benign versus malignant lesions [55, 56]. In an interesting demonstration of this principle, a shape-based metric, based on the deviation from an idealized ellipsoid structure (i.e., eccentricity), was found to provide an indication of metastatic behavior in tumors and showed a strong association with survival in patients with sarcoma [56, 57]. A more advanced extension of this approach has recently been developed, which utilizes a tubular representation of the sarcoma structure with simplified radial analysis of FDG uptake. Interestingly, this approach could be used to distinguish between early phases of tumors characterized by high uptake at the core, and later advanced stages, characterized by central necrotic regions (voids in uptake) [58].

     
  5. (e)
    Textural features: Texture in imaging refers to the relative distribution of intensity values within a given neighborhood. It integrates intensity with spatial information resulting in higher order histograms (probability distributions) as opposed to conventional first-order intensity histograms. It worth emphasizing that texture metrics are independent of tumor position, orientation, size and brightness, and take into account the local intensity-spatial distribution [59, 60]. This is a crucial advantage over direct (first-order) histogram metrics (e.g., mean and SD), which only measure intensity variability independent of the underlying spatial distribution in the tumor microenvironment. Texture methods are broadly divided into three categories: statistical methods (e.g., high-order statistics, co-occurrence matrices, moment invariants), model-based methods (e.g., Markov random fields, Gabor filter, wavelet transform), and structural methods (e.g., topological descriptors, fractals) [61, 62]. Among these methods, statistical approaches based on the co-occurrence matrix and its variants such as the gray level co-occurrence matrix (GLCM), neighborhood gray tone difference matrix (NGTDM), run-length matrix (RLM), and gray level size-zone matrix (GLSZM) have been widely applied for characterizing FDG PET heterogeneity [63]. Four commonly used features from the GLCM include (Table 2): energy, entropy, contrast, and homogeneity [60]. The NGTDM is thought to provide more human-like perception of texture such as (Table 3): coarseness, contrast, busyness, and complexity [64]. RLM and GLSZM emphasize regional effects. Textural features were shown to predict response in cancers of the cervix [38], esophagus [65], head and neck [66], and lung [67]. In addition, textural features from FLT PET were demonstrated to quantify intra-tumor proliferation heterogeneity in breast cancer treated with chemotherapy [68]. MaZda is a dedicated software for image texture analysis [69].
    Table 2

    Selected GLCM (P ij ) features for analysis of PET data

    Co-occurrence feature

    Definition

    Energy

    \( \sum\limits_{i = 1}^{M} {\sum\limits_{j = 1}^{M} {P_{ij}^{2} } } \)

    Contrast

    \( \sum\limits_{i = 1}^{M} {\sum\limits_{j = 1}^{M} {(i - j)^{2} P_{ij} } } \)

    Local homogeneity

    \( \sum\limits_{i = 1}^{M} {\sum\limits_{j = 1}^{M} {\frac{{P_{ij} }}{{1 + (i - j)^{2} }}} } \)

    Entropy

    \( \sum\limits_{i = 1}^{M} {\sum\limits_{j = 1}^{M} {P_{ij} \log [P_{ij} ]} } \)

    Table 3

    Selected NGTDM with s i being the ith entry and p i the probability of occurrence of gray tone i in the PET data

    Gray tone difference feature

    Definition

    Coarseness

    \( \left[ {\varepsilon + \sum\limits_{i = 1}^{M} {p_{i} s_{i} } } \right]^{ - 1} \)

    Contrast

    \( \left[ {\sum\limits_{i = 1}^{M} {\sum\limits_{j = 1}^{M} {(i - j)^{2} P_{ij} } } } \right]\left[ {\frac{1}{{n^{2} }}\sum\limits_{i = 1}^{M} {s_{i} } } \right] \)

    Busyness

    \( {{\left[ {\sum\limits_{i = 1}^{M} {p_{i} s_{i} } } \right]} \mathord{\left/ {\vphantom {{\left[ {\sum\limits_{i = 1}^{M} {p_{i} s_{i} } } \right]} {\left[ {\sum\limits_{i = 1}^{M} {\sum\limits_{j = 1}^{M} {ip_{i} - jp_{j} } } } \right]}}} \right. \kern-0pt} {\left[ {\sum\limits_{i = 1}^{M} {\sum\limits_{j = 1}^{M} {ip_{i} - jp_{j} } } } \right]}} \)

    Complexity

    \( \sum\limits_{i = 1}^{M} {\sum\limits_{j = 1}^{M} {\left\{ {{{\left( {\left| {i - j} \right|} \right)} \mathord{\left/ {\vphantom {{\left( {\left| {i - j} \right|} \right)} {\left( {n^{2} \left( {p_{i} + p_{j} } \right)} \right)}}} \right. \kern-0pt} {\left( {n^{2} \left( {p_{i} + p_{j} } \right)} \right)}}} \right\}\left\{ {p_{i} s_{i} + p_{j} s_{j} } \right\}} } \)

     
Figures 2, 3, 4 show examples of the use of the IVH and texture in different scenarios: in FDG PET of cervical cancer (Fig. 2), FDG PET/CT of lung cancer (Fig. 3), and multi-tracer imaging (FDG/Cu-ATSM PET) of cervical cancer (Fig. 4).
Fig. 2

Left patient A and right patient B data. a PET scan of cervical tumor showing the region of interest (brown) and the 40 % maximum SUV delineated tumor (green). b Intensity–volume histogram (IVH) plots. Surface plots of the co-occurrence matrix for c cervical tumor ROI and d 40 % maximum SUV delineated tumor. Note that patient B’s tumor seems to be more heterogeneous. This could be inferred visually from the shallowness of the IVH, and the spread of the co-occurrence plot (reproduced with permission from Ref. [38]) (color figure online)

Fig. 3

Pre-treatment PET/CT image of a patient with NSCLC who failed locally. a PET/CT overlaid image. b Intensity–volume histograms (IVH) of b CT and c PET, respectively. d, e Are the texture maps of the corresponding region of interest for CT (intensity bins equal 100 HU) and PET (intensity bins equal 1 unit of SUV), respectively. Note the variability between the CT and PET features: the PET IVH and GLCM matrices show much greater heterogeneity for this patient. Importantly, the amount of PET and CT gross disease image heterogeneity varies greatly between patients (color figure online)

Fig. 4

The two rows, referring to an individual patient with primary cervical cancer, show texture maps for FDG (metabolic marker) and Cu-ATSM (hypoxia marker) alone, and overlapping texture maps of the two markers (color figure online)

Dynamic PET features

These features are based on kinetic analysis using tissue compartment models and parameters related to tracer transport and its binding rates [42]. In the case of FDG, a three-compartment model can be used to depict the trapping of FDG-6-phosphate in tumors [70, 71]. In Fig. 5, we show an example of estimation of kinetic parameters from dynamic FDG PET compartmental modeling. The glucose metabolic uptake rate can be evaluated using these estimated kinetic parameters. The uptake rate and other compartment estimates themselves can be used to form “parameter-map” images. Image features, including the previously described static ones such as IVH or texture, can be derived from these parameter maps. The literature reports examples of the use of dynamic features for predicting response. The glucose metabolic rate was correlated with pathologic tumor treatment response in lung cancer [72]. Thorwarth et al. [73, 74] published interesting data on the scatter of voxel-based parameter maps of local perfusion and hypoxia in head and neck cancer. Tumors showing greater variation in local perfusion and hypoxia showed less reoxygenation during a course of radiotherapy and had worse treatment outcomes.
Fig. 5

General compartmental model of tracer kinetics in a tumor. For instance, in case of FDG, C p(t) denotes the plasma input function, which could be estimated from blood sampling or using reference tissue models; C f(t) the concentration of un-phosphorylated (free) FDG; and C b(t) the concentration of FDG-6-phosphate (bound). The bi-directional transport across the membrane via GLUTs is represented by the rate-constants K 1 and k 2 , the phosphorylation of FDG is denoted by k 3 while the action of G6-phophatase is represented with rate constant k 4 . Using estimates of compartmental modeling, measures of metabolic uptake rate (K) could be evaluated by the relation K = K 1  × k 3 /(k2 + k4) by simple solution of the ordinary differential equation of the corresponding system (color figure online)

Outcome modeling

Outcomes in oncology and particularly in radiation oncology are characterized by tumor control probability (TCP) and the surrounding normal tissue complication probability (NTCP) [75, 76]. We have previously presented a detailed review of outcome modeling in radiotherapy [77]. DREES is a dedicated software tool for modeling radiotherapy response [78]. In the context of the modeling of image-based treatment outcomes, the observed outcome (e.g., TCP or NTCP) is considered to be adequately captured by extracted image features [38, 40]. We will highlight this approach using logistic regression and machine learning methods.

Logistic regression

Logistic modeling is a common tool for multi-metric (multi-variable) modeling. In our previous work [79, 80], a logit transformation, which has a sigmoidal response shape, was used:
$$ f({\mathbf{x}}_{i} ) = \frac{{{\text{e}}^{{g({\mathbf{x}}_{i} )}} }}{{1 + {\text{e}}^{{g({\mathbf{x}}_{i} )}} }}, \, i = 1, \ldots ,n, $$
(1)
where n is the number of cases (patients), x i is a vector of the input variable values (i.e., static and/or dynamic image features) used to predict f(x i ) for outcome y i (i.e., TCP or NTCP) of the ith patient. The ‘x-axis’ summation is given by:
$$ g({\mathbf{x}}_{i} ) = \beta_{o} + \sum\limits_{j = 1}^{d} {\beta_{j} x_{ij} } ,\quad i = 1, \ldots ,n,\; j = 1, \ldots ,d, $$
(2)
where d is the number of model variables and the β’s are model coefficients determined by maximizing the probability of the data giving rise to clinical events (i.e., TCP or NTCP). Resampling methods such as cross-validation (e.g., leave-one-out cross-validation or Jackknife) and bootstrapping (e.g., sampling with replacement) methods could be used to determine optimal model order and parameter selection as shown in the example of multi-metric modeling in lung cancer using FDG PET/CT features shown in Fig. 6 [54]. A major weakness in using this formalism, however, is that the model has limited capacity to follow details of the data trends (i.e., the model has a limited learning capacity when dealing with complex relationships that might be embedded in the data). In addition, Eq. (2) requires the user’s feedback to determine whether interaction terms or higher order variables should be added, making it a trial-and-error process. A solution to mitigate this problem is offered by applying machine learning methods as discussed below.
Fig. 6

Multi-metric modeling of local failure from PET/CT features. a Model order selection using leave-one-out cross-validation. b Most frequent model selection using bootstrap analysis. c Plot of local failure probability as a function of patients binned into equal-size groups showing the model prediction and the original data (reproduced with permission from Ref. [54]) (color figure online)

Machine learning

Machine learning is a branch of artificial intelligence that deals with the design and development of computational and statistical methods for learning from data [81, 82]. A class of machine learning methods that is particularly powerful and computationally efficient for image-based outcome prediction applications in oncology includes so-called Kernel-based methods and their most prominent sub-type, support vector machines (SVM). These methods have been applied successfully in many diverse areas including outcome prediction [40, 83, 84, 85, 86].

Learning is defined in this context as estimating dependencies from data [82]. There are two common types of machine learning: supervised and unsupervised. Supervised learning is used to estimate an unknown (input, output) functional mapping from known (input, output) sample pairs (e.g., classification or regression applications). On the other hand, in unsupervised learning no functional mapping is estimated and only input samples are given to the learning system (e.g., clustering or dimensionality reduction applications). In the example of outcome prediction (i.e., discrimination between patients who are at low risk versus patients who are at high risk of local treatment failure), the main function of the kernel-based technique would be to separate these two classes with ‘hyper-planes’ that maximize the margin (separation) between the classes in a nonlinear feature space. The objective here would be to minimize the bounds on the generalization testing error of a model based on previously unseen data (out-of-sample data) rather than to minimize the mean square error over the training dataset itself (data fitting).

Mathematically, the optimization problem could be formulated as minimizing the following cost function:
$$ L({\mathbf{w}},\xi ) = \frac{1}{2}{\mathbf{w}}^{T} {\mathbf{w}} + C\sum\limits_{i = 1}^{n} {\xi_{i} } , $$
(3)
subject to the constraint:
$$ \begin{gathered} y_{i} \left( {{\mathbf{w}}^{T} \varPhi ({\mathbf{x}}_{i} ) + b} \right) \ge 1 - \zeta_{i} \quad i = 1,2, \ldots ,n, \hfill \\ \, \zeta_{i} \ge 0{\text{ for all }}i \hfill \\ \end{gathered} $$
(4)
where w is a weighting vector and \( \varPhi ( \cdot ) \) is a nonlinear mapping function from the input data space to the feature space, where the samples can be easily separated. The ζ i represents the tolerance error allowed for each sample to be on the wrong side of the margin (called hinge loss). Note that minimization of the first term in Eq. (3) increases the separation (margin) between the two group classes, of low versus high risk of treatment failure, whereas minimization of the second term improves fitting accuracy. The trade-off between complexity (or margin separation) and fitting error is controlled by the regularization parameter C. However, such a nonlinear formulation would suffer from the curse of dimensionality (i.e., the dimensions of the problem become too large to solve) [82, 87]. Therefore, the dual optimization problem is solved instead of the primal problem in Eqs. (3, 4), which turns out to be convex and its computational complexity becomes dependent only on the number of samples and not on the dimensionality of the feature space. Moreover, the prediction function in this case is characterized only by a subset of the training data, each of which is then known as a ‘support vector’ s i :
$$ f({\mathbf{x}}) = \sum\limits_{i = 1}^{{n_{\text{s}} }} {\alpha_{i} y_{i} K({\mathbf{s}}_{i} ,{\mathbf{x}}) + \alpha_{0} } , $$
(5)
where n s is the number of support vectors (i.e., samples at the boundary), α i are the dual coefficients determined by quadratic programming, and K(·, ·) is the kernel function. Typical kernels (mapping functionals) include:
$$ \begin{gathered} {\text{Polynomials : }}K({\mathbf{x}},{\mathbf{x^{\prime}}}) = ({\mathbf{x}}^{T} {\mathbf{x^{\prime}}} + c)^{q} \hfill \\ {\text{Radial basis function (RBF): }}K({\mathbf{x}},{\mathbf{x^{\prime}}}) = \exp \left( { - \frac{1}{{2\sigma^{2} }}\left\| {{\mathbf{x}} - {\mathbf{x^{\prime}}}} \right\|^{2} } \right), \hfill \\ \end{gathered} $$
(6)
where c is a constant, q is the order of the polynomial, and σ is the width of the radial basis (Gaussian) functions. Note that the kernel in these cases also acts as a similarity function between sample points (support vectors) in the feature space determining their classification group and their corresponding probabilities. An example of applying kernel-based approaches to TCP modeling in lung cancer is shown in Fig. 7 [88].
Fig. 7

An example of a kernel-based approach for modeling TCP in lung cancer. a Kernel-based mapping from a lower dimensional space (X) to a higher dimensional space (Z) called the feature space, where non-separable classes become linearly separable. b Logistic regression. c Nonlinear kernels with overlaid training points. d Comparison of different TCP models, binned by the predicted rate of local control. Note that the best performance was achieved by the nonlinear model (SVM-RBF) (reproduced with permission from Ref. [88]) (color figure online)

Performance evaluation and validation methods

Evaluation metrics

To evaluate the performance of statistical classifiers in PET-based outcome models, one can use the Matthew’s correlation coefficient (MCC) [89] as a performance evaluation metric for classification. An MCC value of 1 would indicate perfect classification, a value of −1 would indicate anti-classification, and a value close to zero would mean no correlation. Alternatively, one can use the area under the receiver–operating characteristics (AU-ROC) curve [90]; MCC and AU-ROC tend to be proportional, with ROC giving a more pictorial representation of the performance. In the case of PET-based regression outcome models, Spearman rank correlation has been widely applied, as it provides a simple robust estimator of trend, which need not necessarily show a linear relationship as in the case of Pearson correlation coefficient [91].

Statistical validation

Model selection could be conducted and evaluated using information theoretic metrics (e.g., Akaike information criteria or Bayesian information criteria) and statistical resampling methods (e.g., cross-validation or bootstrapping). These methods are useful for performance comparison purposes and when applied properly can provide statistically sound results about bias, variance, confidence intervals, prediction error and the generalizability of a derived outcome prediction model particularly when the available dataset(s) for training, validation and testing is(are) limited [92, 93].

PET-based dose painting

An interesting application for PET-based outcome modeling is found in personalized radiotherapy treatment planning, in which areas of suspected radiation resistance can be painted with higher radiation dose per fraction and total dose to achieve better tumor local control (TCP) and reduce the possible risk of distant failure while maintaining a similar, normal level of tissue toxicity (NTCP). In this context, dose painting is defined as the process of prescribing non-uniform radiation dose distribution to the targeted tumor volume based on functional or molecular imaging information relevant to treatment response [94, 95, 96]. The main strategies that have been considered in the literature can be divided into subvolume boosting and painting by numbers or a hybrid approach of both.

Subvolume boosting

This dose-painting strategy involves dividing the targeted tumor volume into discrete regions following the so-called Fletcher’s volume of cancer hypothesis [97], according to which tumor burden as found from functional imaging can be reduced by simultaneous boost techniques in radiotherapy, for instance. In this case, the radiotherapy plan would consist of delivering the boost (additional radiation doses to the subvolumes) simultaneously with the basic (large-field) treatment in all treatment sessions [98, 99]. Examples of this technique reported in the literature include the successful use of FDG PET to manually delineate tumors into subvolumes for boosting in a phase I study of locally advanced head and neck cancer [100]. Another example, in which FDG PET is used in soft-tissue sarcoma, is shown in Fig. 8; here, the FDG PET uptake in the tumor was thresholded on the basis of percentage SUV levels to define the subvolumes for boosting [101].
Fig. 8

Soft-tissue sarcoma dose-painting distributions and dose–volume histogram (DVH) using subregions defined by FDG PET/CT and MRI information. The figure shows the dose-painting distribution on axial, coronal and sagittal views. The DVHs for the different subregions illustrates the conformality and uniformity of the dose-painting process of the escalated regions. These results were confirmed using Monte Carlo (Ref. [101]) (color figure online)

Dose painting by numbers

This dose-painting strategy involves prescribing dose (D) at the image intensity (I) voxel level, for example this could be given by [102]:
$$ D(I) = D_{\hbox{min} } + \frac{{I - I_{\hbox{min} } }}{{I_{\hbox{max} } - I_{\hbox{min} } }}{ \cdot }(D_{\hbox{max} } - D_{\hbox{min} } ), $$
(7)

As with subvolume boosting, functional and molecular imaging modalities such as PET or MRI could be used for painting by numbers. Several authors have derived more complex mapping schemes that relate the painting process directly or indirectly to predicted TCP [103, 104]. However, the heterogeneity of the resulting dose distribution could be limited by the complexity of radiation delivery in such cases and should be taken into consideration when applying this strategy [95]. Thorwarth et al. [103] demonstrated an example of hypoxia dose painting with FMISO, in which a semi-mechanistic modeling approach was proposed and the radiosensitivity parameters of the linear quadratic model were modified according to the retention of FMISO [104].

Issues and recommendations

Structure definition

The ability to distinguish the structure of interest from neighboring structures, i.e., to segment the tumor from surrounding normal tissues, is a necessary prerequisite to subsequent image-based outcome prediction and can significantly impact on subsequent feature extraction as discussed earlier. This process of contouring or segmentation can be carried out manually, which is a pretty laborious task associated with known intra- and inter-observer variability, or it can be performed using automated or semi-automated segmentation algorithms. It was recently reported that definition of the region of interest can impact on some textural features [105]. In our work on PET-guided treatment planning in radiotherapy, we presented a comparative survey of the current methods applied for PET tumor segmentation that could range from simple thresholding to sophisticated pattern recognition approaches [106, 107]. An AAPM task group (TG-211) is currently classifying the different PET auto-segmentation methods to provide guidelines on their advantages and limitations and on the applicability of each class of methods to the different radiation oncology tasks. A promising approach to improve the robustness of PET segmentation is to combine the information it provides with that derived from other modalities such as CT or MR [108, 109].

Robustness and stability

It is well recognized that image acquisition protocols may affect the reproducibility of features extracted from PET images, and that this may consequently affect the robustness and stability of these features for outcome prediction. This applies both to static features such as SUV descriptors [110, 111, 112] and textural features [113, 114]. Interestingly, texture-based features were shown to have a reproducibility similar to or better than that of simple SUV descriptors [115]. Moreover, textural features from the GLCM seemed to exhibit lower variations than NGTDM features [113]. Nevertheless, some clinical variables can have a confounding effect on reported texture metrics across different datasets. For example, it has been reported that local entropy, a GLCM textural feature, could be dependent on tumor volume below a certain threshold in cervical cancer [105]. Other factors that may affect the stability of these features include signal-to-noise ratio, partial volume effect, motion artifacts, parameter settings, resampling size, and image quantization [38, 114]. In the case of dynamic features, similar concerns are raised with regard to the variability of kinetic parameter estimates along with the extra scanning time requirements involved [116, 117]. Turkheimer et al. [118] proposed using a multi-resolution Bayesian approach to reduce such variability in dynamic PET. Although certain features may exhibit better robustness than others and would be preferable for outcome modeling, some form of standardization of PET acquisition protocols and pre-processing steps, while accounting for possible clinical confounding effects, may still be necessary to avoid issues related to reproducibility of PET-derived features.

Future directions

The field of quantitative PET for predicting cancer treatment outcomes is still in its infancy. Nevertheless, it is a promising area with great potential for advancing outcome prediction and personalizing treatment management for cancer patients. These models could be used to adapt treatment plans to pre-treatment and intra-treatment responses of tumors and to design individualized treatment plans to achieve increased treatment response effectiveness with fewer side effects. Moreover, the advancement of this field will significantly benefit from the identification of novel PET probes of cancer biology as well as new technological developments in PET hardware and software tools. The use of complementary imaging information such as PET/CT or PET/MR will further improve the quality of extracted image features and lead to a superior ability to predict which tumors are likely to fail or need alternative therapy. These model predictions could be used for dose-painting purposes and/or for adaptation of treatment management using longitudinal scanning protocols.

Conclusion

The role of imaging as a biomarker of radiotherapy response is continuously expanding as part of the emerging of field of radiomics, in which imaging features are correlated with biological and clinical endpoints. In this review, we categorized PET extracted features as static (time-invariant) or dynamic (time-varying) features according to the scanning acquisition protocol. Static features include SUV descriptors, IVH, morphological and textural features. Among these features, texture analysis has received the most attention due to its ability to discern tumor uptake heterogeneity. Dynamic features are derived from kinetic analysis and can provide temporal information about PET uptake biodistribution over time. We provided an overview of the statistical modeling techniques that could be applied to integrate these different features for the purpose of developing robust PET-based models of treatment outcomes and we presented examples using logistic regression and machine learning algorithms. We also discussed the application of such PET-based models in dose painting. The use of multiple tracers or multimodality imaging such as PET/CT or PET/MR will provide a wealth of information to improve the prediction power of these models. Current major issues in this field include standardization of tumor segmentation and the acquisition parameter effects on the stability and robustness of these features for predicting outcomes from one institutional dataset to another. PET-based predictive modeling is an evolving area for personalizing cancer treatment that includes applications such as dose painting and adaptive radiotherapy. However, the field is still in its infancy and would significantly benefit from collaborative efforts by the various different communities of stakeholders in nuclear medicine, oncology, radiation biology and bioinformatics to overcome current challenges and realize its potential for promoting informed clinical decision making in oncology.

Notes

Acknowledgments

This work was partially supported by the Canadian Institutes of Health Research (CIHR) under grant MOP-114910 and the Natural Sciences and Engineering Research Council (NSERC) of Canada under grant RGPIN 397711-11.

Conflict of interest

Issam El Naqa declares no conflict of interest.

Human and Animal Studies

All required ethics approvals were properly obtained for the presented data.

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Copyright information

© Italian Association of Nuclear Medicine and Molecular Imaging 2014

Authors and Affiliations

  1. 1.Medical Physics Unit, Department of OncologyMontreal General Hospital, McGill UniversityMontrealCanada

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