Development and CT image-domain validation of a computational lung lesion model for use in virtual imaging trials

Abstract

Purpose:

Computational abnormalities (e.g., lesion models) for use in medical imaging simulation studies are frequently generated using data collected from clinical images. Although this approach allows for highly-customizable lesion detectability studies on clinical computed tomography (CT) data, the ground-truth lesion models produced with this method do not provide a sufficiently realistic lesion morphology for use with current anthropomorphic simulation studies. This work is intended to demonstrate that the new anatomically-informed lesion model presented here is not inferior to the previous lesion model under CT imaging, and can therefore provide a more biologically-informed model for use with simulated CT imaging studies.

Methods:

The lesion model was simulated initially from a seed cell with 10 μm diameter placed in an anatomical location within segmented lung CT and was allowed to reproduce locally within the available solid angle in discrete time-intervals (corresponding to synchronous cell cycles) up to a size of ~200 μm in diameter. Daughter cells of generation G were allowed also to reproduce on the next available time-step given sufficient space. At lesion sizes beyond 200 μm in diameter, the health of subregions of cells were tracked with a Markov chain technique, indicating which regions were likely to continue growing, which were likely stable, and which were likely to develop necrosis given their proximity to anatomical features and other lesion cells. For lesion sizes beyond 500 μm, the lesion was represented with three nested, triangulated surfaces (corresponding to proliferating, dormant, and necrotic regions), indicating how discrete volumes of the lesion were behaving at a particular time. Lesions were then assigned smoothly-varying material properties based on their cellular level health in each region, resulting in a multi-material lesion model.The lesions produced with this model were then voxelized and placed into lung CT images for comparison with both prior work and clinical data. This model was subject to an observer study in which cardiothoracic imaging radiologists assessed the realism of both clinical and synthetic lesions in CT images.

Results:

The useable outputs of this work were voxel- or surface-based, validated, computational lesions, at a scale clearly visible on clinical CT (3–4 cm). Analysis of the observer study results indicated that the computationally-generated lesions were indistinguishable from clinical lesions (AUC = 0.49,95% CI = [0.36, 0.61]) and non-inferior to an earlier image-based lesion model—indicating the advantage of the model for use in both hybrid CT images and in simulated CT imaging of the lungs.

Conclusions:

Results indicated the non-inferiority of this model as compared to previous methods, indicating the utility of the model for use in both hybrid CT images and in simulated CT imaging.

1 |. INTRODUCTION

Virtual imaging trials (VITs) are a growing part of medical imaging research. VITs are a powerful alternative to the current gold-standard of clinical validation: the clinical trial. Standardization of protocols, prohibitively high expenses, and risks to the health of the patient population are all challenges associated with the clinical trial; conversely, these are some of the strengths of virtualization—especially as it relates to characterizing emerging imaging technologies. VITs require robust computational models of human anatomy and physiology, and clinically-relevant simulation platforms within which self-contained studies can take place. Since many imaging exams are done with the intent to locate and analyze in vivo abnormalities, a fundamental component of the VIT pipeline is its representation of pathologies that can be integrated with models of normal anatomy.

Virtual pathologies can come in the form of diffuse disease modeled as texture,¹ microcalcifications,² multipurpose solid tumors,^1,3,4 or any combination of these. Similarly, some tumors are modeled not to explicitly capture morphology, but to enable simulation studies on the efficacy of chemotherapeutic agents⁵ and radiotracer uptake as a function of tumor growth and micro-vessel distribution.⁶ For medical imaging simulation studies, typically, solid tumors are modeled since they are comparatively easier to image and quantify (e.g., with radiomics). These solid lesion models are also more anatomical-location-agnostic than organ-specific disease such as: cirrhosis (liver),^7,8 COPD (lungs),⁹ or microcalcifications (breast; coronary, carotid arteries).^10,11 More general lesions can be used in multiple anatomical locations with minor modifications. Computational lesion models intended for simulated medical imaging^3,4,12–15 use data from clinically imaged lesions as the basis for tuning model parameters; however, this immediately suggests an inconsistency with the representation of image-based computational lesions compared to images of real lesions. Lesions differing in high-frequency content—differences between spiculated margins, for example—can be rendered null by the imaging process. Consequently, this limits the morphological variability that the computational model can produce^16,17 Use of clinical images to produce computational lesions provides only inferential information about lesion growth patterns. Prior computational lesion models have relied on 3D clinical data—like tomosynthesis, CT, or MRI—and mathematical techniques to produce generalizable results. These generalized lesions typically exhibit the same statistical behavior as the original clinical lesions under imaging. However, this does not mean that the computational lesions are accurate representations of ground-truth.

These methods have subtle consequences for the model’s adherence to realism. Since modeling from images necessarily involves some form of extrapolation from existing data, unrealistic outputs are nearly guaranteed; however, it may not be at all obvious that they are unrealistic. Having computational lesions that are unrealistic in subtle ways is a further distortion of ground-truth which can have negative impacts on the studies they are used in—especially in phantom-based simulation studies, where the adherence of the ground-truth to reality is critical in order to achieve meaningful and clinically-actionable results.

However, image-based lesion generation is not the only method for producing computational pathologies. Biological studies on cell dynamics and growing tumors supply enough data to understand disease on microscopic and macroscopic scales. From knowledge of the microenvironment and the mechanical behavior of lung tissue, we were able to simulate probable outcomes for the manifestation of non-small-cell lung cancer tumors. With this new simulation method, we can reduce the degradation of ground-truth that occurs when imaging-based computational lesions are validated with imaging simulations.

In this work, a new model was created with the intent to be informed and validated by—rather than constrained by—imaging data and includes the new incorporation of biological and mechanical data, intended to provide dynamic computational lung lesion models for use in CT simulation applications.

2 |. METHODS

2.1 |. Theoretical justification

This work seeks to circumvent the problems that not all possible lesions can be imaged or will be visible in images or be available from images; that images of lesions provide limited information regarding their true shape; and while attempts to reconstruct the true shape from images may appear reasonable, they may yield lesions that make no sense biologically.

To justify this work, we used an operator framework (cf. chapter 7 of¹⁸). This formally highlighted the relevant limitations of medical imaging systems as related to acquiring images of in vivo lesions, specifically the ramifications of using images as a basis for generating models to be used for imaging studies.

We considered the temporal evolution of an arbitrary lesion $\overrightarrow{\mathbb{L}}\left(t\right)$ which belongs to the set of all physiologically viable, in vivo lesions {L₀}. This lesion was represented from inception to final size (at time of lethal burden) as a directed path through {L₀} as shown in Figure 1. Given a deterministic, continuous-to-discrete imaging operator $\mathscr{H}$ applied to the set of all physiologically possible lesions, {L₀}, and all lesions that can be represented with an image, {L₁}, then:

$$\mathscr{H}\left\{L_0\right\}=\mathscr{H}\left\{L_1\right\}.$$ (1)

FIGURE 1.

The space of all physiologically possible lesions {L₀} is shown as a shaded gray circle with a black outline. The path from t_i to t_f along $\overrightarrow{\mathbb{L}}\left(t\right)$ represents the time-evolution of a lesion $\overrightarrow{\mathbb{L}}\left(t\right)$ from time of inception t_i to time of lethal burden, t_f

In the continuous-to-discrete imaging system, the condition that {L₁} ⊂ {L₀} implied a necessary reduction in the set of lesions that can be characterized with imaging. The reduction in information content due to $\mathscr{H}$ was further compounded because the entirety of {L₁} images were and are not obtainable (i.e., rare, infrequently imaged, unique to an individual patient, etc.). Therefore, it is generally necessary to use the under-sampled space

$$\text{Λ}\mathscr{H}\left(L_0\right)=\mathscr{H}\left\{L_1^{*}\right\},$$ (2)

where the operator Λ removes lesion (images) from $\mathscr{H}\left\{L_0\right\}$ whose image is not available. The space $\left\{L_1^{*}\right\}$ forms the basis for efforts to approximately reconstruct {L₀} by statistically characterizing and generalizing from it. Modeling efforts approximate the pseudoinverse to the imaging operator ${\mathscr{H}}^{+}$ which operates on $\left\{L_1^{*}\right\}$ images such that it estimates the full lesion-space, {L₀}, as $\left\{L_0^{**}\right\}$:

$${\mathscr{H}}^{+}\text{Λ}\mathscr{H}\left\{L_0\right\}=\left\{L_0^{**}\right\}.$$ (3)

A visual representation (in “lesion space”) of the relationship between Equations (1), (2), and (3) is shown in Figure 2. The first failure of the image-based models which this work addressed was the space

$$\left\{L_{\text{inconsistent}}\right\}=\left\{L_0^{**}\right\}\backslash \left\{L_0\right\},$$ (4)

which is inconsistent with reality (i.e., inconsistent with ground-truth in that it does not describe one or more physiologically possible lesions). Among the lesions that exist in {L_inconsistent} are large (» 200 μm), avascular lesions with no core necrosis. The second failure of image-based models which this work addressed was the space {L_insufficient}:

$$\left\{L_{\text{insufficient}}\right\}=\left\{L_0\right\}\backslash \left\{L_0^{**}\right\};$$ (5)

this space represents all real lesions that image-based models cannot robustly characterize.

FIGURE 2.

Data sampling problem of the lesion modeling pipeline. Recreating representations of lesions from the imaging operator’s null space, {L₀} \ {L₁}, when the totality of the data that can be physically acquired due to hardware limitations is the data $\mathscr{H}\left\{L_1\right\}$. Further, only a small subset of the data possible to obtain has been imaged, reducing the clinical lesion image pool to $\mathscr{H}\left\{L_1^{*}\right\}$. The data $\mathscr{H}\left\{L_1^{*}\right\}$ is the only imaging data that can be used to inform the recreation $\left\{L_0^{**}\right\}$ of the full lesion space {L₀}

The primary success of the image-based models is the space

$$\left\{L_{\text{consistent}}\right\}=\left\{L_0^{**}\right\}\cap \left\{L_0\right\}$$ (6)

which describes all lesions that the model can produce that are apparently consistent with reality. The purpose of this modeling effort is to introduce a method that uses both biological and image-acquired information to approximate the full space {L₀}, or equivalently to ensure that the space $\left\{L_0^{**}\right\}$ produced by this model is a more robust approximation to {L₀} than would be possible without the inclusion of biological data.

2.2 |. Computational modeling

To create a computational lesion model that addressed the shortcomings of image-based efforts, a new model was developed that considered fundamental biological properties of growing lesions. To represent not only a realistic instantaneous lesion, but to additionally represent the growing lesion at arbitrary timepoints, the time evolution of individual cells was included in the model. To control for the multiplicity of factors affecting lesions growing in different anatomical locations, a cohort of lung lesions with anatomically-determined oxygen concentration,^19–21 known cell-cycle duration,^22–27 and dynamic local pressure constraints²⁸ were generated using segmentations of lung CT images and solid meshes of those segmentations.

The computational modeling here was limited to non-small-cell lung cancers and was implemented initially on the level of single cells (here represented as ~ 10 μm in diameter). The model was initialized at a physical location (single-precision) corresponding to the voxelized location (16-bit integer) in the lung CT segmentations (unsigned 8-bit) corresponding clinical CT images.^29,30 The lung CT cases used in this work were segmented into 3 tissue classes: parenchyma, vasculature, and airway³¹ as shown in Figure 3.

FIGURE 3.

Projection images (upper-right, lower-left, lower-right) of individual (voxel-based) segmented tissue classes from a lung CT case consisting of parenchyma, blood vessels, and airways. Each tissue class is combined with the original CT image using a colored overlay in the upper-left of the figure

The initial growth (seed) location of the lesion was always chosen to be in a uniform region of parenchyma; the individual replicating cells that composed the growing lesion were treated as rigid spheres of 20 μm diameter which were embedded inside that parenchyma.³² In the initial time-step of the simulation (Δt = duration of 1 cell cycle),the initial cell produced its offspring anywhere in the solid angle surrounding it. Similarly, in the second time step, both existing cells produced their offspring sequentially in non-conflicting locations. The simulation continued this way until the cells were tightly packed and proliferation occurred only on the periphery of the lesion (at a size of approximately 400 μm in diameter).

The cell proliferation computations at this point were too computationally expensive to continue using the same method, so the method of accounting for individual cells within the entire volume of the lesion was replaced with an approximate method that considered the location of the cells and their probable behavior in the next time step of the simulation. At each time step in the approximate method, clusters of cells in units of 13 (one hexagonally-close-packed unit) existed in one of the states described in Figure 4: proliferating, dormant, or necrotic with corresponding probabilities of transitioning between each at the start of each time step. These states were determined based on factors relating to nutrient availability and geometric constraints, including: the oxygen diffusion distance in soft tissue as a function of the oxygen concentration^19–21 as well as the largest free solid angle for each individual cell cluster—that is, a determination as to whether or not a cell cluster physically had sufficient space to undergo cell division.

FIGURE 4.

The markov chain shows possible states for each of the cells in the lesion (proliferating, dormant, necrotic) and assigns the probability of transition from one state to another

When a cell previously blocked from proliferating (i.e., in a dormant state) regained access to free space due to cell migration, etc., it behaved according to Equation (7) and regained its proliferative properties after a fixed period of time (~2Δt). The overall behavior of relative cell cycle timing was determined according to^22–26 and the time-evolution of the size of the lesion was in agreement with the surface-constrained proliferation theorized^33,34 which states that the radius r of a large (i.e., radius > > cell size), growing lesion scales as

$$r\sim {\left(\frac{\beta r{*}^{3}t}{3}\right)}^{\frac{1}{3}},$$ (7)

where β is the fraction of cells near the surface of the lesion proliferating per unit time, r* is the thickness of the proliferating surface layer, and t is a time interval.

To accelerate the computation once the number of cells and cell clusters became a bottleneck for serial calculations, the lesions were partitioned into octal trees (Figure 5). The octal tree method³⁵ allowed determination of cell state and offspring position to be calculated independently for regions that were not spatially adjacent. This allowed for implementation of the cell simulation in a parallelized method. This method resulted in preservation of unique details of the morphology of the lesions and increased the computation speed.

FIGURE 5.

Octal tree partitioning of cells into quasi-independent regions. Spatial partitioning of cells enabled parallelized computation of cell status and decreased the time needed to generate a full lesion

Cell clusters in the dormant state for a long period of time (≥ 10Δt) were treated as stable in that state, so checks on the state of the cell were decreased accordingly to one evaluation per 10Δt. This allowed for processing power to be focused on new cell generation from proliferating cells and spatial conflict checking and resolution.

Cells that were determined to have become necrotic were bounded by a closed, watertight surface and their individual positions were removed from memory since no further computations were necessary with those cells. The surfaces determining the boundary between living and dead cells was recalculated at each time step and resulted in decreased usage of memory.

The probability of transition between states was modeled with a right stochastic matrix (c.f., Figure 4)

$$T_{ij}=\left(\begin{array}{ccc}{P}_{P\to P}& P_{P\to D}& P_{P\to N}\\ P_{D\to P}& P_{D\to D}& P_{D\to N}\\ P_{N\to P}& P_{N\to D}& P_{N\to N}\end{array}\right).$$ (8)

This matrix was calculated and updated based on spatial information and the approximate oxygen concentration due to the vascular density at the location of each cell cluster according to²¹ and a geometric constraint that ensured the minimum acceptable distance between two cells was ≥ 20 μm. This approach was continued until the lesion reach approximately 2 mm in diameter (shown in Figure 6), at which point an additional method used to consider the mechanical impact of the growth of the lesion on its anatomical environment was included.

FIGURE 6.

Nested volume renderings of four unique lesions. Nested inside the outermost surface is every prior lesion surface from 50 identically-spaced timepoints. The lesions shown are approximately 2 mm in diameter

2.2.1 |. Computational modeling: Lesion—environment integration and deformation

The initial “placement” and growth of the lesion was modeled in Section 2. After the lesion growth was simulated to a size at which it was generally visible at computed tomography (CT) resolution (i.e., a lesion size of 2 mm for lung lesions as simulated here), the lesion and its local anatomical environment were segmented by tissue type³¹ as shown in Figure 7. The segmented region was then used to generate a solid mesh of the lesion-local environment for use in finite element analysis (FEA).

FIGURE 7.

Projection images of (voxel-based) segmented lung tissue (upper-left, lower-left). The location of the highlighted spherical regions corresponds to the anatomy present in the cutaway volumetric meshes (upper-right, lower-right)

The solid mesh generation was done with TetGen³⁶ in order to represent both the geometry and topology of the anatomy present in the segmentation. The lesion and lung regions of the segmentation were bounded by separate watertight surfaces with the lesion surface entirely enclosed inside the lung region. The surfaces were meshed as piece-wise linear complexes without modifications to the surfaces meshes. The tetrahedra in the lung and lesion regions were assigned element attributes for lung and lesion tissue classes. The meshes were also adaptively sized such that they preserved fine detail in the morphology of the lesion without generating more small-volume tetrahedra than needed. This was controlled by constraining the maximum allowed radius-edge ratio for tetrahedra to 1.2 and constraining the dihedral angle to 15 ≤ θ ≤ 165 degrees.

The tissues were modeled according to their known aggregate mechanical properties. The parenchyma and blood vessels were modeled as an uncoupled Mooney-Rivlin material with a strain-energy function

$$W=c_1\left({\tilde{I}}_1-3\right)+c_2\left({\tilde{I}}_2-3\right)+\frac{1}{2}K{\left(\ln J\right)}^2,$$ (9)

where c₁, c₂ are material properties related to the Young’s modulus E and Poisson’s ratio ν of the material via c₁ + c₂ = E/(4 + 4ν), ${\tilde{I}}_1$, ${\tilde{I}}_2$ are the first and second invariants of the deviatoric right Cauchy-Green deformation tensor, K is the bulk modulus, and J is the determinant of the deformation gradient tensor. The average value of equivalent material properties (ν = 0.3, E = 5 kPa) were obtained from prior work^37–41 and assigned to the solid mesh elements corresponding to the parenchyma and blood vessels. The airways and the surfaces of the lungs were treated as boundary conditions (i.e., rigid bodies).

The growing lesion was treated as exerting pressure on the surrounding tissue as it grew.^28,42,43 As the lesions grew over a series of simulation time steps, the boundary surface was updated and the pressure exerted by the growing lesion was applied to the tetrahedral faces in the immediately adjacent tissue. This was accomplished by fitting an approximate surface around the growing lesion and using the vertices of the fitted surface to prescribe nodal displacements corresponding to the amount of lesion growth in each region (see Figure 8). The pressure that resulted at the surface of the lesion from the nodal displacement was used iteratively to update the transition matrix T_ij for each region. When the pressure exerted by the surroundings became greater than the pressure exerted by the growing lesion (or encountered a boundary condition), the cells in the affected area stopped proliferating. The time and complexity for this task varied with the complexity of the surrounding tissue and the location and the final size of the lesion, with larger lesions or lesions under more harsh or non-uniform pressure conditions requiring more computation time in both the growth and mechanical analyses. All FEA was completed using GIBBON and FEBio.^44,45

FIGURE 8.

Finite element analysis (FEA) of the mechanical effect of the growth of a lesion growing from approximately 2 to 10 mm in a 4 cm diameter region of lung tissue with each column corresponding to a single time step in the simulation. Nodal displacements are shown in the top row and mechanical stress is shown in the bottom row

The tissue displacement due to the growth of the lesion was stored in the form of a deformation gradient for each step of the finite element growth of the lesion. The corresponding region of the CT image was subsequently Lanczos up-sampled^46–48 (to provide display characteristics for the images that were in line with radiologist expectations in reading similar clinical cases) and the deformation was applied to the affected region of the image iteratively. When the final deformed state of the image was achieved, the image was down-sampled to its original spatial resolution in preparation for the final (image-domain, superposition) insertion of the lesion.

2.3 |. Image-domain lesion insertion

The final lesion specific to its modified anatomical region was assigned CT numbers in accordance with the average contrast of (contrast-enhanced) lesions in the dataset to the background tissue. The live regions of the lesion (proliferating, dormant cells) were assigned HU values distributed according to Solomon et al.¹ with an average contrast of 1000 HU and the necrotic regions of the lesion were assigned HU values such that the average contrast with the rest of the lesion was −200 with the same distribution shape as the live regions of the lesion. The image modulation transfer function (MTF) and noise power spectrum (NPS) were measured from each CT image and applied to the image of the lesion to ensure that the frequency and noise content of the lesion were degraded according to the quality of the surrounding image (see Figure 9). The lesion was then superimposed on the modified target region of the CT image (see Figures 10,11).

FIGURE 9.

A growing lesion subjected to example CT imaging conditions (MTF, NPS) shown growing over time from the time at which it is first visible to approximately 2 cm in diameter

FIGURE 10.

Projection images of spherical CT regions containing lesions inserted using the proposed method. The spherical region prior to the insertion is shown in the leftmost of each green box, with the region post-insertion shown in the center of each green box. The initial and final images are combined on the right side of each green box with new or modified features of the image shown in cyan, old features shown in red, and common features between the two in grayscale

FIGURE 11.

An example lesion (cyan) grown and placed into the CT image using the proposed method. Both the lesion and slight shifts in the lung marking are visible in cyan, with the unaltered details of the image shown tinted red

In order to establish the non-inferiority of the method of lesion insertion as proposed in this work with respect to a prior method as proposed by Solomon et al.,¹ a representative sample of synthetic lesions from both methods were used to create an observer study data set. The data set included 10 lesions from each method (20 total synthetic lesions) and 10 clinical lesions. A custom graphical user interface was designed for this study with modifiable window width and window level as well as slice scrolling capabilities. Each case of the study was automatically opened on the slice of the image on which the lesion was present (to provide the location of the lesion to the observers), though the observers were not constrained to a single slice of the CT image and were encouraged to scroll in the z-direction to evaluate each case as necessary. Observers were instructed to assign a score to each of the 30 cases ranging from 1–9 on the keyboard in the style of a Likert-type scoring system; a score of “1” for a given CT image indicated that the observer evaluated the lesion and determined that it was “definitely a synthetic lesion inserted into a clinical image”, a score of “9” indicated that they evaluated it to be “definitely a real lesion in a clinical image”. Upon entering the score for each case, the study automatically advanced to the next case. The order in which the CT data were shown was randomized for each instance of the study. The interface described was used to facilitate completion of the study with five board-certified cardiothoracic imaging radiologists.

3 |. RESULTS

The results were collected and combined for use with a multi-reader–multi-case (MRMC) analysis method.⁴⁹ The ability of the observers in discriminating between the superposition method of lesion insertion and real clinical lesions was compared to the ability of the observers in discriminating between the proposed (mechanical) method of lesion insertion and real clinical lesions. In order to determine the robustness of these measurements, each of the receiver operating characteristic (ROC) analyses included estimation of the area under the curve (AUC) with 95% confidence intervals (CIs) obtained via a bias-corrected percentile bootstrapping method.^50,51

The AUC corresponding to the radiologists’ discrimination between clinical lesions and synthetic lesions inserted using the proposed method was 0.49, with 95% CI lower and upper bounds of 0.36 and 0.61. The AUC corresponding to the radiologists’ discrimination between clinical lesions and synthetic lesions inserted using the simple superposition was 0.59 with 95% CI lower and upper bounds of 0.45 and 0.72. The ROC curves are shown in Figure 12.

FIGURE 12.

ROC curves comparing radiologist ability to discriminate between real clinical lesions in CT images and synthetic lesions inserted using the proposed method to ability to discriminate between real clincal lesions and synthetic lesions inserted using a simple superposition method. Shaded regions correspond to the 95% confidence interval (CI) for each ROC curve

The radiologist mean and standard deviation for the synthetic lesions inserted with the proposed method were μ ± σ = 5.8 ± 2.3 and for simple superposition insertion were μ ± σ = 5.5 ± 2.4, respectively. The clinical lesions were scored μ ± σ = 5.6 ± 2.3. Scores corresponding to “perfect” observation (correctly classifying each lesion image with full certainty) were μ ± σ = 3.7 ± 3.8.

4 |. DISCUSSION

A realistic VCT can enable robust and comprehensive evaluation and parameter optimization of CT imaging, which can in turn be used to improve or hone the diagnostic utility of medical imaging for specific clinical tasks. Requirements for these studies include robust operational models of imaging physics, a computational patient habitus, and integrated pathologies with a more robust ground-truth than can presently be acquired from imaging alone.

The model proposed in this work was developed and validated to address the problems associated with computational lesion that are modeled using an image-based approach by incorporating biological data specific to non-small-cell lung cancer tumors, local anatomical awareness of vascular density, the mechanical properties of lung tissues under stress conditions consistent with those induced by a growing tumor, and the corresponding pressure on the regions of the growing tumor.

Our developed lesion model can be used in the context of both hybrid CT images (i.e., inserted into clinical images) with robust modifications to the original CT image in order to accommodate the inserted lesion and can additionally be used as ground-truth voxel- or surface-based models that are interoperable with XCAT phantoms. The models created here can be used for both hybrid CT images and the simulated CT image approaches and can be used in longitudinal studies that are intended to quantify changes in the observed morphology or texture of the imaged lesion.

This work enables a more extensive analysis of imaging conditions that may be favorable in particular scenarios that were not previously accessible through the use of other models, particularly those situations in which a voxelized-phantom—ground-truth is necessary (i.e., in XCAT phantom, DukeSim,or other simulated imaging applications) or preferable to image-based, ground-truth—inferred lesion models. This work also enables work in longitudinal VITs in which it will be possible to simulated imaging of a lesion as it grows at arbitrary timepoints.

The lesion model and technique implemented here were simulated on 24 physical CPU cores at 2.67 GHz with 128 GB of DDR3 RAM using 1 Nvidia Titan Xp GPU as needed. The time required to simulate the growth of the lesions ranged from tens of minutes without incorporating FEA to several hours depending on the complexity of the lesion at each stage of growth, the complexity of the surrounding tissue solid mesh, and the proximity to restrictive boundary conditions.

This work has at least two added benefits that prior image-based models do not: first, it is based on information obtained from images as well as biological and mechanical information, and therefore contains an added layer of non-image-based validation; second, due to the awareness of the model to its anatomical surroundings, it provides more possible regions (i.e., more physical space in each CT image) in which it is plausible to insert lesions for use in future studies. This has the added benefit of addressing the problem of decreased variability found in image-only lesion models by incorporating the inherent anatomical variability already present in each patient scan.

This study has several limitations. For the validation of the model, the method of lesion image superposition and blending as utilized by Solomon et al.,¹ was used here with lesions larger and more conspicuous than in prior work, although the ROC-AUC for lesions inserted using that method in this study aligned well (AUC = 0.59) with the previously reported results (AUC = 0.55). Additionally, the model of tissue deformation in the immediate vicinity of the lesion was hyperelastic and therefore included no irreversible damage or destruction of tissue. The tissue material parameters used in the simulations were gathered from studies observing larger-scale lung tissue mechanics rather than lesion-scale local disturbances. The scale of the mechanical deformations to lung tissue during in vivo tumor growth is relatively small and takes place slowly due also to changes in the microenvironment, resulting in some combination of elastic and plastic deformation (i.e., both stretching and damage of tissue) rather than hyperelastic deformation. Modifications of the tissue on the micro-scale are not included in this model, as they occur well beyond the spatial resolution of both clinical CT and also would be challenging to implement computationally due to a lack of available microscale material property measurements and memory requirements associated with simulating changes to structures whose size differs by many orders of magnitude. Direct comparison of the present model and Solomon’s lung lesion model indicate areas of weaknesses and strengths for both: first, the present model has the obvious disadvantage of requiring additional computation and computational time for equivalent hybrid-CT image domain results—making it less efficient for hybrid-CT; however, the present model is more flexible in the domain of entirely digitized patients and CT imaging simulations. For similar studies or applications, Solomon’s method is likely sufficient. For future work with anthropomorphic computational phantoms, however, the present method is preferred.

Although it is not explored in this work, the current lesion model can also be used in imaging simulations that extend beyond CT and other ionizing modalities and can also be useful in non-ionizing imaging simulations due to the biologically-informed anatomical ground-truth that this model offers in both surface- and voxel-based formats. In future work, we envision extension of this model to multiple organs and encompassing multiple common disease types (e.g., hepatocellular carcinoma, renal cell carcinoma), as well as some organ-specific modifications to the model, such as incorporation of finite-element architectural distortion due to lesion-induced formation of fibrous tissue in breast lesions. Lastly, we intend to use the growth features specific to this model in longitudinal virtual imaging studies with dynamic (i.e., 4D) virtual phantoms to assess the quantitative features of growing lesions as a function of time.

5 |. CONCLUSION

Modeling of realistic, biologically-informed pathologies are is a necessary component in the effort to conduct virtual clinical trials virtually. The techniques and model developed in this study, when combined with either clinical CT data (to form a so-called “hybrid” image) or when combined with virtual anthropomorphic phantoms like XCAT and imaged with realistic CT simulators like DukeSim enable the quantification of CT imaging of dynamic tumors.