Fig 1.
The multiscale nature of BE screening.
Biopsy screening for BE scales from stem cells in the crypt (left) to the BE cylindrical segment of the esophagus depicted (right) with rectangles representing biopsy samples taken during endoscopy via the Seattle biopsy protocol. The BE segment may have dysplasia and/or malignant tissue patches that remain untouched after biopsying. During histological preparation, portions of each biopsy are sliced by microtome and placed on slides for pathologic assessment. Diagnosis is made by microscopic interpretation of crypt and cellular architecture, reflecting the most severe tissue grade found from all slides.
Fig 2.
The multistage-clonal expansion model for EAC (MSCE-EAC) cell module.
Normal squamous epithelium may transform to BE with an exponentially distributed onset time with rate ν(t), followed by a ‘two-hit’ tumor initiation process with Poisson initiation rates μ0, μ1, which leads to the stochastic appearance of premalignant progenitor cells in the tissue. Premalignant cells undergo a first clonal expansion described by a birth-death-migration process with cell division rate αP, cell death-or-differentiation rate βP, and malignant transformation rate μ2. Malignant cells, in turn, undergo a second clonal expansion by a birth-death-detection process with cell division and death rates αM and βM, respectively, allowing for stochastic growth and possibly extinction of the malignant tumor. Clinical detection occurs through a size-based detection process with parameter ρ. TSG, tumor suppressor gene.
Table 1.
MSCE-EAC model biological parameters.
Fig 3.
A) Premalignant (dysplastic) clone growth stochastic trajectories are depicted for a sample male BE patient from the 1930 birth cohort, beginning five years before time of initial screen at age 60. Most dysplastic cell progenies from a single initiated cell went extinct before examination by endoscopy (trajectories depicted by gray lines and an ‘x’ at time of extinction). The dysplastic clone trajectories that did not go extinct before index screen are shown in dark pink with final sizes intersecting the vertical dotted line. The dots on trajectory lines correspond to times of asymmetric division of a dysplastic cell to produce one dysplastic cell and one malignant cell. Malignant transformations produce both clones that quickly went extinct before age 60 (black dots) and non-extinct malignancies (red dot). B) BE segment at time of screening. Same simulated male patient from (A) with BE of length 5.1 cm. Dysplastic clones (dark pink), malignant clone (red), and biopsies (black dashed rectangles) are pictured at time of biopsy-based screening, age 60. Clone diffusivity parameter is γ = −2.
Fig 4.
High grade dysplasia prevalences in BE estimated with the MSCE-EAC screening model.
(Left panel) Probability of high grade dysplasia detection among BE patients simulated by the MSCE-EAC screening model for males (red, solid) and females (blue, dash-dotted) at initial screen at age 60 for biopsy sensitivities ranging from 10%–95% and assumed density of σ = 3300 stem cells/mm2 (shaded regions represent sensitivity of results for σ ∈ [2000, 5000]). Since the sensitivity of each study is unknown, literature values for the corresponding probability of HGD detection are depicted as horizontal grey dotted lines at a single percentage level [25, 30–34]. Expected prevalences produced by 100K simulation size of BE patients, shown for males and females. Simulation standard error is less than .001 for all Results. (Right panel) Male HGD prevalences produced by diffusive clone growth on hexagonal BE grid, for diffusivity parameter γ ranging from 1 to −8, versus isotropic, circular clone assumption (red, solid). Solid curve is the same as that shown for males in left panel. Probabilities of finding HGD for spatially simulated diffusive clone growth are shown for σ = 3300 stem cells/mm2 and identical biopsy sensitivities as shown in left panel. As explained in Methods, the assumption of γ = 1 results in almost identical prevalences to the circular clonal growth assumption. Overall, the results from 10K simulated male BE patients yield very similar prevalences regardless of clone shape for mid-range biopsy sensitivities.
Fig 5.
Predicted probability of missed malignancy in positive high grade dysplasia population at index screen.
Percentages of patients diagnosed with HGD during index endoscopy (denominator is population plotted in Fig 4) who concurrently harbored missed, malignant clone(s) present on their BE segments that were not detected on biopsy screen. Since the sensitivity of each study is unknown, literature values for the corresponding probability of missed malignancy are depicted as horizontal grey dotted lines at a single percentage level [25, 30–34]. One publication included percentage of occult malignancy after HGD was diagnosed with either standard or jumbo forcep sizes, as indicated [38]. Expected proportions produced with 100K BE patient simulations each for males (red, solid) and females (blue, dash-dotted) with assumed density of σ = 3300 stem cells/mm2 (shaded regions represent sensitivity of results for σ ∈ [2000, 5000]).
Fig 6.
Predicted EAC cumulative age-specific incidence by the MSCE-EAC screening model after RFA treatment of HGD patients at index screen.
EAC cumulative age-specific incidence for four different ablation efficiencies of detected HGD patients at screening of 60 year old males in year 2010. Survival for the four cell types following ablation modeled are represented by ablation proportion vector ω, with ω = {1, 1, 1, 1} (no treatment, blue line), ω = {.5, .5, .5, .5} (red, circles), ω = {.01, .01, .01, .01} (purple, diamonds), ω = {1, 1, 1, 0} (light blue, triangles), ω = {1, 1, 0, 0} (green, squares). Scenarios plotted for σ = 3300 stem cells/mm2 and 60% biopsy sensitivity, resulting in 6% HGD cases, without detected malignancy, in the non EAC population at screening time (100K BE patient simulation size).