SKOV3.ip.1 parental cells and GFP-stable transfectants were kind gifts of Laurie Hudson and Angela Wandinger-Ness (UNM). This aggressive line was passaged through a nude mouse (Yu et al., 1993). Cells were maintained in RPMI-1640 medium supplemented with 5% heat-inactivated FBS, 1% l-glutamine, 1% sodium pyruvate, and 0.5% penicillin/streptomycin (Invitrogen, Grand Island, NY, USA). SKOV3.ip1-GFP cells were treated with 250 μg/ml hygromycin to maintain GFP expression. To create RFP-expressing SKOV3.ip1 cells, parental cells were transfected with the pTagRFP-N vector (Axxora, San Diego, CA, USA) using Lipofectamine LTX reagent (Invitrogen). Stably fluorescent cells were selected with geneticin sulfate (Invitrogen) for 1 week. Transfectants were sorted for high fluorescence using a Beckman Coulter Legacy MoFlo cell sorter (UNM Flow Cytometry Core Facility).

All mouse procedures were approved by the University of New Mexico Animal Care and Use Committee, in accordance with NIH guidelines for the Care and Use of Experimental Animals.

Nu/nu nude mice (NCI) or nude mice ubiquitously expressing RFP (Anticancer Inc., San Diego, CA, USA) (Yang et al., 2009) were engrafted by intraperitoneal injection with 100 μl of a single cell suspension containing five million SKOV3.ip1 cells expressing GFP. Tumor adhesion and invasion was assessed at 4 days and 2 weeks post-injection. For low magnification assessment of total tumor burden, eight nude mice were imaged using a Pan-A-See-Ya Panoramic Imaging System (Lightools, Inc., Encinitas, CA, USA) 2 or 3 weeks post-injection of SKOV3.ip GFP cells. For improved resolution images (up to 16×, single cell resolution), mice were imaged on the OV100 Olympus whole mouse imaging system (Olympus Corp., Tokyo, Japan) at AntiCancer, Inc., San Diego, CA, USA, as previously reported (Yamauchi et al., 2006).

Where described, sections of intestine and attached mesentery with tumors were excised (Fu and Hoffman, 1993) and fixed in zinc fixative for 30 min (Howdieshell et al., 2011). Samples were mounted on glass slides with ProLong Gold mounting media (Invitrogen). GFP fluorescence and brightfield images were collected on a Nikon TE2000 Microscope (UNM Microscopy Core Facility) using an Axiocam digital color camera and SlideBook Image Acquisition software.

SKOV3.ip1-GFP cells and SKOV3.ip1-RFP cells (2.5 × 10⁶ each population) were harvested from culture by trypsinization and mixed together as a single cell suspension immediately before injecting a total of five million cells into the peritoneum of three nude mice. For consecutive injections, 2.5 million SKOV3.ip1-GFP cells were injected IP into three nude mice followed by injection of 2.5 million SKOV3.ip1-RFP cells a week later. The mice were sacrificed at the end of week 2 and tumors were imaged on the OV100.

Mouse tumors were fixed in formalin or zinc fixative, embedded in paraffin, sectioned and hematoxylin/eosin (H&E) stained by TriCore (Albuquerque, NM, USA) or processed for immunofluorescence using anti-CD31 antibodies (BD Biosciences, San Jose, CA, USA). Images were acquired on a Zeiss AxioSkop or LSM500 confocal microscopes. The area of mesenteric tumors was determined by analysis of images from H&E-stained sections using ImageJ (Schneider et al., 2012). The cross-sectional tumor area corresponding to the hypoxic threshold was calculated to be <104,000 μm² based on the diameter of the spheroid in Figure 7B (364 μm).

Tissue was collected and fixed in 2% glutaraldehyde, post-fixed with osmium tetroxide, dehydrated in ascending alcohols, and embedded in Epon. Ultra-thin sections were stained and imaged on a Hitachi H600 transmission electron microscope (TEM). To identify SKOV3.ip1 cells present in tissue samples, their characteristic nuclear ultrastructure was determined from high magnification TEM images taken of SKOV3.ip1-GFP cells grown as 5,000 cell spheroids in a U-bottom Lipidure-coated 96-well plate (NOF America, Irvine, CA, USA) for 48 h.

We based our model on the following set of major assumptions that are inspired by the biology and empirical data.

The three-dimensional (3-D) tissues we model consist of ovarian tumor (SKOV3.ip1), mesothelial, adipocyte, endothelial, and smooth muscle cells, as well as ECM fibers and peritoneal fluid.

In the OvTM, five cell types are considered: ovarian tumor (SKOV3.ip1), mesothelial, adipocyte, endothelial, and smooth muscle. ECM fibers and peritoneal fluid are represented as special types. This cell-based model describes cell growth, division, death, and chemotactic migration within a 3-D tissue environment that mimics the specific organ site.

Cells are domains on a 3-D lattice. Each cell has an ID number, S, on each lattice site i of the cell domain, and an associated cell type τ. Cell–cell and cell–environment interactions are specified by an “effective energy”: (1)H=∑i,jJτSi,τSj1-δSi,Sj+∑SλVS-Vt(S)2+∑iμCi.

The parameter J describes the cell-type-dependent adhesion. Adhesion coefficients (J) for the cell types in each model are listed in Tables 2 and 3. The Kronecker delta function δ ensures no energy is within cells where ID numbers are the same, limiting adhesion to cell boundaries. A cell’s volume V is elastically constrained to V^t, the target cell volume; V^t is constant for the tissue cells, but is set to increase linearly for proliferating cells. μ is the chemical potential describing the strength of chemotaxis, and C is the chemical concentration at the cell. This term applies to cancer and endothelial cells when their respective chemoattractant signals are above threshold activation values.

A modified Metropolis algorithm was used to simulate cell dynamics. A cell boundary lattice site is selected at random; the cell number, S, is copied to an unlike neighbor site S′ (selected at random). This copying corresponds to the cell S protruding a unit volume into the neighboring cell S′. The difference between the effective energies before and after the protrusion event, E, determines if this copying event will be accepted. If the energy decreases, the protrusion is accepted; if it increases, the protrusion is accepted with a Boltzmann probability, exp(−E/T). The effective temperature, T, describes the amplitude of cytoskeletal fluctuation (Mombach et al., 1995). By such microscopic membrane protrusion and retraction, the cells perform biased random walks, and rearrange themselves, within the constraints of their volumes and chemical guidance.

To recapitulate the essential steps in ovarian cancer relapse from minimal residual disease in the peritoneum, five million SKOV3.ip1 human ovarian cancer cells expressing GFP were injected into the peritoneum of nude mice as a single cell suspension. Mice were euthanized after 2 weeks and mounted on the stage of an OV100 fluorescence imaging system. As shown in Figure 1A, macroscopic tumors developed on numerous organs in the peritoneum during this period. The main sites of attachment were the omentum (Figures 1A,B), the surface of the stomach (Figure 1C) and small intestine, the mesentery (Figure 1D) and the spleen (Figure 1E). Tumors also developed on the liver in half of the mice examined. The largest tumors grew from the omentum and expanded into the peritoneum, reaching volumes up to 200 mm³ by 2 weeks. Even within this short time frame, the tumors are well vascularized with vessels penetrating and wrapping around the outside of the largest tumors. Many smaller tumors can be found attached to the mesentery, often visible to the naked eye, ranging in size from 0.4 μm³ to 1 mm³.

It has been hypothesized that ovarian cancer cells aggregate and form spheroids when suspended in peritoneal fluid and that these spheroids then attach to the peritoneal surface and form large tumors (Shield et al., 2009). To test this hypothesis and to assess the clonality of the tumors at distinct sites, a mixture of SKOV3.ip1-GFP and SKOV3.ip1-RFP cells were co-injected into nude mice as a single cell suspension. The resulting tumors were imaged 2 weeks later. Tumors on the omentum developed as well-mixed chimeras, with both green and red fluorescence throughout (Figures 2A,B). In higher magnification images, small areas with predominantly red fluorescence can be distinguished from areas with predominantly green fluorescence, but there are no large sections of tumor expressing a single fluorescent protein (Figure 2C). The majority of the observed mesenteric tumors (92 ± 2% of 51 observed tumors) also have mixed green and red fluorescence, indicating that even these small tumors originated from a mixed spheroid (Figures 2D,E). The few small tumors consisting solely of GFP-positive or RFP-positive cells may represent rare instances where a single cell, or a small group of singly fluorescent cells, was able to adhere and grow (Figure 2E, arrow).

These data provided the first essential parameters for initialization of our OvTM mathematical model, since adhesion is a predominant feature of the cellular Potts framework (Graner and Glazier, 1992). Simulations were initiated with an adherent spheroid on the surface of the intestine. The spheroid subsequently pushes through the mesothelium. This process has been observed in vitro, where tumor spheroids cause retraction of the mesothelium using a myosin-mediated process (Iwanicki et al., 2011).

The in silico experiments using OvTM showed that only by assigning high homotypic adhesion strength to the cancer cells could the model reproduce spheroid cohesiveness and growth (Figure 2F). For details on how the adhesion parameters were optimized, see Section “Materials and Methods” (Table 3). Simulations in which cancer cells adhered more strongly to other cancer cells than to any other cell type, produced the most rounded tumor morphology that closely resembled the xenograft tumors. Adding a cellular surface area constraint maintained the integrity of the cells themselves. Since the model indicated that tumor cell homotypic adhesion is an essential feature governing dissemination and growth, this concept was further tested experimentally by sequentially introducing fluorescent cancer cells into the peritoneum (Figure 3). In this experiment, tumors were first established by injection of 2.5 million SKOV3.ip1-GFP cells. After a period of 1 week to permit engraftment of the green-fluorescent cells, an equal number of SKOV3.ip1-RFP cells were injected. Following another week, the relative distribution and burden of both green and red fluorescent tumor cells were evaluated. As expected, SKOV3.ip1-GFP tumors formed on the omentum, mesentery, and spleen. Notably, the majority of red fluorescent cells adhered to and enveloped the pre-existing GFP-positive tumors as can be seen on the omental tumors (Figure 3A) and on the spleen (Figure 3B), rather than forming tumors independently. Although some exclusively RFP-positive tumors were present on the mesentery (Figure 3C, arrows), 70% of the 24 RFP-positive tumors examined were also GFP-positive.

Our next goal was to identify specific features of the microenvironment that underlie differences in ovarian tumor morphology by examining the structure of external tissue layers facing the peritoneum. Both normal and tumor-associated tissues were extracted and prepared for TEM imaging. The micrograph in Figure 4A illustrates the open architecture of the normal mesentery, with loosely packed fat cells below the mesothelium. The mesothelial layer is remarkably thin in some areas, ranging from 0.4 to 2.5 μm in thickness. A second image (Figure 4B) shows a cross-section of mesentery excised from mice engrafted with SKOV3.ip1 human ovarian cancer cells. Labels mark the locations of probable tumor cells, identified by the characteristic ultrastructure of their nuclei. The tumor cells are interior to the mesothelium and adjacent to a small blood vessel.

To understand how tumors are established in the mesentery, SKOV3.ip1-GFP cells were injected into the peritoneum and 4 days later segments of the mesentery were removed for whole mount imaging. As shown in Figures 4C,D, images from this early time point provide a window into the initial steps in the engraftment process. Small groups of fluorescent cancer cells were seen within the mesenteric adipose layer (Figure 4C) or beneath the adipose layer immediately adjacent to vessels (Figure 4D).

We next used OvTM to evaluate the conditions necessary for cancer cells to migrate to mesenteric vessels within this short time period. The cellular Potts model is particularly well suited for this type of modeling, since it specifically represents cell–cell interactions and cell movement, which is governed by local contacts and chemotactic gradients. The 3-D stochastic model was populated with heterogeneous cell types (cancer cells, adipocytes, endothelial cells, and mesothelium) and geometric features (shape, location, organization, and thickness of tissue layers) based on TEM images. Extracellular factors, such as chemokines and oxygen, are described by diffusion equations with sources and sinks. In each case, cancer cells push through the mesothelial layer and degrade the underlying ECM, as shown experimentally (Sodek et al., 2008). Simulations can then demonstrate the extent of tumor invasion in response to different chemotactic environments.

Figure 5 shows results from three scenarios that were considered in these simulations. Movies for representative simulations are provided in Supplementary Data (Movies S1–S3 in Supplementary Material). For each case, a spheroid of seven cancer cells was initially positioned on a 3-D geometrical model of the mesentery. Mesothelial cells form the boundary with the peritoneum; adipocytes are dispersed within the interior, and a single vessel transverses the tissue.

In the first scenario, there is no local production of chemotactic factors imposed. The spheroid is positioned such that it is in contact with the ECM. In the absence of chemotactic factors, the spheroid dissolves the ECM and presses into the adipose tissue after 2 days (Figure 5A). This progression is too slow to explain cancer cell localization near mesenteric blood vessels in the mouse model.

SKOV3.ip1 cells have been shown to home toward chemokine-producing adipocytes and upregulate the IL-8 receptor (CXCR1) when co-cultured with adipocytes (Nieman et al., 2011). Therefore, in the second scenario, simulation parameters were modified such that all adipocytes within the mesentery secrete IL-8 at a rate of 2.2 × 10⁻⁴ pg/min/cell (Bruun et al., 2004), which diffuses at 1.5 × 10⁴ μm²/min (Li Jeon et al., 2002). Cancer cells are then allowed to chemotax up the resulting IL-8 gradient. In our model, spheroid invasion of the ultra-thin mesothelium is rapid, occurring at a rate of 10 μm/h based upon the in vitro experiments of Iwanicki et al. (2011). The pseudo-colored image in Figure 5B shows the predicted distribution of IL-8 in the mesenteric tissue at steady state, illustrating the initial conditions experienced by the tumor spheroid. Simulated IL-8 concentrations within the peritoneum agree with those measured experimentally (Barcz et al., 2002). When IL-8 chemotaxis is included in the simulation, the spheroid moves past the mesentery barrier and pushes between adipocytes to settle near the center of the adipose layer where the IL-8 concentration is greatest (Figure 5D). This occurs within 500 min after initialization. In this case, rapid chemotaxis occurs, but the cancer cells do not localize near the vessel.

In the final case, both adipose and endothelial cells are assumed to produce chemotactic factors that attract cancer cells. We introduce a new chemotactic factor (Chemotactic Factor 2) that originates from the mesenteric vessel. Steady-state values represented in the pseudo-colored profile in Figure 5C show that a significant gradient can be established by endothelial cell secretion of Chemotactic Factor 2 at a rate of 1.8 × 10⁻⁴ pg/min/cell, which is comparable to that of IL-8 secretion from the adipocytes, and assuming diffusion and decay rates similar to VEGF. When cells are arranged in this geometry, the presence of both chemotactic gradients causes spheroids to penetrate the mesothelial layer, move by chemotaxis through the loose adipose layer toward the vessel, and halt at the tightly adherent barrier of the vessel wall (Figure 5E). Together with the experimental data, these results support the conclusion that both adipocytes and endothelial cells are likely sources of chemokines that attract ovarian tumor cells.

We next focused on explanations for the distinct morphology of tumors attached to the stomach or small intestine, which do not invade the tissue and instead grow outward into the peritoneal cavity (Figure 6A). We again sought insight from high resolution TEM images. As shown Figure 6C (mesentery) and Figure 6D (stomach), the outer mesothelial layer remains relatively thin over these organs (typically 0.5 μ thick). The next layer is distinguished by dense collagen deposits. Prominent smooth muscle layers can be seen in both the small intestine and stomach, where the muscle cells are closely opposed and connected by gap junctions (Friend and Gilula, 1972) (arrows, Figure 6B).

The morphology of a tumor attached to the outer rim of the lower intestine is seen at a lower magnification in Figure 6E, which shows a representative section from a formalin-fixed, paraffin block stained with H&E (hematoxylin and eosin). The smooth muscle of the small intestine remains intact at the tumor/tissue interface. Thus, tumors attached to the exterior of the gut are presented with a discrete barrier and adapt by growth into the available and flexible space between organs. The intestine has a capillary bed that provides oxygen to the mesothelium and contributes to the oxygenated peritoneal environment (Figure 6F). Because of the lack of a smooth muscle barrier, these vessels may provide a more accessible endothelial source for neoangiogenesis critical to tumor success.

Microscopic evaluations provide support for this hypothesis (Figures 6B,E). Fluorescence imaging shows the remarkable extent of tumor vascularization, even in young GFP-positive tumors attached to the intestinal wall at 2 weeks post-engraftment (Figure 6B). A red arrowhead in Figure 6E points to a vessel visible within the tumor cross-section. This evidence led us to conduct simulations to explain the rapid onset of neovascularization in the absence of invasion.

For the in silico model of angiogenesis, micron-scale geometric parameters for the tissue surface architecture were again determined from TEM images. For the gut, adhesion between smooth muscle cells is set sufficiently high as to prevent spheroid penetration below the mesothelial and collagen layers. Under these constraints, simulations of tumor adhesion and growth result in the formation of spherical tumors that are consistent with the morphology of engrafted tumors on mouse intestine (compare Figures 6A and 7C). Since these simulations incorporate published values for oxygen content in the peritoneal fluid and oxygen diffusion rate (MacDougall and McCabe, 1967; Kizaka-Kondoh et al., 2009), it is possible to calculate the distribution of oxygen in all locations during tumor growth. By coarse-graining the model (1 voxel = 1 cell), we were able to determine the oxygen concentration gradients for large spheroids suspended in the peritoneal fluid. In spheroids of varying sizes, oxygen concentration decreased within the core. However, spheroids up to 336 μm in diameter (58,000 cells) approach the hypoxic threshold of 19 mm Hg of O₂ (Höckel and Vaupel, 2001), but are not yet hypoxic at their core (Figure 7A). Continued growth to 364 μm in diameter (74,000 cells) results in a hypoxic core with an oxygen concentration of 0.5 mm Hg (Figure 7B), leading to the prediction that the hypoxic threshold is reached when the spheroid is between these two sizes. Tumor sizes in mouse samples were compared based on the cross-sectional area of tumors in H&E-stained sections. Mesenteric tumor vascularization with respect to tumor area is shown as scatter dot plots in Figure 7E. Of the 76 tumors measured, all tumors above the predicted hypoxic threshold (red) were vascularized. However, 57% of small tumors with an area of <104,000 μm² (below the predicted hypoxic threshold) were also vascularized. These results suggest that angiogenesis is not solely hypoxia-driven in the SKOV3.ip1 model.

In the next series of simulations, we examined how angiogenesis might originate from these spheroids in the absence of hypoxic signaling. There is experimental evidence that SKOV3.ip1 cells constitutively express VEGF in vivo and in vitro even when maintained in well-oxygenated tissue culture conditions (Yoneda et al., 1998). Secretion of VEGF by the cancer cells was therefore incorporated into these simulations. Small spheroids attached to the gut penetrate the mesothelial layer, permitting VEGF secreted from cancer cells to initiate chemotactic gradients and attract endothelial cells that line blood vessels in the sub-mesothelial layer. The process of angiogenesis is driven by endothelial cell chemotaxis toward VEGF, and adhesive interactions between endothelial sprout cells and cancer cells. To produce vasculature visually similar to that in very small xenograft tumors, latent endothelial cells must begin to proliferate and migrate as soon as the spheroid comes close enough to the vessel to allow diffusion of low concentrations of VEGF. Given spheroid VEGF production of 3.82 × 10⁻⁷ pg/min/SKOV3.ip1 cell, the threshold for the switch from latent to sprouting endothelial cells was set at 2.08 × 10⁻⁸, to initiate angiogenesis when the spheroid is ∼5 μm from the vessel.

Angiogenesis in the OvTM model follows validated methods that treat VEGF as diffusible molecules whose gradient, together with the biophysical environment, drives endothelial migration and proliferation, and eventually morphogenesis of vessel sprouts (Bauer et al., 2007; Shirinifard et al., 2009). Parameters and model assumptions are described in the Materials and Methods. Simulation results show that constitutive production of VEGF from even a small spheroid of SKOV3.ip1 cells should be capable of initiating vascular outgrowths that penetrate the spheroid within 12 h of attachment (Figure 7D; Movie S4 in Supplementary Material). Results of the computational model are consistent with our experimental observations that even very small tumors, comprised of less than 20,000 SKOV3.ip1 cells, are fully vascularized (Figure 7F). They are also consistent with 3-D images of tumor slices stained for confocal fluorescence imaging that show extensive tumor vascularization 3 weeks post-injection (Figure 7G). In this final image, an anti-CD31 antibody (red) marks endothelial cells, Hoechst (blue) stains the cell nuclei and an anti-GFP antibody (green) labels the GFP-positive cancer cells. A rotating 3-D view of this tumor section is found in Movie S5 in Supplementary Material.