An Integrated Computational/Experimental Model of Lymphoma Growth

<div><p>Non-Hodgkin's lymphoma is a disseminated, highly malignant cancer, with resistance to drug treatment based on molecular- and tissue-scale characteristics that are intricately linked. A critical element of molecular resistance has been traced to the loss of functionality in proteins such as the tumor suppressor <i>p53</i>. We investigate the tissue-scale physiologic effects of this loss by integrating <i>in vivo</i> and immunohistological data with computational modeling to study the spatiotemporal physical dynamics of lymphoma growth. We compare between drug-sensitive <i>Eμ-myc Arf-/-</i> and drug-resistant <i>Eμ-myc p53-/-</i> lymphoma cell tumors grown in live mice. Initial values for the model parameters are obtained in part by extracting values from the cellular-scale from whole-tumor histological staining of the tumor-infiltrated inguinal lymph node <i>in vivo</i>. We compare model-predicted tumor growth with that observed from intravital microscopy and macroscopic imaging <i>in vivo</i>, finding that the model is able to accurately predict lymphoma growth. A critical physical mechanism underlying drug-resistant phenotypes may be that the <i>Eμ-myc p53-/-</i> cells seem to pack more closely within the tumor than the <i>Eμ-myc Arf-/-</i> cells, thus possibly exacerbating diffusion gradients of oxygen, leading to cell quiescence and hence resistance to cell-cycle specific drugs. Tighter cell packing could also maintain steeper gradients of drug and lead to insufficient toxicity. The transport phenomena within the lymphoma may thus contribute in nontrivial, complex ways to the difference in drug sensitivity between <i>Eμ-myc Arf-/-</i> and <i>Eμ-myc p53-/-</i> tumors, beyond what might be solely expected from loss of functionality at the molecular scale. We conclude that computational modeling tightly integrated with experimental data gives insight into the dynamics of Non-Hodgkin's lymphoma and provides a platform to generate confirmable predictions of tumor growth.</p> </div

Prediction of lymphoma growth based on the calibrated model parameters.

<p>Simulated mean tumor diameter (solid red line) bounded by variation in the measured oxygen diffusion distance (dashed red lines) falls within the range of values measured for the tumor growth observed <i>in vivo</i> (denoted by the triangles and squares with vertical error bars). Note that the simulated growth is the same for both <i>Eμ-myc Arf-/-</i> and <i>Eμ-myc p53-/-</i> tumors.</p

Lymphoma tumor characteristics.

<p>Histological measurements are shown <i>Eμ-myc Arf-/-</i> (black) and <i>Eμ-myc p53-/-</i> (gray) tumors along the five sets of sections (S1 through S5) of the lymphoma: (A) Endothelial cells per area; (B) hypoxic cells per area; (C) proliferating cells per area; (D) apoptotic cells per area. Sections S1 and S5 are at the tumor top and bottom, respectively, while the other sections are in the interior with S3 being in the middle. Dashes in panels (A) and (C) indicate that no data was obtained; in panel (C), no proliferation was detected for <i>Eμ-myc p53-/-</i> cells in sets S4 and S5, and none for <i>Eμ-myc Arf-/-</i> in set S5, probably due to sample defects. All error bars represent standard deviation from at least n = 3 measurements in each section; asterisk indicates statistical significance (p<0.05) determined by Student's t-test with α = 0.05. The data shows that for <i>Eμ-myc p53-/-</i> there is higher vascularization in the center, higher hypoxic density on the periphery, and higher overall apoptotic density compared to <i>Eμ-myc Arf-/-</i>.</p

Schematic showing integrated computational/experimental modeling strategy involving both cell- and tumor-scale measurements.

<p>(<b>A</b>) Functional relationships involving cell-scale parameters such as proliferation (Ki-67), apoptosis (Caspase-3), and hypoxia (HIF-1α) are defined based on experimental observations, e.g., from immunohistochemistry the density of viable tissue as a function of vascularization is shown in the third panel (red: highest density; yellow: lowest; blue: vessels). These functional relationships as well as parameter values measured experimentally are then used as input to the model to create simulations of lymphoma growth. A sample simulated tumor cross-section showing vascularized viable tissue (highest density in red, lowest in yellow, with vessel cross-sections as small blue dots) is shown at the far right. (<b>B</b>) Lymphoma observations regarding size, morphology, and vasculature from macroscopic imaging of an inguinal lymph node in live mice provide part of the tumor-scale information to validate the model simulations. Note the pre-existing vasculature in the lymph node (in the center of each frame) from which oxygen and nutrients are supplied to the tissue. For comparison, a control group of lymph nodes in animals without tumors is also shown.</p

Vasculature and angiogenesis in the lymph node tumor.

<p>Observations in living mice using intravital microscopy (A, B, C: red – functional blood vessels; shown for <i>Eμ-myc p53-/-</i> tumor) provide information to qualitatively compare the vessel formation (D, E, F: red – highest flow; white – lowest; dots indicate vessel points of origin from pre-existing vasculature (not shown)) in the computational model (calibrated from other data, see <b><a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003008#pcbi.1003008.s004" target="_blank">Text S1</a></b>). The modeling of diffusion of cell substrates (e.g., oxygen and cell nutrients) within the tumor enables prediction of the spatial distribution of lymphoma cells (inset, shown for one vessel cross-section; brown: highest concentration of cells; white: lowest concentration of cells) as their viability is modulated by access to the oxygen and nutrients diffusing from the vasculature into the surrounding tissue (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003008#pcbi.1003008.e002" target="_blank"><b>Eq. 2</b></a>).</p

Scheme to obtain the cellular-scale experimental data.

<p>Lymphomas (shown as large orange sphere) were grown <i>in vivo</i> by tail vein injection of either drug-sensitive <i>Eμ-myc/Arf-/-</i> or drug-resistant <i>Eμ-myc/p53-/-</i> lymphoma cells. The inguinal lymph node tumor was excised, fixed, and sliced for histology sections (5 µm apart) every 100 µm along the tumor. A total of five sets (S1 through S5) of histology sections were obtained (for simplicity, the figure only shows three sets). The sections in each set were stained for cell viability (H&E), hypoxia (HIF-1α), proliferation (Ki-67), apoptosis (Caspase-3), and vascularization (CD-31).</p

Algorithm flowchart.

<p>Refer to <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003008#s2" target="_blank"><b>Materials and Methods</b></a> and <b><a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003008#pcbi.1003008.s004" target="_blank">Text S1</a></b> for equations. Using the cellular-scale data, we measured values for proliferation and apoptosis for both drug-sensitive and drug-resistant tumors and calculated corresponding values for the model mitosis and apoptosis parameters <i>λ</i>_M and <i>λ</i>_A. We solved <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003008#pcbi.1003008.e002" target="_blank">Eq. (2)</a> for the local levels of cell substrates <i>n</i> at each time step of simulation of tumor growth. The parameters were input into <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003008#pcbi.1003008.e010" target="_blank">Eq. (3)</a> to numerically calculate the source mass terms <i>S_i</i>, which were then used in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003008#pcbi.1003008.e001" target="_blank">Eq. (1)</a> to compute the volume fractions of viable <i>ρ</i>_V and <i>ρ</i>_D dead tissue. These fractions were used in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003008#pcbi.1003008.e011" target="_blank">Eq. (4)</a> to obtain the tumor tissue growth velocity.</p

Lymphoma tumor cell viability.

<p>Viability per area was measured along the five sets (S1 through S5) of histology sections for <i>Eμ-myc Arf-/-</i> (black) and <i>Eμ-myc p53-/-</i> (gray) tumors. All error bars represent standard deviation from at least n = 3 measurements in each section. Asterisks show level of statistical significance determined by Student's t-test with α = 0.05 (one asterisk, p<0.05; two asterisks, p<0.01).</p

Fluorescent Magnetic Nanoparticles for Magnetically Enhanced Cancer Imaging and Targeting in Living Subjects

Early detection and targeted therapy are two major challenges in the battle against cancer. Novel imaging contrast agents and targeting approaches are greatly needed to improve the sensitivity and specificity of cancer theranostic agents. Here, we implemented a novel approach using a magnetic micromesh and biocompatible fluorescent magnetic nanoparticles (FMN) to magnetically enhance cancer targeting in living subjects. This approach enables magnetic targeting of systemically administered individual FMN, containing a single 8 nm superparamagnetic iron oxide core. Using a human glioblastoma mouse model, we show that nanoparticles can be magnetically retained in both the tumor neovasculature and surrounding tumor tissues. Magnetic accumulation of nanoparticles within the neovasculature was observable by fluorescence intravital microscopy in real time. Finally, we demonstrate that such magnetically enhanced cancer targeting augments the biological functions of molecules linked to the nanoparticle surface

Fluorescent Magnetic Nanoparticles for Magnetically Enhanced Cancer Imaging and Targeting in Living Subjects

Early detection and targeted therapy are two major challenges in the battle against cancer. Novel imaging contrast agents and targeting approaches are greatly needed to improve the sensitivity and specificity of cancer theranostic agents. Here, we implemented a novel approach using a magnetic micromesh and biocompatible fluorescent magnetic nanoparticles (FMN) to magnetically enhance cancer targeting in living subjects. This approach enables magnetic targeting of systemically administered individual FMN, containing a single 8 nm superparamagnetic iron oxide core. Using a human glioblastoma mouse model, we show that nanoparticles can be magnetically retained in both the tumor neovasculature and surrounding tumor tissues. Magnetic accumulation of nanoparticles within the neovasculature was observable by fluorescence intravital microscopy in real time. Finally, we demonstrate that such magnetically enhanced cancer targeting augments the biological functions of molecules linked to the nanoparticle surface