BioMed Research International

Volume 2017 (2017), Article ID 8569328, 12 pages

https://doi.org/10.1155/2017/8569328

*In Vitro/In Silico* Study on the Role of Doubling Time Heterogeneity among Primary Glioblastoma Cell Lines

^{1}Department of Medicine, University of Crete, Heraklion, Greece^{2}Computational Bio-Medicine Laboratory, Institute of Computer Science, Foundation for Research and Technology-Hellas, Heraklion, Greece^{3}Neurosurgery Clinic, University General Hospital of Heraklion, Heraklion, Greece^{4}Gene Expression Laboratory, Institute of Molecular Biology and Biotechnology, Foundation for Research and Technology-Hellas, Heraklion, Greece^{5}Department of Biology, University of Crete, Heraklion, Greece

Correspondence should be addressed to V. Sakkalis

Received 5 May 2017; Accepted 18 September 2017; Published 31 October 2017

Academic Editor: Sara Piccirillo

Copyright © 2017 M.-E. Oraiopoulou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The application of accurate cancer predictive algorithms validated with experimental data is a field concerning both basic researchers and clinicians, especially regarding a highly aggressive form of cancer, such as Glioblastoma. In an aim to enhance prediction accuracy in realistic patient-specific environments, accounting for both inter- and intratumoral heterogeneity, we use patient-derived Glioblastoma cells from different patients. We focus on cell proliferation using* in vitro* experiments to estimate cell doubling times and sizes for established primary Glioblastoma cell lines. A preclinically driven mathematical model parametrization is accomplished by taking into account the experimental measurements. As a control cell line we use the well-studied U87MG cells. Both* in vitro* and* in silico* results presented support that the variance between tumor staging can be attributed to the differential proliferative capacity of the different Glioblastoma cells. More specifically, the* intratumoral heterogeneity* together with the overall proliferation reflected in both the* proliferation rate* and the* mechanical cell contact inhibition* can predict the* in vitro* evolution of different Glioblastoma cell lines growing under the same conditions. Undoubtedly, additional imaging techniques capable of providing spatial information of tumor cell physiology and microenvironment will enhance our understanding regarding Glioblastoma nature and verify and further improve our predictability.

#### 1. Introduction

Glioblastoma (GB), a grade IV glioma as categorized by the World Health Organization (WHO) [1], is one of the most aggressive brain cancer types [2] with a poor prognosis for the patient [3], despite the rapid advances in technology and novel therapeutics. One of the most characteristic features of GB that limits therapeutic potential is heterogeneity [4]; both different molecular GB subtypes [5, 6] and subclonal cell populations coexist within the same tumor [7–9]. Hence, the importance of individualized GB treatment and understanding of patient-specific GB pathophysiology is evident and research plans towards this aim are of great interest.

The use of the widely scientifically studied common GB cell lines passaged in lab conditions for decades [10] is nowadays questionable with respect to their clinical relevance in therapeutic outcome prediction and to their ability of representing the extensive heterogeneity observed among patients [11]. To this front, a common GB trend is the use of patient-derived GB cells to enable preclinical physiologic estimations and personalize therapeutic strategy. Basic researchers cooperate with clinicians in order to isolate GB cells and promote the establishment of short-term primary GB cell cultures [12–15], which provide additional results back to the patient. Established methods for biological research and early drug discovery utilize cell lines grown on plastic culture flasks. Over the years, the ability of these* in vitro* systems to provide biologically relevant answers and describe drug effects is limited due to the fact that they are too simplistic and do not include key players of the phenomenon. Hence, researchers seem to mobilize more realistic experimental approaches such as 3-dimensional (3D) cell cultures [16–20] and/or* ex/in vivo* implantations [14, 21–23] to better imitate cancer in a mechanistic and conditional way. Biological 3D models comprise an important step to describe the early phases of tumor progression before going to the complexity of* in vivo* systems.

Biological experiments are strongly linked with computational and mathematical (*in silico*) models.* In silico* models offer a systematic framework of understanding the underlying biological processes integrating knowledge and information from multiple biological experiments and/or clinical examinations [24]. By predicting the behavior of the system, new targeted experiments can be designed. In that way, the process of mathematical modeling validation is an iterative refinement procedure [25], which terminates when a valid and biologically plausible and concrete description of the system that reproduces the observed cellular behaviors and growth patterns is found. Several mathematical approaches have been proposed to describe the complex, multiscale spatiotemporal tumor evolution. According to their mathematical perspective, these approaches can be classified into continuum and discrete models. Continuous mathematical models are commonly used to describe tumors at tissue level focusing more on the collective, averaged behavior of tumor cells [26–28]. On the other hand, individual-cell-based models using discrete and hybrid discrete-continuous (HDC) mathematics can describe the behavior of each cancer cell individually as it interacts with its microenvironment. Individual-cell-based models are in general more suitable to describe* in vitro* experiments, animal models, and small-sized tumors [29–34].

In general, such mathematical models attempt to translate tumor physiology hallmarks [35] into computational parameters and the predicted output is subsequently validated using as ground truth either the experimental [36, 37] or the clinical results [38, 39]. As it is well-understood, both cell division and local spreading are responsible for cancer expansion [40, 41] comprising the most important aspects for cancer progress [30, 42].* Doubling time* is defined as the average duration of cell growth and division as reflected by the cell cycle “clock” [43]. GB tumors have a remarkable rapid growth that has a critical role regarding the space-occupation and the development of intracranial pressure, usually the main reason of the GB symptomatology [44]. In previous studies, the significance of the proliferative rate has been shown. More specifically, in [45], the proliferation rates of different breast cancer patients are estimated from subsequent Magnetic Resonance (MR) images in conjunction with a simple logistic tumor growth model and show that the proliferation rate estimates could discriminate patient’s survival and response to therapy. In another study [46], the role of experimental and simulated diffusion gradients in 3D tumors affecting nutrient, oxygen, and drug availability within the tumor and subsequently controlling cell proliferative rate is examined. A mathematical model parameterized from monolayer experiments is used to quantify the diffusion barrier in 3D experiments. In the recent study [40], acquisition of physiologic parameters from multicellular tumor spheroids including proliferation and death spatial profiles is used to constrain and parametrize a mathematical agent-based model that addresses several cell growth mechanisms necessary to explain the experimental observations and reductively translates them to tumor progress over time.

This work utilizes primary tumor cells collected from GB patients and subsequently cultivated* in vitro* as 3D tumor spheroids. As an initial step towards understanding the GB heterogeneity among patients, we focus on proliferation. The aim of this work is first to mathematically study the important components affecting the growth dynamics of tumor spheroids when motility is inhibited, mainly including the inter- and intratumoral heterogeneity with respect to cell proliferation and, second, to parametrize the mathematical model based on experimentally estimated parameter values of primary GB cell lines in order to increase clinical relevance. Doubling times and the average cell sizes of in-house-established primary GB cell lines from three different patients are used. The well-known U87MG GB cell line is also used as control in the experiments. All the biological experiments are performed simultaneously under the same initial and growth conditions. A hybrid, individual, cell-based mathematical model is used to predict the growth curves of the tumor spheroids and parametrized based on the experimental data. Variations in several mathematical model parameters are explored in order to quantify their effect on tumor growth expansion. The simulated results are compared to the experimental data from the relevant 3D cell cultures and show that, in combination with the proliferation rate, additional factors like the mechanical cell contact inhibition are necessary to predict the* in vitro* evolution of the different GB cell lines under study.

#### 2. Methods

##### 2.1. Sampling Procedure

Brain tissue sample is collected from the lesions during biopsy or gross resection of patients with indications of GB based on symptoms and MR images, while still naïve from treatment and later histologically proved to be GB cases. For the purposes of this study, we used the primary cells of three different patients. The first is a 70-year-old male patient with de novo GB close to the left brain motor area, also called GBP03 cells. The second, called GBP06 cell line, was collected from a 47-years-old female patient with a tumor in the medulla proven to be a secondary GB, which was gradually evolved to grade IV from lower grades within a time period of approximately 20 years. The third sample, called GBP08, was provided by a 53-year-old male patient with also primary GB in the temporal-occipital left hemisphere. All samples are anonymously provided with the informed patients’ consent by the Neurosurgical Clinic of the General University Hospital of Heraklion, Crete, Greece, while the protocol has been approved by the Institutional Ethical Committees. Because of the relatively low success rate of the primary cell culture establishment, we are limited to these three GB cases for this work.

##### 2.2. Primary Cell Cultures

Later to tissue sampling in saline solution, the specimens are immediately transferred to the lab where they are mechanically dissociated into smaller parts and supplemented culture medium is added (Dulbecco’s modified Eagle medium (DMEM) with 10% fetal bovine serum (FBS) and 1% gentamycin). After gradually removing all cell debris and dead tissue parts, cancer GB cells are cultured as monolayers in standard lab conditions.

As explained before, there is much heterogeneity between GB cases and the protocol of tissue handling is slightly modified per case. An ectopic, subcutaneous implantation to immunodeficient mice is a procedural step that takes place whether the conditional stability cannot be preserved* in vitro* so that it cannot be assured that the isolated GB cells will survive and proliferate in flask. Therefore, lab animals serve as “living incubators” and usually, after the first implantation, the cells are collected and recultured until the cell culture is successfully established. In this work, GBP03 cells are passaged once, while GBP06 and GBP08 cells are directly used. All possible steps are taken to avoid animal suffering at each stage of the experiments.

##### 2.3. Doubling Time Assay

We use the GBP03, GBP06, and GBP08 primary cell lines as well as the U87MG cells (ATCC® HTB-14™, USA) as control line. In order to measure the doubling time intervals of the different cell types used we apply a simple protocol in adherent cultures. In a 24-well plate, 20000 cells/ml of supplemented DMEM are seeded per cell type at day zero. The plate is incubated in standard lab conditions for approximately a week. Whenever needed, cell culture medium is carefully renewed avoiding the adherent (active) cell population to be disturbed.

Every 24 hours after seeding, the culture medium of one well per cell type is removed and trypsin-EDTA (Sigma-Aldrich, Germany) 1x solution is added for 1-2 minutes. After another 1 minute of trituration in order to produce a single cell solution, all the context is removed from the well and is transferred to a 2 ml Eppendorf tube. As a final step, 4% formaldehyde is added to permanently fix the cells within the tube which is stored to the refrigerator for further use. The procedure is repeated up to the point that 100% cell confluence is achieved. The cell concentration for each cell type is measured with a 24-hour interval by using a hemocytometer.

##### 2.4. Cell Size Estimation

A divided Petri dish is plated with a single cell solution of ~2000 cells/ml and is incubated in standard lab conditions overnight to let the cells adhere in the surface of the dish. Accordingly, brightfield images of attached single cells are captured in 40x magnification and known acquisition parameters to an inverted light microscope (Leica, Germany). To check size and shape homogeneity between each cell population so that to assure that the estimated average cell size will be representative, we capture a photograph of a single cell solution within the fixed grid dimensions of the hemocytometer.

##### 2.5. D Spheroid Generation

We use the hanging-drop technique in order to produce spheroids from each cell type, as recommended in [16, 17, 47]. A single cell solution of 625 cells/50 ul of supplemented double-filtered DMEM is initially seeded per well in a 96-well hanging-drop plate (3D Biomatrix, USA). Two rows of wells per cell type are plated so that approximately 24 spheroids are produced. Agarose solution of 1% w/v is added to plate’s reservoirs to prevent evaporation of the droplets. After 2–4 days of cells aggregating at the bottom of each droplet, we can consider that the spheroids are finally formed. The growth progress of the spheroids is monitored over time via photographs taken under set acquisition parameters to an inverted light microscope (Leica, Germany) for predecided critical time points (2-day interval).

##### 2.6. Data Analysis

The average doubling time of each cell line is estimated using exponential linear regression on the doubling time data. The average cell size of each cell line is estimated by segmenting the area of approximately 10 randomly selected cells in brightfield images to ImageJ [48] and averaging. The tumor expansion of the 3D spheroids is again estimated based on the area shown in their brightfield images. The growth curve is estimated by the mean area value ± standard deviation over time. All the above measurements are evaluated per cell type and many experiments are performed for each cell type.

##### 2.7. Computational Model Implementation of Tumor Spheroids

A simplistic HDC mathematical model is used to describe the observed tumor growth of the 3D* in vitro* experiments. In the context of the HDC model, each individual cell is described by a discrete cellular automaton, while the local microenvironment is approximated by partial differential equations (PDE). In the following, a concise description of the HDC model is provided, while more thorough description can be found in [49].

###### 2.7.1. Computational Domain

To simulate a central slice of the 3D* in vitro* tumor spheroids, we set up a 2D regular lattice of size = 5 mm. We assume that each square lattice site fits a single cell; thus the lattice site defines the cell size as well. The same lattice is used by both the discrete and the continuous compartments.

###### 2.7.2. Continuous Compartment

For simplicity, we assume that oxygen is the only limiting molecule required by the cells in order to proliferate. The spatiotemporal evolution of oxygen is described by the partial differential equation (PDE) shown in (1). Oxygen is assumed to diffuse through the domain with diffusion coefficient , decays naturally at a rate , and is consumed by the tumor cells at a rate . The term is 1 if there is a tumor cell at the location or 0 otherwise.

###### 2.7.3. Discrete Compartment

Each tumor cell is an individual entity with its own traits. Sets of these traits are assumed to represent a cellular phenotype. A more detailed description of the cell life cycle can be found in [49, 50].

In this work, two mechanisms of tumor cells are mainly considered: proliferation and death. Cellular movement has been neglected considering that the protocol of the* in vitro* experiments does not conditionally allow cell motility. Cells die if the local oxygen concentration drops below a defined threshold . When a cell dies, its location is immediately treated as empty space. On the other hand, the live cells incrementally prepare for proliferation at every time step, until the cell age reaches their doubling time. At that moment, the cell searches for a nearby empty space at the 1-Moore neighborhood. If no empty space is available, the search is expanded to the 2-Moore neighborhood (see Figure 1) and the process is repeated up to -Moore neighborhood, where is defined as the proliferation depth and determines the maximum neighborhood size. Examples of Moore neighborhood can be seen in Figure 1. If more than one empty space is found in the same neighborhood, one of them is randomly chosen.