Evolutionary dynamics of tumor-stroma interactions in multiple myeloma

Cancer cells and stromal cells cooperate by exchanging diffusible factors that sustain tumor growth, a form of frequency-dependent selection that can be studied in the framework of evolutionary game theory. In the case of multiple myeloma, three types of cells (malignant plasma cells, osteoblasts and osteoclasts) exchange growth factors with different effects, and tumor-stroma interactions have been analysed using a model of cooperation with pairwise interactions. Here we show that a model in which growth factors have autocrine and paracrine effects on multiple cells, a more realistic assumption for tumor-stroma interactions, leads to different results, with implications for disease progression and treatment. In particular, the model reveals that reducing the number of malignant plasma cells below a critical threshold can lead to their extinction and thus to restore a healthy balance between osteoclast and osteoblast, a result in line with current therapies against multiple myeloma

A New Parallel Approach for Accelerating the GPU-Based Execution of Edge Detection Algorithms

Real-time image processing is used in a wide variety of applications like those in medical care and industrial processes. This technique in medical care has the ability to display important patient information graphi graphically, which can supplement and help the treatment process. Medical decisions made based on real-time images are more accurate and reliable. According to the recent researches, graphic processing unit (GPU) programming is a useful method for improving the speed and quality of medical image processing and is one of the ways of real-time image processing. Edge detection is an early stage in most of the image processing methods for the extraction of features and object segments from a raw image. The Canny method, Sobel and Prewitt filters, and the Roberts’ Cross technique are some examples of edge detection algorithms that are widely used in image processing and machine vision. In this work, these algorithms are implemented using the Compute Unified Device Architecture (CUDA), Open Source Computer Vision (OpenCV), and Matrix Laboratory (MATLAB) platforms. An existing parallel method for Canny approach has been modified further to run in a fully parallel manner. This has been achieved by replacing the breadth-first search procedure with a parallel method. These algorithms have been compared by testing them on a database of optical coherence tomography images. The comparison of results shows that the proposed implementation of the Canny method on GPU using the CUDA platform improves the speed of execution by 2–100× compared to the central processing unit-based implementation using the OpenCV and MATLAB platforms

Effect of initial frequencies on the dynamics for scenario 1.

<p>Different initial frequencies of OC, OB, and MM cells do not change the final state of the population. Parameters as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0168856#pone.0168856.g002" target="_blank">Fig 2</a>.</p

Effect of group size in scenario 1.

<p>The effect of group size <i>N</i> on the position of the fixed points on the OC-OB and OC-MM edges. Same parameters as <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0168856#pone.0168856.g002" target="_blank">Fig 2</a>.</p

Comparison with models with pairwise interactions.

<p>A comparison of our model and the pairwise game of Dingli et al. [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0168856#pone.0168856.ref013" target="_blank">13</a>] with <i>b</i>>1 (row A), <i>b</i><1, <i>b+d</i><1 (row B) or <i>b</i><1, <i>b+d</i>>1 (row C). The arrows show the direction of the dynamics, and the colors show its speed (the euclidean distance between the frequencies at time <i>t</i> and <i>t</i>+1).</p

Effect of reducing the fraction of MM cells.

<p>(<b>A</b>) If a population is modified by reducing the fraction of MM cells (1, dotted arrow), it can be moved into the basin of attraction of the stable point on the OC-OB edge, and it will then evolve (2, continuous arrow) to the healthy OC-OB equilibrium. (<b>B</b>) Changes in frequencies over time corresponding to panel <b>A</b>, without therapy (dotted lines) or with therapy (continuous line) introduced at generation 300. (<i>c</i>₁ = 1.2, <i>c</i>₂ = 1, <i>c</i>₃ = 1.4).</p

Multiplication factors for tumor-stroma interactions in multiple myeloma.

<p>Multiplication factors for tumor-stroma interactions in multiple myeloma.</p

Fitness of the three cell types as a function of their contribution (cost) for scenario 1.

<p>As the value of cost increases the fitness of OC and MM increases and the fitness of OB decreases. Same parameters as <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0168856#pone.0168856.g002" target="_blank">Fig 2</a>.</p

Examples of the dynamics for scenario 3.

<p>(<b>A</b>) For small group size (<i>N</i> = 10) the game has one stable point on the MM vertex. (<b>B</b>) If group size increases (<i>N</i> = 50) the game has two stable points. (<i>c</i>₁ = 1, <i>c</i>₂ = 1.2, <i>c</i>₃ = 0.8). The arrows show the direction of the dynamics, and the colors show its speed (the euclidean distance between the frequencies at time <i>t</i> and <i>t</i>+1).</p

Examples of the dynamics for scenario 2.

<p>When <i>c</i>₁ = <i>c</i>₂ = <i>c</i>₃ = 1, the game has (<b>A</b>) one stable point on the OC-OB edge if <i>a</i><<i>b</i> and <i>a</i><2<i>N</i>/(<i>N</i>-1); (<b>B</b>) two stable points on the OC-OB and OC-MM edges if <i>a</i><<i>b</i> and <i>a</i><2<i>N</i>/(<i>N</i>-1), <i>b</i>+<i>d</i>><i>a</i> and <i>b<</i>2<i>N</i>/(<i>N</i>-1); (<b>C</b>) one stable point on the OC-MM edges if <i>b</i>+<i>d</i>><i>a</i> and <i>b<</i>2<i>N</i>/(<i>N</i>-1). When the costs are not equal (bottom panels: <i>c</i>₁ = 1, <i>c</i>₂ = 1.2, <i>c</i>₃ = 1.4) the dynamics and the equilibria are different. <i>N</i> = 10. The arrows show the direction of the dynamics, and the colors show its speed (the euclidean distance between the frequencies at time <i>t</i> and <i>t</i>+1).</p