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Diffusion01:12

Diffusion

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Diffusion is the passive movement of substances down their concentration gradients—requiring no expenditure of cellular energy. Substances, such as molecules or ions, diffuse from an area of high concentration to an area of low concentration in the cytosol or across membranes. Eventually, the concentration will even out, with the substance moving randomly but causing no net change in concentration. Such a state is called dynamic equilibrium, which is essential for maintaining overall...
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Diffusion01:21

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Diffusion is a type of passive transport. In passive transport, a substance tends to move from an area of high concentration to an area of low concentration until the concentration is equal across the space. For example, take the diffusion of substances through the air. When someone opens a perfume bottle in a room filled with people, the perfume is at its highest concentration in the bottle and is at its lowest at the edges of the room. The perfume vapor will diffuse, or spread away, from the...
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Network Covalent Solids02:18

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Network covalent solids contain a three-dimensional network of covalently bonded atoms as found in the crystal structures of nonmetals like diamond, graphite, silicon, and some covalent compounds, such as silicon dioxide (sand) and silicon carbide (carborundum, the abrasive on sandpaper). Many minerals have networks of covalent bonds.
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Metallic Solids02:37

Metallic Solids

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Metallic solids such as crystals of copper, aluminum, and iron are formed by metal atoms. The structure of metallic crystals is often described as a uniform distribution of atomic nuclei within a “sea” of delocalized electrons. The atoms within such a metallic solid are held together by a unique force known as metallic bonding that gives rise to many useful and varied bulk properties.
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Structures of Solids02:22

Structures of Solids

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Solids in which the atoms, ions, or molecules are arranged in a definite repeating pattern are known as crystalline solids. Metals and ionic compounds typically form ordered, crystalline solids. A crystalline solid has a precise melting temperature because each atom or molecule of the same type is held in place with the same forces or energy. Amorphous solids or non-crystalline solids (or, sometimes, glasses) which lack an ordered internal structure and are randomly arranged. Substances that...
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Theories of Dissolution: Diffusion Layer Model01:15

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Dissolution, the process by which drug particles dissolve in a solvent, is explained by the diffusion layer model, a theoretical framework that simulates the absorption of oral drugs and allows us to analyze experimental data.
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A DCE-MRI Driven 3-D Reaction-Diffusion Model of Solid Tumor Growth.

Thais Roque, Laurent Risser, Veerle Kersemans

    IEEE Transactions on Medical Imaging
    |March 14, 2018
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    This study introduces a novel image-driven model for predicting avascular tumor growth using MRI data. The model accurately forecasts tumor evolution and cell density, showing promise for cancer research.

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    Area of Science:

    • Oncology
    • Mathematical Modeling
    • Medical Imaging

    Background:

    • Accurate prediction of tumor growth and therapy response is crucial in cancer research.
    • Existing tumor growth models face challenges in predicting spatio-temporal evolution.
    • Dynamic contrast-enhancement MRI offers valuable longitudinal data for tumor analysis.

    Purpose of the Study:

    • To introduce, calibrate, and verify a novel image-driven reaction-diffusion model for avascular tumor growth.
    • To utilize longitudinal MRI data for constraining and parameterizing the tumor growth model.
    • To predict the spatio-temporal evolution of tumor volume and cell densities.

    Main Methods:

    • Developed a reaction-diffusion model incorporating cell proliferation, death, nutrient distribution, and hypoxia.
    • Constrained the model using time-series dynamic contrast-enhancement MRI data.
    • Estimated tumor-specific parameters from early time points to predict later tumor evolution.

    Main Results:

    • In silico testing on 15 synthetic tumors showed small volume errors (<5%) and high Dice overlaps (>97%).
    • Model parameters were successfully recovered and accurately predicted tumor growth in simulations.
    • Preliminary application to seven pre-clinical breast carcinoma cases demonstrated promising results, especially for early time point estimations.

    Conclusions:

    • The image-driven reaction-diffusion model shows significant potential for predicting avascular tumor growth.
    • Parameter estimation from early MRI data enables accurate short-term tumor evolution prediction.
    • Future improvements could incorporate angiogenesis and apoptosis for enhanced long-term prediction accuracy.