Reactions problems from the FEBio test suite. These files are run through FEBio after each compilation to ensure that it is working as intended.
Owner: FEBio Team
reactions
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cr01.feb
This analysis reproduces the results of the study by DiMicco and Sah (2003) who examined the onedimensional spatial distribution of synthesized cartilage matrix products under the following assumptions: (1) Cells synthesize matrix products in soluble form, at a constant rate. (2) The soluble matrix product binds to the preexisting solid matrix. (3) The bound product may subsequently degrade into a soluble waste product. Their analysis may be represented by three chemical reactions:
Soluble Synthesis: [cells]+[nutrients] > [cells] + [soluble matrix product]
Binding: [soluble matrix product] > [bound matrix product]
Degradation: [bound matrix product] > [soluble degraded product]
In this analysis, cells and nutrients are not modeled explicitly. The [soluble matrix product] is modeled as a solute named 'soluble', the [soluble degraded product] is modeled as a soluted named 'degraded', and the [bound matrix product] is modeled as a solidbound molecule named 'bound'. Three chemical reactions are defined in this mixture, named 'soluble synthesis', 'binding' and 'degradation'. The analysis is performed over a onedimensional domain.
reactions
cr02.feb
Solid remodeling of a onedimensional bar with square crosssection, fixed on one end (z=0) and subjected to a compressive normal traction on the other end (z=10) and a uniform shear traction on its lateral boundaries. The solid material of the bar behaves as a neoHookean material with Young's modulus varying as a power law of the apparent solid density (a CarterHayes material). The solid remodels by adjusting the apparent solid density until the specific strain energy (strain energy per mass) becomes uniform. The remodeling process is described by a chemical reaction,
[cells] + [nutrients] > [cells] + [solid matrix]
where [cells] and [nutrients] are not modeled explicitly. The [solid matrix] is modeled with a solidbound molecule called 'solid'. The initial value of the solid apparent density is set to 1.0. No upper bound is placed on this solid apparent density. The reaction rate is dependent on the difference between the current and userspecified homeostatic specific strain energy according to the Huiskes model, which may produce positive or negative rates of solid matrix deposition (growth or degradation). Since chemical reactions are currently implemented only in multiphasic mixtures, the analysis necessarily includes a fluid phase in the porous solid, though the fluid pressure is prescribed to be zero on the boundaries. The remodeling process achieves a steadystate response.
reactions
cr03.feb
Dissociation of NaCl using reversible chemical reaction,
[NaCl] <> [Na+] + [Cl]
The three chemical species are described by three solutes in a multiphasic mixture. Initially the mixture contains only NaCl at a concentration of 1, which then dissociates reversibly into its cation and anion components. The analysis is performed in a domain consisting of a single finite element suitable for describing homogeneous processes. Since [Na+] and [Cl] are charged, and since their concentrations are not prescribed on the boundaries of the finite element domain, it is necessary to ground the mixture electrically to prevent unbounded fluctuations in the electric potential. Therefore two additional ions are included in the mixture, [K+] and [HCO3], with prescribed boundary conditions that enforce zero electric potential.
reactions
cr04.feb
Interstitial growth of engineered cartilage using chemical reactions that convert soluble sulfate ion into solidbound charged chondroitin sulfate (CS), based on the availability of glucose which is needed for CS synthesis as well as cell metabolism. The tissue construct consists of a scaffold (modeled as a solid porous matrix), cells (not modeled explicitly), the CS solidbound molecule, and an interstitial fluid containing Na+, Cl, Mg++ and SO4. Two chemical reactions occur in this analysis:
Glucose Consumption: [cells] + [glucose] > [cells] + [waste products]
Chondroitin sulfate synthesis: [cells] + [glucose] + [sulfate] > [cells] + [chondroitin sulfate]
Cells and waste products are not modeled explicitly. The [glucose] is modeled as a solute named 'Glc', the [sulfate] is modeled as a soluted named 'SO4', and the [chondroitin sulfate] is modeled as a solidbound molecule named 'CS'. The second chemical reaction explicitly enforces charge conservation between reactants and products, exchanging two negative charges between SO4 and CS. The initial CS concentration is zero. The analysis domain is a cylindrical disk, modeled as a wedge to take advantage of axisymmetry. Fixed glucose, NaCl and MgSO4 concentrations are prescribed on the top and lateral boundaries, whereas the bottom boundary is impermeable to all solutes and solvent. Over time, CS is deposited throughout the disk, increasing its fixed charge density and causing it to swell due to the resulting Donnan osmotic pressure. Since CS deposition is dependent on the availability of Glc, and since Glc concentration is nonuniform due to competitive diffusionconsumption effects, the CS deposition and construct swelling also become inhomogeneous.
reactions
cr05.feb
Onedimensional analysis of interstitial growth where the net reaction molar volume is not zero. This analysis models the chemical reaction
[nutrient] > [solid]
where the molar volume of the solid is different from that of the nutrient. The [nutrient] is not modeled explicitly, whereas the [solid] product is modeled as a solidbound molecule.The 1D analysis is performed on a cube of height h=1. The multiphasic material consists of a solid and a fluid phase (no explicit solutes). The top surface of the cube is tractionfree and freedraining. Continuous interstitial solid deposition decreases the solid matrix porosity and concomitantly pressurizes the interstitial fluid as it squeezes it out of the decreasing pore volume. The progressive interstitial pressurization causes the tissue to swell initially, until the fluid pressure achieves a steadystate value that drives fluid out at the same rate as the pore volume decreases, producing a steadystate swelling response.
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