Differential Equations (1/2) by Alex https://padlet.com/bmes698/eseev86jp5slvszu en-us 2023-09-17 22:53:01 UTC 2023-11-01 04:45:52 UTC hello@padlet.com Diffusion equation alexguevel https://padlet.com/bmes698/eseev86jp5slvszu/wish/2707727061 \dot{u} = D\triangle{u}]]> 2023-09-17 22:55:57 UTC https://padlet.com/bmes698/eseev86jp5slvszu/wish/2707727061 New equation alexguevel https://padlet.com/bmes698/eseev86jp5slvszu/wish/2707727943 write in latex, then highlight, click on pi symbol]]> 2023-09-17 22:58:26 UTC https://padlet.com/bmes698/eseev86jp5slvszu/wish/2707727943 Question Formulation Technique alexguevel https://padlet.com/bmes698/eseev86jp5slvszu/wish/2710848439 1) How many equations do we need for a system?
2) How do we make good/proper assumptions?
3) What assumptions can we make to solve these equations?
4) What phenomena do these equations model?
5) How do we interpret the role of each variable and understand its graphical meaning?
6) How do we formulate models from real world problems?
7) What are the BME applications of differential equations?
8) How do we create a differential equation from experimental data?]]> 2023-09-19 13:33:14 UTC https://padlet.com/bmes698/eseev86jp5slvszu/wish/2710848439 The Michaelis-Menten Equation bbrennen https://padlet.com/bmes698/eseev86jp5slvszu/wish/2711205417 V=\frac{V_{max} S}{K_m+S}]]> 2023-09-19 16:45:20 UTC https://padlet.com/bmes698/eseev86jp5slvszu/wish/2711205417 End goal alexguevel https://padlet.com/bmes698/eseev86jp5slvszu/wish/2711223189 Connecting types of differential equations and BME applications. We can envision building a big table summarizing these connections.]]> 2023-09-19 16:56:18 UTC https://padlet.com/bmes698/eseev86jp5slvszu/wish/2711223189 Navier-Stokes Equation https://padlet.com/bmes698/eseev86jp5slvszu/wish/2711255765 \rho\frac{d\bar{u}}{dt}=-\nabla p+\mu\nabla ^2\bar{\mu}+\rho\bar{F}]]> 2023-09-19 17:15:50 UTC https://padlet.com/bmes698/eseev86jp5slvszu/wish/2711255765 The Standard Solid Model (Bone mechanics) https://padlet.com/bmes698/eseev86jp5slvszu/wish/2711344949 2023-09-19 18:12:20 UTC https://padlet.com/bmes698/eseev86jp5slvszu/wish/2711344949 Maxwell - Faraday Equation svyvyan1 https://padlet.com/bmes698/eseev86jp5slvszu/wish/2711346494 2023-09-19 18:13:20 UTC https://padlet.com/bmes698/eseev86jp5slvszu/wish/2711346494 The Bloch equations carledge3 https://padlet.com/bmes698/eseev86jp5slvszu/wish/2711594852 These equations are used in NMR and MRI to describe the 3-D changes in nuclear magnetization (Mx, My, & Mz).]]> 2023-09-19 21:45:00 UTC https://padlet.com/bmes698/eseev86jp5slvszu/wish/2711594852 Pharmacokinetic Differential Equation in DCE MRI carledge3 https://padlet.com/bmes698/eseev86jp5slvszu/wish/2711596958 Common pharmacokinetic model that is used in DCE MRI that describes how a contrast agent perfuses into and away from a tissue of interest (commonly a tumor). This is commonly referred to as: The Extended Tofts Model. ]]> 2023-09-19 21:48:13 UTC https://padlet.com/bmes698/eseev86jp5slvszu/wish/2711596958 Laplace Transform Formula wtwilson https://padlet.com/bmes698/eseev86jp5slvszu/wish/2711614421 2023-09-19 22:16:31 UTC https://padlet.com/bmes698/eseev86jp5slvszu/wish/2711614421 Logistic model of tumor growth sgphilli https://padlet.com/bmes698/eseev86jp5slvszu/wish/2711876718 2023-09-20 02:06:31 UTC https://padlet.com/bmes698/eseev86jp5slvszu/wish/2711876718 OpenSim Musculoskeletal Model Dynamics Equations https://padlet.com/bmes698/eseev86jp5slvszu/wish/2711903975 Equations driving muscle contraction and activation dynamics given a specific set of activation's (a) and external forces (F).]]> 2023-09-20 02:22:10 UTC https://padlet.com/bmes698/eseev86jp5slvszu/wish/2711903975 Fisher-KPP Equation https://padlet.com/bmes698/eseev86jp5slvszu/wish/2712271653 Nonlinear reaction-diffusion equation, where u is the population size wrt both a spatial and a temporal component. D is the diffusion constant, r is the growth rate, and K is the carrying capacity.]]> 2023-09-20 06:51:47 UTC https://padlet.com/bmes698/eseev86jp5slvszu/wish/2712271653 Analysis of Pressure Distribution in Transfemoral Prosthetic Socket for Prefabrication Evaluation via the Finite Element Method rayers15 https://padlet.com/bmes698/eseev86jp5slvszu/wish/2712753514 https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6956391/]]> 2023-09-20 12:54:03 UTC https://padlet.com/bmes698/eseev86jp5slvszu/wish/2712753514 Modeling of a damper leakage https://padlet.com/bmes698/eseev86jp5slvszu/wish/2712798190 2023-09-20 13:19:54 UTC https://padlet.com/bmes698/eseev86jp5slvszu/wish/2712798190 Characterizing Shperoids shortsamantha071 https://padlet.com/bmes698/eseev86jp5slvszu/wish/2712811397 These equations model tumor cell growth, diffusion, and traction forces.
https://www.nature.com/articles/s41598-020-68324-4]]> 2023-09-20 13:27:29 UTC https://padlet.com/bmes698/eseev86jp5slvszu/wish/2712811397 Euler-Lagrange Equation leholmes https://padlet.com/bmes698/eseev86jp5slvszu/wish/2719454565 2023-09-25 14:32:14 UTC https://padlet.com/bmes698/eseev86jp5slvszu/wish/2719454565 Gray-Scott model for reaction-diffusion dlizanet https://padlet.com/bmes698/eseev86jp5slvszu/wish/2771678457 2023-11-01 04:02:30 UTC https://padlet.com/bmes698/eseev86jp5slvszu/wish/2771678457 Winkessel flow dlizanet https://padlet.com/bmes698/eseev86jp5slvszu/wish/2771720269 2023-11-01 04:45:52 UTC https://padlet.com/bmes698/eseev86jp5slvszu/wish/2771720269