Mathematical modeling of intracellular osmolarity and cell volume stabilization: The Donnan effect and ion transport.

The presence of impermeant molecules within a cell can lead to an increase in cell volume through the influx of water driven by osmosis. This phenomenon is known as the Donnan (or Gibbs-Donnan) effect. Animal cells actively transport ions to counteract the Donnan effect and regulate their volume, actively pumping Na+ out and K+ into their cytosol using the Na+/K+ ATPase (NKA) pump. The pump-leak equations (PLEs) are a system of algebraic-differential equations to model the membrane potential, ion (Na+, K+, and Cl-), and water flux across the cell membrane, which provide insight into how the combination of passive ions fluxes and active transport contribute to stabilizing cell volume. Our broad objective is to provide analytical insight into the PLEs through three lines of investigation: (1) we show that the provision of impermeant extracellular molecules can stabilize the volume of a passive cell; (2) we demonstrate that the mathematical form of the NKA pump is not as important as the stoichiometry for cell stabilization; and (3) we investigate the interaction between the NKA pump and cation-chloride co-transporters (CCCs) on cell stabilization, showing that NCC can destabilize a cell while NKCC and KCC can stabilize it. We incorporate extracellular impermeant molecules, NKA pump, and CCCs into the PLEs and derive the exact formula for the steady states in terms of all the parameters. This analytical expression enables us to easily explore the effect of each of the system parameters on the existence and stability of the steady states.

Mixed burn injury to thigh secondary to D-cell lithium battery explosion.

There is an increasing trend globally of fire incidents as a direct consequence of battery failures[1-6], but a dearth of reporting in medical literature regarding injuries associated with primary lithium cell explosions. We present the case of an electrical engineer referred to the burns team as a chemical burn secondary to a D-cell lithium battery explosion. Initial assessment revealed an entry wound on the anteromedial thigh leaking contaminated fluid. Orthogonal X-rays demonstrated the battery casing lodged within the posterior thigh compartment. The wound was managed similar to that of a ballistic injury with staged debridement, washout and delayed primary closure. This is the first reported case of a lithium-thionyl chloride battery explosion causing injury. The case highlights various issues for attending teams, including appropriate first aid for chemical burns, consideration of significant soft tissue trauma deep to seemingly innocuous wounds and safeguarding concerns surrounding domestic explosive devices.