Intracellular water preexchange lifetime in neurons and astrocytes
If intracellular water can be considered as “well mixed” (i.e., cell dimensions are small relative to the diffusion‐driven, water root‐mean‐square displacements that occur over the characteristic time of a given measurement), Fick's laws of diffusion for water transiting across the cell membrane relate JOURNAL/mrim/04.02/01445475-201803000-00042/math_42MM4/v/2018-01-24T161827Z/r/image-png directly to the diffusional water permeability, JOURNAL/mrim/04.02/01445475-201803000-00042/math_42MM5/v/2018-01-24T161827Z/r/image-png , according to Equation : JOURNAL/mrim/04.02/01445475-201803000-00042/math_42MM6/v/2018-01-24T161827Z/r/image-png where JOURNAL/mrim/04.02/01445475-201803000-00042/math_42MM7/v/2018-01-24T161827Z/r/image-png is the volume of intracellular water and JOURNAL/mrim/04.02/01445475-201803000-00042/math_42MM8/v/2018-01-24T161827Z/r/image-png is the surface area of the cell membrane 8. Although it is generally assumed that transcytolemmal water exchange is purely diffusive (i.e., thermally driven by Brownian motion), recent reports have also implicated energy‐dependent ion channels as significant “active transport” vehicles for this exchange 4. JOURNAL/mrim/04.02/01445475-201803000-00042/math_42MM9/v/2018-01-24T161827Z/r/image-png describes the accumulated total flux of all active and passive exchange processes.
All physical measurements have an associated characteristic time, and JOURNAL/mrim/04.02/01445475-201803000-00042/math_42MM10/v/2018-01-24T161827Z/r/image-png sets a limit (vide infra) on the characteristic time over which the tissue–water MR signal can be modeled as separable, compartment‐specific, water signals from intra‐ and extracellular compartments, rather than being a compartment‐inseparable signal resulting from exchange (mixing) between the compartments. Indeed, it is difficult, if not impossible, to construct a meaningful biophysical model for tissue–water MR measurements, such as T112 or apparent diffusion coefficient (ADC) 13, without knowledge of JOURNAL/mrim/04.02/01445475-201803000-00042/math_42MM11/v/2018-01-24T161827Z/r/image-png . For example, to address the biophysical mechanism(s) underlying the rapid and remarkable decrease in brain–water ADC after ischemic stroke 14, various hypotheses invoke the two‐compartment (i.e., intracellular and extracellular) diffusion model, and hence require assignment of values for compartment‐specific ADCs 16. However, strategies to measure compartment‐specific ADCs and changes therein in response to injury, a subject of considerable debate, generally require knowledge of JOURNAL/mrim/04.02/01445475-201803000-00042/math_42MM12/v/2018-01-24T161827Z/r/image-png6.
Considerable effort has focused on measuring JOURNAL/mrim/04.02/01445475-201803000-00042/math_42MM13/v/2018-01-24T161827Z/r/image-png using different MR strategies, including T2‐based methods 20, T1‐based methods 6, and diffusion‐based methods 3. A rather wide range of JOURNAL/mrim/04.02/01445475-201803000-00042/math_42MM14/v/2018-01-24T161827Z/r/image-png values in mammalian cells has been reported, from approximately 10 ms in erythrocytes 20 to approximately 1 s in rat skeletal muscle 12 and 2 s in human white matter 3. Of greatest relevance to this study, there are three reports of JOURNAL/mrim/04.02/01445475-201803000-00042/math_42MM15/v/2018-01-24T161827Z/r/image-png in central nervous system (CNS) tissue 3 and one report of JOURNAL/mrim/04.02/01445475-201803000-00042/math_42MM16/v/2018-01-24T161827Z/r/image-png in cultured glioma cells 24. Derived JOURNAL/mrim/04.02/01445475-201803000-00042/math_42MM17/v/2018-01-24T161827Z/r/image-png values vary substantially across these reports: 1.25 to 2.5 s 3, 0.55 s 6, 0.3 s 19, and 0.05 s 24.
In this study, we determine the intracellular water preexchange lifetime for microbead‐adherent neurons and glia (astrocytes), respectively, using a thin‐slice‐selection, inversion‐recovery, spin‐echo (IRSE) MR spectroscopy (MRS) method in concert with rapid flow of the extracellular perfusing media (Fig. 1) 7. The microbead‐adherent cell culture is modeled as a two‐compartment (intra‐ and extracellular water) system with first‐order transcytolemmal water exchange at equilibrium, which is often regarded as a “two‐site‐exchange” system 5. At equilibrium/steady state (static cell volume), the intra‐ and extracellular water volume fractions ( JOURNAL/mrim/04.02/01445475-201803000-00042/math_42MM18/v/2018-01-24T161827Z/r/image-png and JOURNAL/mrim/04.02/01445475-201803000-00042/math_42MM19/v/2018-01-24T161827Z/r/image-png , respectively) and water exchange rate constants (or preexchange lifetimes) are related as follows: JOURNAL/mrim/04.02/01445475-201803000-00042/math_42MM20/v/2018-01-24T161827Z/r/image-pngJOURNAL/mrim/04.02/01445475-201803000-00042/math_42MM21/v/2018-01-24T161827Z/r/image-png
Here, JOURNAL/mrim/04.02/01445475-201803000-00042/math_42MM22/v/2018-01-24T161827Z/r/image-png is the first‐order water exchange rate constant in the intra‐to‐extracellular direction, the inverse of which is the intracellular water preexchange lifetime, JOURNAL/mrim/04.02/01445475-201803000-00042/math_42MM23/v/2018-01-24T161827Z/r/image-png .