## Print version ISSN 0034-7094On-line version ISSN 1806-907X

### Rev. Bras. Anestesiol. vol.57 no.3 Campinas May/June 2007

#### http://dx.doi.org/10.1590/S0034-70942007000300012

LETTER TO THE EDITOR

The relative density of a solution. Unmasking concepts

Dear Editor,

Anesthesiologists control the level of spinal analgesia with the help of the relative density because local anesthetics are more or less dense than the cerebrospinal fluid (CSF).

Several terms (specific mass or absolute density, specific weight, relative density) are frequently used to describe the characteristics of the anesthetic solutions used for spinal anesthesia. Thus, it is important to define the following: absolute density, specific weight, and relative density. The absolute density (r) of a solution is the coefficient between the mass (m) of a portion of the substance and the volume (V) that it occupies. The specific weight (d) of a substance is the ratio between the weight (P) of a portion of this substance and the volume (V) that it occupies. The relative density is the ratio between the specific mass (absolute density) of a substance and the specific mass of another substance used as reference. Thus, relative density is a pure number (non-dimensional value). Stating that mercury is heavier (more dense) than water means that a certain volume of mercury is heavier than an equal volume of water, and we can say that relative density is the number of times that a substance is heavier than an equal amount of water, considering the same gravity acceleration (the relative density can also be described as: d = P/Po — when the bodies have the same volume, in which Po is the weight of the reference substance).

The unit of absolute density in the International System of Units (SI) is kilogram per cubic meter (kg/m3). Other units are used also, such as the gram per cubic centimeter (g/cm3), and the kilogram per liter (kg/L). These units are, thus, standardized because we work with substances in different physical states: solid, liquid, and gaseous.

Usually, the relative density of solids and liquids is defined relative to water at 4°C (absolute density of water at 4°C = 1 g/cm3 = 1 kg/L = 103 kg/m3). It is possible to use standards of reference other than water. The relative density of gases is usually relative to oxygen.

We believe that to understand the dispersion of the different solutions of local anesthetics, we should compare both relative densities (anesthetics and CSF). Therefore, the pharmaceutical companies would have to provide the relative densities of the anesthetics (relative to water at 4°C); obviously the temperature of the CSF would be 37°C. Thus, we could observe their values and state that the relative density of one of them is greater than the other. The term baricity is not very adequate, because it gives the idea of pressure. (Note that the specific mass of a gas varies considerably with pressure, but not the specific mass of a liquid, i.e., gases are easily compressible, but not fluids. Therefore, this term would be better used for gases.)

To understand definitively the dispersion of the different solutions of local anesthetics, it would be important that the pharmaceutical industry provided us with their relative density relative to water at 4°C or to the spinal fluid and the temperature.

Sincerely,

Luiz Eduardo Imbelloni, TSA, M.D.
Marildo A Gouveia, TSA, M.D.
Rogean Rodrigues Nunes, TSA — graduate student in Electronic Engineering

REFERENCES

01. Halliday D, Resnick R, Walker R — Fundamentos de Física, 6ª Ed, Rio de Janeiro, LTC, 2002;v.2;48-49.

02. Calçada CS, Sampaio JL — Física Clássica: Termologia, Fluidomecânica e Análise Dimensional, 2ª Ed, São Paulo, Editora Atual, 1998;1-2.

03. Serway RA — Física para Cientistas e Engenheiros, 3ª Ed, Rio de Janeiro, LTC, 1996;332-333.