Analytical model of phototherapy for neonatal jaundice. Influence of bilirubin kinetics on skin colour during phototherapy

Summary Recent progress in diode-array detector technology and signal processing methods, and in the optical modelling of tissues allow: i) real-time, multispectral analysis of reflected spectra with relatively simple and compact devices; and ii) improved correlations between reflectance spectra and pigment distribution in tissues. Second-generation transcutaneous bilirubinometers relying on the changes in the optical properties of the skin at selected wavelengths due to changes in its optical components are being developed. To extend the use of transcutaneous bilirubinometry to the phototherapy cycle, the modelling of the complex mechanisms of bilirubin photochemistry and metabolism in the various body compartments is required. As a first step toward this aim, the influence of bilirubin photochemistry occurring during the initial stage of phototherapy on the reflectance spectrum of an icteric tissue is analysed. A four-layer model is assumed. The transformation of bilirubin into its configurational isomers is considered in detail, while the role of the structural isomer on bilirubin elimination is taken into account with a loss term in the equation of motion of bilirubin concentration. The phototherapeutic process makes the illumination in the bile pigment layer depend on time. However, in the specific cases here considered, this time variation is negligible, and the differential equations describing the time evolution of bile pigment concentrations can be solved in a closed form. The bilirubin kinetics produces significant changes of the diffuse reflectance spectra during phototherapy, and the difference of the colour after the phototherapeutic treatment of a known duration can be put in close correspondence with the model of the jaundiced skin and permits quantitative estimates of pigment concentrations.