The basic three-parameter vocal tract area function model of Fant  has been extended to allow for asymmetry and variable length of the tongue hump section as well as variations of the VT overall length. An important class of articulations are those that conform with this model, mostly vowel sounds and consonants without apical modification or a secondary posterior articulation. Staring out from a theory of small perturbations [1,4], we calculate the shift in the VT parameter accompanying a certain set of shifts in F1, F2, and F3. This is done from a set of three linear differential equations expressing the shifts in each of F1, F2, and F3 as the sum of the contributions from the unknown shifts in each of the VT parameters. These are solved at each small step of a pathway from a reference starting point to the target formant-pattern. The overall length is optimized by reference to F4 and some available measured data. A resynthesis of a time varying F-pattern from a set of articulatory targets has been attempted with a possible application in articulatory synthesis.
Bibliographic reference. Lin, Qiguang / Fant, Gunnar (1989): "Vocal-tract area-function parameters from formant frequencies", In EUROSPEECH-1989, 2673-2676.