Limits...
Scaling, growth and cyclicity in biology: a new computational approach.

Delsanto PP, Gliozzi AS, Guiot C - Theor Biol Med Model (2008)

Bottom Line: In nonlinear problems it allows the nonscaling invariance to be retrieved by means of suitable redefined fractal-dimensioned variables.As an example of its implementation, the method is applied to the analysis of human growth curves.The excellent quality of the results (R2 = 0.988) demonstrates the usefulness and reliability of the approach.

View Article: PubMed Central - HTML - PubMed

Affiliation: Dept, Physics, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy. pier.delsanto@polito.it

ABSTRACT

Background: The Phenomenological Universalities approach has been developed by P.P. Delsanto and collaborators during the past 2-3 years. It represents a new tool for the analysis of experimental datasets and cross-fertilization among different fields, from physics/engineering to medicine and social sciences. In fact, it allows similarities to be detected among datasets in totally different fields and acts upon them as a magnifying glass, enabling all the available information to be extracted in a simple way. In nonlinear problems it allows the nonscaling invariance to be retrieved by means of suitable redefined fractal-dimensioned variables.

Results: The main goal of the present contribution is to extend the applicability of the new approach to the study of problems of growth with cyclicity, which are of particular relevance in the fields of biology and medicine.

Conclusion: As an example of its implementation, the method is applied to the analysis of human growth curves. The excellent quality of the results (R2 = 0.988) demonstrates the usefulness and reliability of the approach.

Show MeSH
Separate plots of the curves U2 and T1. Separate plots of the curves U2 and T1 (see Eqs. (5) and (20)) for the case presented in Figs. 3 and 4. The minimum and maximum of the T1 curve coincide with the times for which the rate of growth is expected to have a minimum or a maximum, in correspondence with the inflection points in the y(t) curve.
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Figure 5: Separate plots of the curves U2 and T1. Separate plots of the curves U2 and T1 (see Eqs. (5) and (20)) for the case presented in Figs. 3 and 4. The minimum and maximum of the T1 curve coincide with the times for which the rate of growth is expected to have a minimum or a maximum, in correspondence with the inflection points in the y(t) curve.

Mentions: Our method allows us to fit Davenport's curve without the need to consider coupled logistic curves. In Figure 3 we show the original data, relative to human weight development from birth to maturity, and the fitting obtained with the curve U2/T1. The value of R2 = 0.998 confirms the correctness of the PUN classification and the accuracy and reliability of the approach. The presence of cyclicity is betrayed by the plot b(a) in Fig. 4, which clearly exhibits a loop (a very distorted ellipse). Since the curve of Fig. 3 was obtained from 'transversal', instead of 'longitudinal' data, it has been possible to detect only the overall "macroscopic" periodicity. In addition, by separately plotting the curves U2 and T1 vs. time, it is confirmed that the minima and maxima of the T1 curve fall at about 6 years and 17 years, i.e. where the complete U2/T1 curve has its inflection points (see Fig.5).


Scaling, growth and cyclicity in biology: a new computational approach.

Delsanto PP, Gliozzi AS, Guiot C - Theor Biol Med Model (2008)

Separate plots of the curves U2 and T1. Separate plots of the curves U2 and T1 (see Eqs. (5) and (20)) for the case presented in Figs. 3 and 4. The minimum and maximum of the T1 curve coincide with the times for which the rate of growth is expected to have a minimum or a maximum, in correspondence with the inflection points in the y(t) curve.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2289804&req=5

Figure 5: Separate plots of the curves U2 and T1. Separate plots of the curves U2 and T1 (see Eqs. (5) and (20)) for the case presented in Figs. 3 and 4. The minimum and maximum of the T1 curve coincide with the times for which the rate of growth is expected to have a minimum or a maximum, in correspondence with the inflection points in the y(t) curve.
Mentions: Our method allows us to fit Davenport's curve without the need to consider coupled logistic curves. In Figure 3 we show the original data, relative to human weight development from birth to maturity, and the fitting obtained with the curve U2/T1. The value of R2 = 0.998 confirms the correctness of the PUN classification and the accuracy and reliability of the approach. The presence of cyclicity is betrayed by the plot b(a) in Fig. 4, which clearly exhibits a loop (a very distorted ellipse). Since the curve of Fig. 3 was obtained from 'transversal', instead of 'longitudinal' data, it has been possible to detect only the overall "macroscopic" periodicity. In addition, by separately plotting the curves U2 and T1 vs. time, it is confirmed that the minima and maxima of the T1 curve fall at about 6 years and 17 years, i.e. where the complete U2/T1 curve has its inflection points (see Fig.5).

Bottom Line: In nonlinear problems it allows the nonscaling invariance to be retrieved by means of suitable redefined fractal-dimensioned variables.As an example of its implementation, the method is applied to the analysis of human growth curves.The excellent quality of the results (R2 = 0.988) demonstrates the usefulness and reliability of the approach.

View Article: PubMed Central - HTML - PubMed

Affiliation: Dept, Physics, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy. pier.delsanto@polito.it

ABSTRACT

Background: The Phenomenological Universalities approach has been developed by P.P. Delsanto and collaborators during the past 2-3 years. It represents a new tool for the analysis of experimental datasets and cross-fertilization among different fields, from physics/engineering to medicine and social sciences. In fact, it allows similarities to be detected among datasets in totally different fields and acts upon them as a magnifying glass, enabling all the available information to be extracted in a simple way. In nonlinear problems it allows the nonscaling invariance to be retrieved by means of suitable redefined fractal-dimensioned variables.

Results: The main goal of the present contribution is to extend the applicability of the new approach to the study of problems of growth with cyclicity, which are of particular relevance in the fields of biology and medicine.

Conclusion: As an example of its implementation, the method is applied to the analysis of human growth curves. The excellent quality of the results (R2 = 0.988) demonstrates the usefulness and reliability of the approach.

Show MeSH