Research Article: Mathematical modelling of the growth of human fetus anatomical structures

Date Published: July 8, 2016

Publisher: Springer Japan

Author(s): Krzysztof Dudek, Wojciech Kędzia, Emilia Kędzia, Alicja Kędzia, Wojciech Derkowski.

http://doi.org/10.1007/s12565-016-0353-y

Abstract

The goal of this study was to present a procedure that would enable mathematical analysis of the increase of linear sizes of human anatomical structures, estimate mathematical model parameters and evaluate their adequacy. Section material consisted of 67 foetuses—rectus abdominis muscle and 75 foetuses- biceps femoris muscle. The following methods were incorporated to the study: preparation and anthropologic methods, image digital acquisition, Image J computer system measurements and statistical analysis method. We used an anthropologic method based on age determination with the use of crown-rump length—CRL (V–TUB) by Scammon and Calkins. The choice of mathematical function should be based on a real course of the curve presenting growth of anatomical structure linear size Ύ in subsequent weeks t of pregnancy. Size changes can be described with a segmental-linear model or one-function model with accuracy adequate enough for clinical purposes. The interdependence of size–age is described with many functions. However, the following functions are most often considered: linear, polynomial, spline, logarithmic, power, exponential, power-exponential, log-logistic I and II, Gompertz’s I and II and von Bertalanffy’s function. With the use of the procedures described above, mathematical models parameters were assessed for V-PL (the total length of body) and CRL body length increases, rectus abdominis total length h, its segments hI, hII, hIII, hIV, as well as biceps femoris length and width of long head (LHL and LHW) and of short head (SHL and SHW). The best adjustments to measurement results were observed in the exponential and Gompertz’s models.

Partial Text

Medical literature analysis reveals that foetal growth assessment requires construction of mathematical models that may be extrapolated out of the observation period. This problem is poorly discussed in available literature (Sztencel and Żelawski 1984). This may result from scarce foetal material as well as the rare combination of morphological sciences and mathematics. Foetal period is still poorly recognized. Our own studies (Dudek et al. 2014; Kedzia et al. 2010a; 2011a, b, 2013a, b; Woźniak et al. 2012, 2014) have enabled the assessment of foetal structures by geometric dimension increase curve. Neither sexual dimorphism nor asymmetry was very characteristic. Other observations based on less material comprising a smaller age span (Badura et al. 2011a, b; Grzonkowska et al. 2014; Szpinda et al. 2011, 2013) revealed similar results.

Section material consisted of rectus abdominis muscle of 67 foetuses and biceps femoris muscle of 75 foetuses (Table 1). The following methods were incorporated into the study: preparation and anthropologic methods, image digital acquisition, Image J computer system measurements and statistical analysis method. We used an anthropologic method based on age determination with the use of crown-rump length—CRL (V-TUB) by Scammon and Calkins (Scammon and Calkins 1929). Studies were conducted on post mortem material and approved by the ethical committee. Table 1Statistics characterizing examined foetusesVariableGroup I (rectus abdominis m.) N = 75Group II (biceps femoris m.) N = 67Age (weeks) M ± SD21.5 ± 2.022.4 ± 2,1 Me (Q1; Q3)22 (21; 23)22 (21; 24) Min ÷ Max17 ÷ 2618 ÷ 28V-PL (mm) M ± SD240 ± 36256 ± 32 Me (Q1; Q3)245 (220; 263)252 (233; 278) Min ÷ Max132 ÷ 310191 ÷ 334CRL (mm) M ± SD166 ± 22177 ± 22 Me (Q1; Q3)170 (158; 180)175 (161; 189) Min ÷ Max110 ÷ 212130 ÷ 237Body mass (g) M ± SD313 ± 117316 ± 112 Me (Q1; Q3)310 (245; 375)312 (247; 379) Min ÷ Max85 ÷ 61998 ÷ 622 n (%) female foetuses22 (29.3 %)33 (49.3 %)M mean, SD standard deviation, Me median, Q1 lower quartile, Q3 upper quartile, Min minimum, Max maximum, N number, (%) percentage

The choice of mathematical function should be based on a real course of the curve presenting growth of anatomical structure linear size Ύ in subsequent weeks t of pregnancy. Size changes can be described with a segmental-linear model or one-function model with accuracy adequate enough for clinical purposes. The interdependence of size–age is described with many functions. However, the following functions are most often considered: linear, polynomial, spline, logarithmic, power, exponential, power-exponential, log-logistic I and II, Gompertz’s I and II and von Bertalanffy’s function. With the use of procedures described above, mathematical models parameters were assessed for V-PL (the total length of body) and CRL body lengths increases, rectus abdominis total length h and its segments hI, hII, hIII, hIV as well as biceps femoris length and width of long head (LHL and LHW) and of short head (SHL and SHW).

In their surveys, Szpinda et al. (Szpinda et al. 2011) studied musculus biceps femoris and defined its increase in foetuses aged 17–30 weeks with the use of linear function. No significant sex differences were found (p > 0.05). All the parameters were found to increase in a linear fashion during gestation and significant positive correlations were found. There were significant laterality differences only in relation to either parameter of the short head of the biceps femoris.

Human foetal anatomical structure changes can be described accurately enough for clinical and prognostic purposes with segmental-linear models or one-function models. The degree of adjustment of model parameters and measurement results is influenced by the function form and especially the structure size absolute value. For bigger structures, e.g., femoral musculus adductor longus, determination index is comprised within the range 58–83 %, whereas in the case of smaller structures, e.g., musculus adductor longus width, the R2 value amounts to 52–75 %.

 

Source:

http://doi.org/10.1007/s12565-016-0353-y

 

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