A biomechanical study regarding the effect of tissue harvesting from the thorax on its movement during inspiration

Figures & data

Figure 1. Mechanism of inspiration. Left: Normal inspiration. Ribs (indicated by beams) are connected with springs. As the springs contract, the ribs exhibit concerted movement. Right: When parts of the beams are removed, the movement exhibits disharmony.

Figure 2. CT data from 16 patients (left) were transformed into 3D models consisting of beams and non-linear springs (right). See also Figure 3.

Figure 3. Inspiration muscles were modeled with non-linear springs. The red and yellow segments in the figure indicate springs simulating muscle fibers of the diaphragm and external intercostal muscles, respectively. The bones – simulated with beams – are shown thinner than in actuality to enhance the spring elements.

Table I.  Young's moduli for bone and cartilage (MPa).

Tissue	Range	Median
Bone
Cortical bone	8800–25200	17000
Cancellous bone	780–1890	1340
Costal cartilage	20–186	103

Table II.  Stress-strain relationships for respiratory muscles.

Strain	0.1	0.2	0.3	0.4	0.5	0.6	0.7
Stress (MPa)	0.002	0.004	0.0068	0.0080	0.014	0.022	0.038

Table III.  Stress-strain relationships for ligaments.

Strain	0.01	0.02	0.03	0.04	0.05	0.06	0.07
Stress (MPa)	0.8	1.5	4.3	5.8	9.2	12	15.4

Figure 4. Examples of models representing each of the harvesting patterns. Costal cartilages or ribs are harvested from the regions indicated by circles. Types II-a, II-b, and II-c are viewed from behind.

Figure 5. An example of thoracic transformation presented by a Type I-b model. The left and right figures indicate thorax shapes before (left) and after (right) inspiration. The dotted lines in the figures at right indicate the thorax shape before inspiration. The contours indicate the degree of deviation in millimeters.

Figure 6. Upper and lower bounds of the thorax.

Figure 7. Position of the sternum before (left) and after (right) inspiration. θpre and θpost are the inclinations that the sternum presents relative to the coronal plane. The difference between θpost and θpre was defined as the angle of sternal rotation (ASR) and was evaluated.

Table IV.  Angle of sternal rotation (ASR).

	Range (°)	Median (°)	Statistical significance
Normal (n = 16)	−4.0 to 3.6	0.5
I-a (n = 16)	−4.8 to 3.3	0.3	NS
I-b (n = 16)	−1.8 to 8.6	3.4	p = 0.05
II-a (n = 16)	−5.2 to 4.3	0.4	NS
II-b (n = 16)	−1.2 to 6.9	2.8	p = 0.05
II-c (n = 16)	0.8 to 7.3	4.0	p = 0.01

Table V.  Increase in right thoracic volume (ΔRTV).

	Range (ml)	Median (ml)	Statistical significance
Normal (n = 16)	146–198	171	–
I-a (n = 16)	142–194	168	NS
I-b (n = 16)	144–188	166	NS
II-a (n = 16)	145–189	167	NS
II-b (n = 16)	142–197	170	NS
II-c (n = 16)	147–197	172	NS

Table VI.  Increase in left thoracic volume (ΔLTV).

	Range (ml)	Median (ml)	Statistical significance
Normal (n = 16)	128–208	168	–
I-a (n = 16)	125–211	171	NS
I-b (n = 16)	124–208	166	NS
II-a (n = 16)	120–218	169	NS
II-b (n = 16)	108–196	152	p = 0.01
II-c (n = 16)	77–127	101	p < 0.0001

Table VII.  Measured values as a percentage of calculated values for three volunteer subjects. Numbers in parentheses indicate the measured value (numerator) and calculated value (denominator).

	Point 1	Point 2	Point 3	Point 4	Point 5
1	108 (2.8/2.6)	104 (5.2/5.0)	100 (7.4/7.4)	108 (4.3/4.0)	105 (6.3/6.0)
2	107 (3.2/3.0)	103 (7.2/7.0)	100 (9.4/9.4)	95 (3.8/4.0)	98 (8.0/8.2)
3	93 (3.9/4.2)	105 (8.2/7.8)	100 (8.6/8.6)	102 (4.6/4.5)	104 (7.2/6.9)

Figure 8. Left: Inspiration pattern of normal thorax. With the elevation of the ribs, the volume of the thorax increases. Center: Elevation of the thorax can occur even after the removal of costal cartilages, although some ribs (indicated with arrows) exhibit deviation during inspiration. Right: Elevation of the thorax is impaired when ribs are removed from the lateral parts.