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21
EXPERIMENTAL INVESTIGATION OF ANATOMICAL AND GEOMETRICAL
PARAMETERS OF A HUMAN HIP
A.V. Sotin*, P.A. Garyaev**, N.D. Demchuk**
* Perm State Technical University, 29a, Komsomolsky Prospect, 614600, Perm, Russia ** Perm State Medical Academy, 39, Kuibyshev Street, 614000, Perm, Russia
Abstract: Data for the forces influencing on the hip under a physiological load are necessary for biomechanical modeling of the processes in the bone. Calculation of the muscle force includes physiological cross-sectional area as a parameter. This work is devoted to measuring anatomical cross-sectional area of 24 muscles of the hip and the pelvis. Two male cadaver specimens and one computed tomogram of an alive patient were investigated. The results were correlated with the anthropometric data for the specimens. The maximum isometric forces of different muscles were calculated.
Key words: physiological cross-sectional area of muscle, maximum isometrical force of muscle, computed tomogram of the lower limb
Introduction
Muscle forces are taken into account by many researchers during the calculation of stress and strain arising in the hip [1-4]. Physiological cross-section area of muscle (Sph) is used as a parameter in different investigation devoted to determination of muscle efforts during walking [5,6]. Solving a problem by the method of static optimization Crowninshield and Brand [7] used Sph when constructing of a purposeful function. Dependence of maximum isometrical muscle force (Fmax) on Sph allows calculating admissible solution constraint [1, 7, 8]. Different authors note that Sph value depends on the method of measurement, age, sex and anthropometric data of specimens [6,9]. In our work measurement was carried out based on two adult male cadaver specimens with similar habitus and one alive man (according to the computed tomogram of the lower limb). 24 muscles of the right hip and the pelvis were investigated. Measured values were anatomical cross-sectional area (San), mass, the lengths of the venter and the tendon of each muscle. Using the results of measurement some relative parameters of the lower limb muscle were calculated. The use of the computed tomogram permitted to compare the results obtained on corpses with the data in vivo.
Materials and Methods
Two male corpses of the similar habitus and one computed tomogram of an alive man were used for carrying out this experiment. The basic anthropometric data are shown in Table 1.
Table 1. Basic anthropometric data of objects of investigation.
Data Object
1* 2* 3*
Height (cm) 170 165 168
Mass (kg) 70 65 77
Age (years) 54 55 74
1* - cadaver specimen; 2* - cadaver specimen; 3* - alive man.
Measurements on corpses were performed in the period no longer than 3 days after the deaths. Every excised muscle was weighed, the lengths of the whole muscle, the venter as well as the proximal and distal tendons were measured. Measurement of cross-section area was performed in general in five sections: in the center of the distal and proximal tendon and in the central, distal, proximal sections of the venter. The section was colored and imprint of San was made on the paper. Two imprints of each side of section were made to get more exact results. The results of measurement m.Rectus femoris are shown in Fig. 1.
Average meaning San for each section was calculated on the basis of four imprints. Standard deviation of measures was no more than 10%. The maximum value of all obtained San for distal, central, proximal sections of the muscle venter was used for calculation.
The ratio mentioned in the works [1,7,8] was used to calculate maximum isometrical force of muscle:
Fmax = K Sph cos a, (1)
sy
where K is the specific muscle force (~ 40 N/cm ); a is an angle of the pinnation. Taking into account that for spindle-shaped muscle Sph = San, and cos a =1, we obtain:
Fmax = K San. (2)
In addition, the length of the tendon to which attached the pinnate muscular fibers (LT) and an average width of muscle along this portion (hm) were measured for m.Rectus femoris. The maximum isometrical force of muscle was calculated with use of the formula:
Fmax = K San (LT/hm) sin a. (3)
The obtained values for several muscles were compared with the cross-section areas (Stom) of the hip of the alive man measured on the tomogram (Fig. 2).
m.Rectus femoris
m.Biceps femoris (long head)
m.Semitendinosus
m.Sartorius m.Gracilis m.Semimembranosus
Fig. 2. Tomogram of the femur diaphysis. Arrows show some muscle of the hip. Scale 5 cm.
A
f
g
Fig. 3. Points of additional anthropometric measurements. Capital letters (A, B, C, D) - points of measurement perimeters, small letters (a-g) - points of measurement distance between marks.
The plane of tomogram does not coincide with the section of the muscle, therefore it is necessary to take into consideration the direction of the muscle in the space during a calculation of San if Stom is known. The angle of the incline of muscular fibers to plane of tomogram was calculated on the basis of the data of the work [10] which analyses the points of attachment of the muscles to the bones (the hip and the pelvis) and the muscle is regarded as the straight line. The values of Stom are given for m.Iliopsoas and m.Rectus femoris because the direction of the muscular fibers in m.Iliopsoas changes and the straight line model is not suited, as for m.Rectus femoris it is impossible to measure the angle of the pinnation.
Some external sizes of the hip and the pelvis were measured to receive relative values of the parameters investigated (Fig. 3). Additional anthropometric data of investigated objects are shown in Table 2.
d
c
e
Tab e 2. Additional anthropometric data of investigated object.
Data Object
(mm) 1* 2* 3*
P(A)** 820 810 1020
P(B) 490 400 540
P(C) 460 400 520
P(D) 420 370 490
l(a) (distantia cristarum) 300 272 320
l(b) (distantia spinarium) 250 247 286
l(c) (distantia trochanterica) 320 288 360
l(d) 160 159 170
l(e) 390 350 360
l(f) 470 450 450
l(g) 390 360 325
1* - cadaver specimen; 2* - cadaver specimen; 3* - alive man.
**Capital letters (P(A)- P(D)) - measured perimeters of the hip and the pelvis, small letters (l(a) -l(g)) - measured distance (see Fig. 3).
Results
The results of the investigation are shown in Tables 3-5. In Table 3 the following symbols are used: San.max - maximum value of the anatomic cross-section of muscle; Fmax - the maximum isometric force of muscle; m - the mass of muscle.
In Table 3 the following symbols are used: % Lven - length of the venter relative to the length of the whole muscle; % Lten - length of the tendon relative to the length of the whole muscle; Lmuscie - length of the muscle; Lrel - length of the muscle relative to l; l - external parameter of the hip (see Table 2).
In Table 5 the following symbols are used: Sanrel - the relative value of San calculated with the use of Sanrel= San/Sm.S; Fmaxrel - the relative value of Fmax calculated with the use of Fmaxrel = Fmax/(9.8Mo); mrel - the relative value mass of muscle calculated with the use of mrel=m/mm.S; where Sm.S - value of San measured for m.Sartorius; m -the mass of muscle; mm.S -the mass of m.Sartorius; MB -the mass of the body.
Discussion
The results of anatomical cross-sectional area (San) measurements obtained in this investigation correlate well with the values of physiological cross-sectional area (Sph) in female cadaver specimen shown in the work [6]. In our investigation we used objects with similar anthropometric data. It allowed us to avoid the scatter in values received in [6] (in our work it was no higher than 2.5 times). The data for the muscle and tendon length obtained in our work correlate well with the results received by other investigators [9,10]. Comparison of the values of maximum isometric force of muscle (Fmax) with the data of other authors revealed that efforts of muscles during walking calculated in the works [1,5,6] in some cases exceeded our values of Fmax, therefore it is necessary to take into account physiological limit during the research.
Table 6 presents m.Sartorius sizes relative to external anthropometric data with the aim of using relative values during calculation of muscle parameters based on the measured external sizes in patients with different anthropometric results.
Table 3. Absolute values of measured muscle parameters.
Name of muscle o max / „,2\ San. (cm ) Fmax (N) m (gm)
1* 2* 3* 1* 2* 3* 1* 2*
Psoas major 11.29 4.61 15.55 451.6 184.4 622.0 185 -
Iliacus 12.43 11.50 11.31 497.2 460.0 452.4 175 140
Gemellus superior 0.96 - - 38.4 - - 7 -
Gemellus inferior 2.23 - - 89.1 - - 10 -
Obturator externus 7.84 5.99 - 313.8 239.6 - 40 40
Obturator internus 10.75 - - 430.0 - - 59 -
Piriformis 4.99 2.22 4.01 199.5 88.8 160.4 11 20
Quadratus femoris - 8.09 - - 323.6 - - 70
Pectineus 6.81 3.60 6.54 272.5 144.0 261.5 58 75
Adductor minimus 3.80 - - 152.0 - - 30 -
Adductoe brevis 6.46 9.61 9.45 258.4 384.4 378.1 70 110
Adductor longus 12.29 9.40 11.23 491.8 376.0 449.1 176 180
Adductor magnus 26.09 11.26 32.61 1043.6 450.4 1304.2 490 260
Adductor magnus (ant) 10.40 - - 415.9 - - 180 -
Adductor magnus (med) 6.14 11.26 - 245.8 450.4 - 130 260
Adductor magnus (post) 9.55 - - 382.0 - - 180 -
Gluteus minimus 18.43 14.51 9.58 737.2 580.4 383.2 98 120
Gluteus minimus (ant) 5.85 5.77 - 234.1 230.8 - 28 45
Gluteus minimus (med) 8.21 5.35 - 328.4 214.0 - 50 45
Gluteus minimus (post) 4.37 3.39 - 174.9 135.6 - 20 30
Gluteus medius 30.31 21.01 29.44 1212.4 840.4 177.4 265 160
Gluteus medius (ant) 5.61 6.93 - 224.5 277.2 - 30 50
Gluteus medius (med) 10.81 7.74 - 432.5 309.6 - 78 50
Gluteus medius (post) 13.89 6.34 - 555.5 253.6 - 157 60
Gluteus maximus 43.64 30.36 34.83 1745.6 1214.4 393.1 760 700
Gluteus maximus (inf) 19.85 8.67 - 794.1 346.8 - 420 380
Gluteus maximus (sup) 23.79 21.49 - 951.5 859.6 - 340 320
Tensor fascia latae 8.74 4.07 9.04 349.7 162.8 361.7 110 50
Semimembranosus 11.58 7.68 6.43 463.3 307.2 257.3 228 190
Semitendinosus 8.88 4.62 8.55 355.3 184.8 342.2 202 105
Gracilis 3.21 3.86 5.57 128.4 154.4 222.6 100 85
Sartorius 3.13 2.68 3.36 125.2 107.2 134.5 141 125
Rectus femoris 12.69 6.77 10.73 428.0** 383.6** 429.4 258 165
Biceps femoris (long) 10.50 7.86 14.89 420.0 314.4 595.5 166 -
Biceps femoris (brev) 8.87 4.82 4.68 354.6 192.8 187.2 128 95
* - cadaver specimen; 2* - cadaver specimen; 3* - tomogram data. ** Value Fmax for this muscle was calculated with the use of the formula (3).
Table 4. Absolute and relative length of muscle.
Name of muscle % Lven % Lten Lmuscle(mm) Lrel l
1* 2* 1* 2* 1* 2* D* 1* 2*
Psoas major 0.58 0.47 0.42 0.53 190 170 91** 0.40 0.38 l(f)
Iliacus 0.81 0.91 0.19 0.09 270 110 91** 0.57 0.24 l(f)
Gemellus superior 0.67 - 0.33 - 75 - 90 0.23 - l(c)
Gemellus inferior 0.67 - 0.33 - 75 - 71 0.23 - l(c)
Obturator externus 0.94 0.94 0.06 0.06 85 85 104 0.27 0.30 l(c)
Obturator internus 0.57 0.63 0.43 0.38 140 80 80** 0.44 0.28 l(c)
Piriformis 0.64 0.65 0.36 0.35 110 108 140 0.34 0.38 l(c)
Quadratus femoris - 1.00 - 0.00 - 52 63 - 0.18 l(c)
Pectineus 1.00 1.00 0.00 0.00 116 110 141 0.36 - l(c)
Adductor minimus 1.00 - 0.00 - 110 - 126 0.34 - l(c)
Adductor brevis 1.00 1.00 0.00 0.00 170 163 138 0.53 0.57 l(c)
Adductor longus 0.96 0.97 0.04 0.03 260 330 199 0.67 0.92 (g)
Adductor magnus (ant) 1.00 - 0.00 - 280 - - 0.72 - l(g)
Adductor magnus (med) 1.00 1.00 0.00 0.00 320 315 185 0.82 0.88 l(g)
Adductor magnus (post) 1.00 - 0.00 - 300 - 348 0.77 - l(g)
Gluteus minimus (ant) 0.86 0.75 0.14 0.25 70 110 107 0.18 0.31 (g)
Gluteus minimus (med) 0.80 0.68 0.20 0.32 100 125 125 0.26 0.35 l(g)
Gluteus minimus (post) 0.86 0.50 0.14 0.50 70 130 124 0.18 0.36 (g)
Gluteus medius (ant) 1.00 0.91 0.00 0.09 75 117 136 0.19 0.33 l(g)
Gluteus medius (med) 1.00 0.92 0.00 0.08 100 120 168 0.26 0.33 (g)
Gluteus medius (post) 1.00 0.90 0.00 0.10 150 104 154 0.38 0.29 l(g)
Gluteus maximus (inf) 1.00 1.00 0.00 0.00 220 210 209 0.69 0.73 l(c)
Gluteus maximus (sup) 1.00 1.00 0.00 0.00 173 210 - 0.54 0.73 l(c)
Tensor fascia latae 0.23 0.24 0.77 0.76 480 470 515 1.02 1.04 l(f)
Semimembranosus 0.68 0.72 0.32 0.28 390 355 398 0.83 0.79 l(f)
Semitendinosus 0.57 0.49 0.43 0.51 495 478 399 1.05 1.06 l(f)
Gracilis 0.67 0.66 0.33 0.34 450 420 387 0.96 0.93 l(f)
Sartorius 0.85 0.77 0.15 0.23 620 646 515 1.32 1.44 l(f)
Rectus femoris 0.53 0.61 0.47 0.39 562 560 453 1.20 1.24 l(f)
Biceps femoris (long) 0.70 0.72 0.30 0.28 379 374 409 0.81 0.83 l(f)
Biceps femoris (brev) 0.84 0.82 0.16 0.18 160 310 - 0.34 0.69 l(f)
1* - cadaver specimen; 2* - cadaver specimen; D - length of muscles calculated with the use of data from research [7].
** For the muscles changing their directions the length of the straight line of the muscle is used.
Table 5. Relative values of measured musc
e parameters.
Name of muscle q rel San c rel ' max mrel
1* 2* 3* 1* 2* 3* 1* 2*
Psoas major 3.61 1.72 4.63 0.66 0.29 0.82 1.31 0.00
Iliacus 3.97 4.29 3.37 0.72 0.72 0.60 1.24 1.12
Gemellus superior 0.31 0.00 0.00 0.06 - - 0.05 0.00
Gemellus inferior 0.71 0.00 0.00 0.13 - - 0.07 0.00
Obturator externus 2.50 2.24 0.00 0.46 0.38 - 0.28 0.32
Obturator internus 3.43 0.00 0.00 0.63 - - 0.42 0.00
Piriformis 1.59 0.83 1.19 0.29 0.14 0.21 0.08 0.16
Quadratus femoris 0.00 3.02 0.00 - 0.51 - 0.00 0.56
Pectineus 2.18 1.34 1.95 0.40 0.23 0.35 0.41 0.60
Adductor minimus 1.21 0.00 0.00 0.22 - - 0.21 0.00
Adductor brevis 2.06 3.59 2.81 0.38 0.60 0.50 0.50 0.88
Adductor longus 3.93 3.51 3.34 0.72 0.59 0.60 1.25 1.44
Adductor magnus 8.34 4.20 9.71 1.52 0.71 1.73 3.48 2.08
Adductor magnus (ant) 3.32 0.00 0.00 0.61 - - 1.28 0.00
Adductor magnus (med) 1.96 4.20 0.00 0.36 0.71 - 0.92 2.08
Adductor magnus (post) 3.05 0.00 0.00 0.56 - - 1.28 0.00
Gluteus minimus 5.89 5.41 2.85 1.07 0.91 0.51 0.70 0.96
Gluteus minimus (ant) 1.87 2.15 0.00 0.34 0.36 - 0.20 0.36
Gluteus minimus (med) 2.62 2.00 0.00 0.48 0.34 - 0.35 0.36
Gluteus minimus (post) 1.40 1.26 0.00 0.25 0.21 - 0.14 0.24
Gluteus medius 9.68 7.84 8.76 1.77 1.32 1.56 1.88 1.28
Gluteus medius (ant) 1.79 2.59 0.00 0.33 0.44 - 0.21 0.40
Gluteus medius (med) 3.45 2.89 0.00 0.63 0.49 - 0.55 0.40
Gluteus medius (post) 4.44 2.37 0.00 0.81 0.40 - 1.11 0.48
Gluteus maximus 13.94 11.33 10.37 2.54 1.91 1.85 5.39 5.60
Gluteus maximus (inf) 6.34 3.24 0.00 1.16 0.54 - 2.98 3.04
Gluteus maximus (sup) 7.60 8.02 0.00 1.39 1.35 - 2.41 2.56
Tensor fascia latae 2.79 1.52 2.69 0.51 0.26 0.48 0.78 0.40
Semimembranosus 3.70 2.87 1.91 0.68 0.48 0.34 1.62 1.52
Semitendinosus 2.84 1.72 2.54 0.52 0.29 0.45 1.43 0.84
Gracilis 1.03 1.44 1.66 0.19 0.24 0.29 0.71 0.68
Sartorius 1.00 1.00 1.00 0.18 0.17 0.18 1.00 1.00
Rectus femoris 4.05 2.53 3.19 0.62 0.61 0.57 1.83 1.32
Biceps femoris (long) 3.35 2.93 4.43 0.61 0.49 0.79 1.18 0.00
Biceps femoris (brev) 2.83 1.80 1.39 0.52 0.30 0.25 0.91 0.76
* - cadaver specimen; 2* - cadaver specimen; 3* - tomogram c ata.
Table 6. m.Sartorius sizes relative to external anthropometric data.
Size Object
1* 2* 3*
San/ P2(C) 1.48 10° 1.68 10° 1.24 10°
m/MB 2.01 10-3 1.92 10-3 -
1* - cadaver specimen; 2* - cadaver specimen; 3* - alive man.
In Table 6 the following symbols are used: San - anatomic cross-sectional area of the muscle; P(C) - the perimeter of the hip (see Fig. 3.); m - the mass of the muscle; MB - the mass of the body.
The alive patient's tomogram data allow calculating exact individual values of San and
F
1 max■
To receive more exact results it is necessary in the future to perform a greater number of experiments. The scatter in absolute and relative values in our work may be connected with the fact that measurements of San of the second object was performed at the third day after the death.
References
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ЭКСПЕРИМЕНТАЛЬНОЕ ИССЛЕДОВАНИЕ АНАТОМИЧЕСКИХ И ГЕОМЕТРИЧЕСКИХ ПАРАМЕТРОВ БЕДРА ЧЕЛОВЕКА
А.В. Сотин, П.А. Гаряев, Н.Д. Демчук (Пермь, Россия)
Данные о силах, действующих на бедро, необходимы при биомеханическом моделировании процессов происходящих в костной ткани. В некоторых задачах, например, при прогнозировании развития асептического некроза головки бедренной кости нужно учитывать не только контактную силу в суставе, но и силы мышц,
огибающих головку. При расчетах оптимальной конструкции эндопротеза используют значения сил, возникающих в мышцах при ходьбе. Различные алгоритмы определения мышечных сил включают в качестве параметра площадь физиологического поперечного сечения мышц. К примеру, некоторые авторы при поиске решения в качестве ограничений используют максимальную изометрическую силу, развиваемую мышцей, которая линейно зависит от площади физиологического поперечника, у других исследователей целевая функция включает в себя площадь физиологического поперечного сечения.
В нашей работе измерялись некоторые анатомические и геометрические характеристики мышц таза и бедра правой ноги. Исследования проводились на двух мужских трупах схожего телосложения и одном живом человеке (по компьютерной томограмме нижней конечности). Исследовались 24 мышцы нижней конечности. Измеряемыми величинами являлись: площадь анатомического поперечного сечения, масса, длина брюшка и сухожилия каждой мышцы. По результатом измерений были вычислены некоторые относительные параметры мышц нижней конечности, а также максимальная изометрическая мышечная сила. Для сравнения полученных результатов использовались томографические снимки бедра и таза живого человека. Выявлено хорошее соответствие между измеряемыми параметрами для объектов с одинаковыми антропометрическими данными. Приведены данные для вычисления площади анатомического поперечного сечения и длины мышцы через внешние геометрические размеры бедра и таза. Описана методика использования томографических данных при исследовании параметров мышц in vivo. Библ. 10.
Ключевые слова: площадь физиологического поперечного сечения мышцы, максимальная изометрическая сила мышцы, компьютерная томограмма нижней конечности
Received 07 September 1999
