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Automatic zero strain compensation of in vivo bone strain recordings
W-
TECHNICAL
NOTE
AUTOMATIC ZERO STRAIN COMPENSATION IJV I’IVO BONE STRAIN RECORDINGS*
IVTRODUCTION
9?90:82’0806?1 I.3 W3.00’0 Pcrgamon Press Ltd.
OF
decelerating leg at the end of the swing phase. The small plateau between I and 2 corresponds to tht swmg phase
Strain gauges have been employed in horses and sheep fo measure in citw bone strain during locomotion (Lanyon, 1973 ; Turner et ai.. 1975 ; Rybicki er al., 1977 ; Carter er at.. 1980; Hartman and Lammertink. 1981). The determination of ‘zero’ strain in the living animal presnts practical problems, because the bone is under the conrinuous influence of intrinsic musck contractions and forces of inertia and gravity. Usually. the zero level is set when the animal is standing at ease with the instrumented leg lifted from the ground (Lanyon, 1973: Carter er al.. 1980). If necessary. the zero level is manually shifted to the plateau in the swing phase after recording of the locomotion strain pattern (Lanyon, 1973). Turner et 01. (1975) assumed that the bone was under zero strain when the animal was recovering from general anaesthe& lying quietly in lateral recumbency. Obviously, subjtctiw criteria will interfere when using each of these methods. To improve consistency and as a step towards an objective method, we developed a computer algorithm that minimizes the amplitudes of the two principal strains during the swing phase by the addition of a zero strain compensation.
Zero srroii,
compensariotl
required calculation of the maximum (cl) and minimum (Q) principal strains and the angle between the leading strain and the long axis of the bone were carried out using standard formulae (Dally and Riley, 1978). The procedure for the determination of the zero strain compensation (ZSClis illustrated in Fig. 2. Manualiy shifting the zero level is optional. The first step in the compensation procedure is the determination ofrhepoints markedti toein Fig. 1. Startingat an arbitrary point within the swing phase the sum P of squared amplitudes of the A, B and C-gauge data is calculated. Shifting the site of calculation into the support phase the maximum of P (marked a) is located and corresponds in this example with the minImum of the B-gauge signal. The onset of the support phase is found by going back in time until P is less than 0.1 times the maximum (marked h). Thereafter, The
~__. _
_
A
METHODS Signal
L.
s/tape
A three element. 45‘ strain gauge rosette (Tokyo Sokki Kenkyuio Co.. Ltd., type FRA-2-11) was bonded in the middle of the diaphysis on the caudal surface of the tibia of a horse. Figure 1 is a recording of the strain pattern obtained from the A. B and C gauges of this rosette when the animal was walkmg normally. The zero level was set when the animal was standing at ease with the instrumented leg lifted by the Investigator so that the tibia was held nearly horizontal. After recording of the data the zero level was shifted to the plateau in the swing phase. as indicated by the horizontal broken lines (Fig. 1). The B gauge, being aligned nearly paiallel with the long axis of the bone, shows a biphasic pattern during the support phase (between 2 and 3). The top of the tracing preceding the support phase (21 may be due lo inertia of the
*Received 20 July 1981 ; in final form 11 March 1982. t Correspondence to : Dr. H. C. Schamhardt, Department of Veterinary Anatomy, University of Utrecht, Yalelaan 1, 3584 CL Utrecht. The Netherlands. 621
_ -
-
B
e
c 6
0
-500
I
a b
C
Fig. 1. Strain pattern obtained’during normal walk from the A. B and C gauges of a 45’ strain gauge rosette. bonded to the caudal surface of the tibia of a horse. The zero level was set when the animal was standing at ease with the Instrumented leg lifted from the ground. After recording the zero level was shifted, asindicated by the horizontal broken lines. 1-2. swing phase; 2-3, support phase; u:f. see text.
Technical Note
622
Table 1. Maximum (c,) and minimum (cJ principal strains ( 10b6) on the caudal surface of the tibia of a horse at the first top of the support phase (Fig. 3, lower panel, marked p) and during the preceding swing phase
No compensation
Shifting zero level
Automatic zsc*
ZSC~
0
ZSCB
0
305
290.9
zscc
0
165
162.0
-63
- 53.4
Support phase
k
61
691
82 a*
- 1456 14.4
468 -1131
490
-1146
12.8
12.9
Swing phase I:1
161.0
2.2
1.4
I:2
- 151.7
- 12.4
3.0
* ZSC, zero strain compensation of the A, B and C gauges of a 45” strain gauge rosette; a, the angle between the leading strain and the long axis of the bone (degrees).
[calculateZSC from aQ/&,-01
procedure. The covered data points are used to direct the value of
to its minimum by addition ofa ZSC to the strain values of the A: B and C-gauges, in such a way that aQ/ac, = 0, where i = A, B or C. The ZSC value is found using a direct search minimization routine (Fletscher and Powell, 1963). The next step is to add ZSC to the original strain dataand to calculate cr and t:z once again. The result is a better approximation of the principal strain curves during the swing phase. However, the chosen window c toe partrally covers data out of the presupport top. Therefore, we assumed that the optimal site for ZSC calculation is that site where the contribution to Q of the strainvalues between e and d - 1 equals that from d + 1 to c, i.e. d-L
location of minimun
lprccede in time to O.l*maximum
(f)l
and
P
d+t
As a symmetry index we used: SI =
Fig. 2. Flow chart of the procedure for automatic zero strain compensation (ZSC). A. B, C, amplitudes of the A, B and C gauge signals; a tof, see Fig. 1 and text.
the ‘pre-support top’ (marked 2) is passed backwards until half its maximum value is reached (marked c). Initially, a window ofninedatapoints (180 ms)isset fromc toe. centered d. The data between d and c partially belong to the presupport top, while the remainder corresponds to the swing phase. The window will be better located in the course of the
IL - s,, + L - %,I St, + s,, + L f s,, .
To achieve optimal symmetry the window e to c is shifted backwards into the swing phase, and the ZSC procedure is repeated, until SI < 0.075. The strain values within this optimal window are saved for later calculations. The program proceeds to calculate ZSC for the subsequent strides, starting from the pointf’where P is less than 0.1 times the preceding maximum. The averaged ZSC for the complete run is then calculated from the gathered strain values belonging to all strides in the run. REWJLTS Table 1 summarizes the results of the application of the three methods of zero strain compensation (ZSC) on the
Technical Note
623
where ZSC is computed will be at similar locations in the strain curve, although their amplitude may differ from the level of absolute zero strain. Automatic ZSC is especially useful when recordings are compared which were obtained from the same animal after interference on the locomotor system. Our program uses some default values for window width, required degree of symmetry, etc., which are adapted to the use of small ponies (10-250 kg) with a characteristic, rapid gait. These values can be changed easily to fit strain patterns from other animals with a similar walking pattern. The problem of determining ZSC objectively has already been mentioned by several authors (Lanyon. 1973: Turner er al.. 1975: Carter et al.. 1980). They obtained a ‘zero’ level from techniques which allowed subjective criteria to interfere. Two arguments were used to justify their methods: 1. It is impossible to obtain the exact level ofzero strain in the living animal; 2. ZSC is usually small as compared with the maximum amplitudes of c1 and I:~,hence an error in ZSC hardly affects the strain pattern during the support phase. However, a nproducibk method, as described in this note, to ehminate as much subjective criteria as possible from the procedure of zeroing the strain tracings may be helpful in the study of the locomotion strain pattern. Fig. 3. Pattern of principal strains (c, and c2)calculated from original I..~,cg and cc data (upper panel) and after automatic zero strain compensation (ZSC) (lower panel). The corresponding ZSC values have been given in Table 1. p. first maximum of cI and c1 during the support phase.
principal strain data of a representative step (between 1 andf, Fig. 1). The first column presents data which were obtained after zeroing the strain signals when the animal stood at ease w’ith its leg lifted. It appears, that very large values of (:I and c2 were obtained, especially during the swing phase (Fig. 3, upper panel). The irregularity of the analyzed curves is clear. After manually shifting the zero level (column 2) these deviations were greatly reduced, while c, and c2 were also markedly affected. Automatic ZSC further minimized the values of I:, and c2 during the swing phase (column 3), but hardly changed the values during the support phase. The strain pattern after automatic ZSC is shown in Fig. 3, lower panel. DISCUS!3ON The first
section of the algorithm presented for automa!ic zero strain compensation (ZSC), which enables the input of manually determined ZSC, is optional. When the recorded data are used directly, it is possible that the program will find an incorrect ZSC, especially when ZSC is relatively large. Usually, an irregularity will reveal itself by a wrong site or amplitude of ZSC. One should notice, however, that a manually predetermined ZSC does not affect the program calculated ZSC values. The assumptions in the algorithm that zero strain and symmetrical i:, and I:~curves can be found at a given point during the swing phase may not be true. However, the sites
Aoailabilir)
A source text of the algorithm, written in FORTRAN IV, IS available (free of charge) from the authors. The minimization routine FMFP is part of the library of the Academic Computer Center Utrecht. The Netherlands.
Departmenr of Veterinary Anaromj University of Utrecht Yalelam
H. C.
SCHAMHARDT HARTMAN
W.
1
Vtrecht The Netherlands
REFERENCES Carter, D. R., Smith, D. J.. Spengler, D. M., Daly, C. H. and Frankel, V. H. (1980) Measurement and analysis of in rioo bone strains on the canine radius and ulna. J. Biomechanics 13.27-38. Dally, J. W. and Riley. W. F. (1978) Experimentul Stress Analysis. pp. 321-322. McGraw-Hill, New York. Fletscher, R. and Powell, M. J. D. (1963) A rapid descent method for minimization. Comput. J. 6, 163-168. Hartman, W. and Lammertink, J. L. M. A. (1981 )Bone strain in the tibia of the pony. Acta morph. neer/.-scond. 19, 260. Lanyon, L. E. (1973) Analysis of surface bone strain in the calcaneus of sheep during normal locomotion. J. Biomechanics 6, 41-49.
Rybicki, E. F., Mills, E. J., Turner, A. S. and Simonen, F. A. (1977) In oiuo and analytical studies of forces and moments in equine long bones. J. Biomechanics 10, 701-705. Turner, A. S., Mills, E. J. and Gabel, A. A. (1975) III vioo measurement of bone strains in the horse. Am. J. wf. Res. 36, 1573-1579.
TECHNICAL
NOTE
AUTOMATIC ZERO STRAIN COMPENSATION IJV I’IVO BONE STRAIN RECORDINGS*
IVTRODUCTION
9?90:82’0806?1 I.3 W3.00’0 Pcrgamon Press Ltd.
OF
decelerating leg at the end of the swing phase. The small plateau between I and 2 corresponds to tht swmg phase
Strain gauges have been employed in horses and sheep fo measure in citw bone strain during locomotion (Lanyon, 1973 ; Turner et ai.. 1975 ; Rybicki er al., 1977 ; Carter er at.. 1980; Hartman and Lammertink. 1981). The determination of ‘zero’ strain in the living animal presnts practical problems, because the bone is under the conrinuous influence of intrinsic musck contractions and forces of inertia and gravity. Usually. the zero level is set when the animal is standing at ease with the instrumented leg lifted from the ground (Lanyon, 1973: Carter er al.. 1980). If necessary. the zero level is manually shifted to the plateau in the swing phase after recording of the locomotion strain pattern (Lanyon, 1973). Turner et 01. (1975) assumed that the bone was under zero strain when the animal was recovering from general anaesthe& lying quietly in lateral recumbency. Obviously, subjtctiw criteria will interfere when using each of these methods. To improve consistency and as a step towards an objective method, we developed a computer algorithm that minimizes the amplitudes of the two principal strains during the swing phase by the addition of a zero strain compensation.
Zero srroii,
compensariotl
required calculation of the maximum (cl) and minimum (Q) principal strains and the angle between the leading strain and the long axis of the bone were carried out using standard formulae (Dally and Riley, 1978). The procedure for the determination of the zero strain compensation (ZSClis illustrated in Fig. 2. Manualiy shifting the zero level is optional. The first step in the compensation procedure is the determination ofrhepoints markedti toein Fig. 1. Startingat an arbitrary point within the swing phase the sum P of squared amplitudes of the A, B and C-gauge data is calculated. Shifting the site of calculation into the support phase the maximum of P (marked a) is located and corresponds in this example with the minImum of the B-gauge signal. The onset of the support phase is found by going back in time until P is less than 0.1 times the maximum (marked h). Thereafter, The
~__. _
_
A
METHODS Signal
L.
s/tape
A three element. 45‘ strain gauge rosette (Tokyo Sokki Kenkyuio Co.. Ltd., type FRA-2-11) was bonded in the middle of the diaphysis on the caudal surface of the tibia of a horse. Figure 1 is a recording of the strain pattern obtained from the A. B and C gauges of this rosette when the animal was walkmg normally. The zero level was set when the animal was standing at ease with the instrumented leg lifted by the Investigator so that the tibia was held nearly horizontal. After recording of the data the zero level was shifted to the plateau in the swing phase. as indicated by the horizontal broken lines (Fig. 1). The B gauge, being aligned nearly paiallel with the long axis of the bone, shows a biphasic pattern during the support phase (between 2 and 3). The top of the tracing preceding the support phase (21 may be due lo inertia of the
*Received 20 July 1981 ; in final form 11 March 1982. t Correspondence to : Dr. H. C. Schamhardt, Department of Veterinary Anatomy, University of Utrecht, Yalelaan 1, 3584 CL Utrecht. The Netherlands. 621
_ -
-
B
e
c 6
0
-500
I
a b
C
Fig. 1. Strain pattern obtained’during normal walk from the A. B and C gauges of a 45’ strain gauge rosette. bonded to the caudal surface of the tibia of a horse. The zero level was set when the animal was standing at ease with the Instrumented leg lifted from the ground. After recording the zero level was shifted, asindicated by the horizontal broken lines. 1-2. swing phase; 2-3, support phase; u:f. see text.
Technical Note
622
Table 1. Maximum (c,) and minimum (cJ principal strains ( 10b6) on the caudal surface of the tibia of a horse at the first top of the support phase (Fig. 3, lower panel, marked p) and during the preceding swing phase
No compensation
Shifting zero level
Automatic zsc*
ZSC~
0
ZSCB
0
305
290.9
zscc
0
165
162.0
-63
- 53.4
Support phase
k
61
691
82 a*
- 1456 14.4
468 -1131
490
-1146
12.8
12.9
Swing phase I:1
161.0
2.2
1.4
I:2
- 151.7
- 12.4
3.0
* ZSC, zero strain compensation of the A, B and C gauges of a 45” strain gauge rosette; a, the angle between the leading strain and the long axis of the bone (degrees).
[calculateZSC from aQ/&,-01
procedure. The covered data points are used to direct the value of
to its minimum by addition ofa ZSC to the strain values of the A: B and C-gauges, in such a way that aQ/ac, = 0, where i = A, B or C. The ZSC value is found using a direct search minimization routine (Fletscher and Powell, 1963). The next step is to add ZSC to the original strain dataand to calculate cr and t:z once again. The result is a better approximation of the principal strain curves during the swing phase. However, the chosen window c toe partrally covers data out of the presupport top. Therefore, we assumed that the optimal site for ZSC calculation is that site where the contribution to Q of the strainvalues between e and d - 1 equals that from d + 1 to c, i.e. d-L
location of minimun
lprccede in time to O.l*maximum
(f)l
and
P
d+t
As a symmetry index we used: SI =
Fig. 2. Flow chart of the procedure for automatic zero strain compensation (ZSC). A. B, C, amplitudes of the A, B and C gauge signals; a tof, see Fig. 1 and text.
the ‘pre-support top’ (marked 2) is passed backwards until half its maximum value is reached (marked c). Initially, a window ofninedatapoints (180 ms)isset fromc toe. centered d. The data between d and c partially belong to the presupport top, while the remainder corresponds to the swing phase. The window will be better located in the course of the
IL - s,, + L - %,I St, + s,, + L f s,, .
To achieve optimal symmetry the window e to c is shifted backwards into the swing phase, and the ZSC procedure is repeated, until SI < 0.075. The strain values within this optimal window are saved for later calculations. The program proceeds to calculate ZSC for the subsequent strides, starting from the pointf’where P is less than 0.1 times the preceding maximum. The averaged ZSC for the complete run is then calculated from the gathered strain values belonging to all strides in the run. REWJLTS Table 1 summarizes the results of the application of the three methods of zero strain compensation (ZSC) on the
Technical Note
623
where ZSC is computed will be at similar locations in the strain curve, although their amplitude may differ from the level of absolute zero strain. Automatic ZSC is especially useful when recordings are compared which were obtained from the same animal after interference on the locomotor system. Our program uses some default values for window width, required degree of symmetry, etc., which are adapted to the use of small ponies (10-250 kg) with a characteristic, rapid gait. These values can be changed easily to fit strain patterns from other animals with a similar walking pattern. The problem of determining ZSC objectively has already been mentioned by several authors (Lanyon. 1973: Turner er al.. 1975: Carter et al.. 1980). They obtained a ‘zero’ level from techniques which allowed subjective criteria to interfere. Two arguments were used to justify their methods: 1. It is impossible to obtain the exact level ofzero strain in the living animal; 2. ZSC is usually small as compared with the maximum amplitudes of c1 and I:~,hence an error in ZSC hardly affects the strain pattern during the support phase. However, a nproducibk method, as described in this note, to ehminate as much subjective criteria as possible from the procedure of zeroing the strain tracings may be helpful in the study of the locomotion strain pattern. Fig. 3. Pattern of principal strains (c, and c2)calculated from original I..~,cg and cc data (upper panel) and after automatic zero strain compensation (ZSC) (lower panel). The corresponding ZSC values have been given in Table 1. p. first maximum of cI and c1 during the support phase.
principal strain data of a representative step (between 1 andf, Fig. 1). The first column presents data which were obtained after zeroing the strain signals when the animal stood at ease w’ith its leg lifted. It appears, that very large values of (:I and c2 were obtained, especially during the swing phase (Fig. 3, upper panel). The irregularity of the analyzed curves is clear. After manually shifting the zero level (column 2) these deviations were greatly reduced, while c, and c2 were also markedly affected. Automatic ZSC further minimized the values of I:, and c2 during the swing phase (column 3), but hardly changed the values during the support phase. The strain pattern after automatic ZSC is shown in Fig. 3, lower panel. DISCUS!3ON The first
section of the algorithm presented for automa!ic zero strain compensation (ZSC), which enables the input of manually determined ZSC, is optional. When the recorded data are used directly, it is possible that the program will find an incorrect ZSC, especially when ZSC is relatively large. Usually, an irregularity will reveal itself by a wrong site or amplitude of ZSC. One should notice, however, that a manually predetermined ZSC does not affect the program calculated ZSC values. The assumptions in the algorithm that zero strain and symmetrical i:, and I:~curves can be found at a given point during the swing phase may not be true. However, the sites
Aoailabilir)
A source text of the algorithm, written in FORTRAN IV, IS available (free of charge) from the authors. The minimization routine FMFP is part of the library of the Academic Computer Center Utrecht. The Netherlands.
Departmenr of Veterinary Anaromj University of Utrecht Yalelam
H. C.
SCHAMHARDT HARTMAN
W.
1
Vtrecht The Netherlands
REFERENCES Carter, D. R., Smith, D. J.. Spengler, D. M., Daly, C. H. and Frankel, V. H. (1980) Measurement and analysis of in rioo bone strains on the canine radius and ulna. J. Biomechanics 13.27-38. Dally, J. W. and Riley. W. F. (1978) Experimentul Stress Analysis. pp. 321-322. McGraw-Hill, New York. Fletscher, R. and Powell, M. J. D. (1963) A rapid descent method for minimization. Comput. J. 6, 163-168. Hartman, W. and Lammertink, J. L. M. A. (1981 )Bone strain in the tibia of the pony. Acta morph. neer/.-scond. 19, 260. Lanyon, L. E. (1973) Analysis of surface bone strain in the calcaneus of sheep during normal locomotion. J. Biomechanics 6, 41-49.
Rybicki, E. F., Mills, E. J., Turner, A. S. and Simonen, F. A. (1977) In oiuo and analytical studies of forces and moments in equine long bones. J. Biomechanics 10, 701-705. Turner, A. S., Mills, E. J. and Gabel, A. A. (1975) III vioo measurement of bone strains in the horse. Am. J. wf. Res. 36, 1573-1579.