Under various psychological settings, the spine load sharing and methods of Load Distribution Measurement

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The spine's primary function is to support the body's weight. It is critical to accurately evaluate the load distribution among passive and active components of the human trunk during different activities. The aim of determining this distribution is to develop performance improvement strategies, determine optimum posture, and efficiently avoid, assess, and manage spinal associated disorders (Hansson and Roos). Several experiments have been performed with the aim of indirectly estimating spinal muscle pressures and internal loads by calculating intradiscal pressure or load on fixation devices. ­­­­­­­­­­­The absence of noninvasive techniques has made biomechanical models indispensable while determining the muscle forces as well as the internal passive loads. The literature has proposed some approaches as a way of overcoming the presence of kinetic redundancy in the system equations (Andresen, Werner and Schober). These approaches are based on reduction method, the EMG-assisted models, optimization methods, and any combination of the approaches. The success of biomedical models has been documented in various literatures like journals, books, and articles. In this paper, an article “Load Sharing within a Human Thoracic Vertebral Body” will be analyzed. The article is an illustration of the load sharing on spine.

Verification of dynamic and static equilibrium for the balance of external moments is among the major challenges facing the available biomechanical models. This shortcoming has been identified at the lower lumbar levels within the spine. A linear finite element model has been developed and been reported to evaluate muscle recruitment and internal lumbar loads during maximum and sub-maximum efforts (Hansson and Roos). This has been seen as a way of overcoming the biomedical model deficiency. It also aims at satisfying the equilibrium in different directions at all lumbar levels as well as accounting for the passive ligamentous resistance. Recently, a novel iterative and an approach based on kinematics that priori known kinematics of the spine at different levels under given external loads, along with passive properties, were exploited in a nonlinear finite element model to evaluate unknown muscle and internal loads, resulting in a synergistic solution of the entire active and passive system (King, Prasad and Ewing). The relative validity of various models and the accuracy in their predictions under different loading and postural conditions, though naturally dependent on their assumptions (e.g., the choice of cost functions or strategies to distribute reactive moments amongst spinal muscles), need yet to be established (Cao, Grimm and Yang).

In addition to the system’s redundancy on the equations developed to determine the load sharing, muscle forces, and internal loads, in the recent years, the spine stability have attracted considerable attention from scholars and medics. From the previous studies, it has been reported that the lumbar spine and the passive ligamentous thoracolumbar have exhibited large displacements referred to as the hypermobility while subjected to loads below 100N (King, Prasad and Ewing). This means the instability for an imperfect system such as the spine. It is important to bear in mind that these forces are only a small fraction of the forces carried by the spine while carrying out daily chores. There arises then the issue of system stabilization.

Literature has also suggested various stabilizing mechanisms from the investigation carried out. For instance, wrapping compression loading that follows the curvature of the spine to remain normal to disc mid-planes, changes in the posture, the intra-abdominal pressure, and muscle activation or co-activation are some of the proposed mechanisms (Cao, Grimm and Yang). The model for estimating the role of the muscular reflexive activities during spine stabilization has been developed. The posture in standing position can be minimally adjusted with an aim of minimizing the required moments of equilibrium when subjected to different or varying load parameters. As such, it is possible to quantify and support the function of posture while influencing both the equilibrium and stability of the spine. The kinematics-based approach can be applied for the evaluation of muscle forces and subsequent investigation of system stability while accounting for the preceding optimal postures (Hansson and Roos).

System stability is examined using both linear buckling and nonlinear analyses, assuming various muscle stiffness values. The former is performed using the updated geometry and stressed condition of the spine at the final configuration. These analyses of such an imperfect system are more accurate and reliable than the linear stability analyses often performed on the un-deformed and unstressed system (King, Prasad and Ewing). Finally, the effect of prescribed co-activation in abdominal muscles on extensor muscle forces, internal loads, and stability margin in standing postures is quantified.

Study Design

A series of non-destructive compressive testing on excised/isolated human thoracic vertebral bodies were carried out (McBroom, Hayes and Edwards). The testing procedure undertaken involved removing certain parts of the vertebrae in steps. Re-testing of these parts was carried out to investigate the relevant weights of each element with respect to the overall load ratio of the column. The figure 1 below clarifies the different methods used for calculating the load capacity for the vertebrae and the testing sequence followed.

Figure 1: Different methods used for calculating the load capacity for the vertebrae and the testing sequence followed

The testing sequence for the removed vertebrae consisted of:

An initial vertebrae column that was intact.

A portion of the vertebrae at the bottom center of the end plate was removed creating a narrow entry to allow access to the trabecular core.

A cross section area of the trabecular bone was removed from the center (25 %)

A second portion of the trabecular bone was removed, 25 %, that is adjacent to the central quarter.

The next step involved removing a third portion with the same ratio of 25 %. This third part is laterally located in relation to the second quarter.

This was the last step and it involved removing the last section adjacent to the cortex. The vertebrae formed a conical bone with a hollow center following the removal of this section of the trabecular bone.

Each step involved measuring with a strain gauge the strain values for the cortex. The load applied is proportional to the strain value; hence, an increase in the load applied resulted in a consequent increase in the strain value and vice versa. The resultant values for the strain gave the clue for the loading differences on the vertebrae column in comparison to other methods for removing the sections (Hansson and Roos). The vertebrae loading ration was then computed by dividing the measured strain values in each step by the value obtained from the hollow section.

Specimen Preparation

The seven specimens used for this study were the cadaver spines. The spines fall under the levels of T5 section to T12 section. The experiment excluded the spine portions with deformations and fractures by performing radiography of the entire vertebrae. The experiment used one of the spines from the seven available as the control/pilot experiment at the initial stage. The remainder 46 vertebrae (six spines) were used for the actual study (Mazess). Experimental data collection for the bone mineral density in units of g/cm2 were carried out by subjecting the spines to the dual energy X-ray absorptiometry using the Hologic set of scanners. The scan procedures involved taking the measures with the spines in the anteroposterior position while they were simulating water bath that contained water to the brim depicting as the human body tissues (Faulkner, Cann and Hasegawa). The bone mineral density (BMD) data obtained was categorized in accordance to their respective T-scores. Spines with T-score ranked above -1 were placed in the category of normal tissues; those with a score ranging from -1 to -2.5 were in the category of osteopenic. The table below summarizes the classification. For specimen and donors with a corresponding test score less than -2.5, they were categorized under the class of osteoporotic. The overall results were recorded in a table. The next step of the experiment involved separating the 46 vertebrae. Using a bone saw, the vertebrae column division was achieved by cutting the pedicles at the bone junctions. The end plate and the cortex were to remain intact through the entire procedures. The tissues covering the cortex were carefully removed to access it.

Specimen No.



cause of death

BMD (g/cm2)





Shotgun would to chest






Cardial arrest












Acute hemopericardium






Cardiopulmonary arrest






Cardiopulmonary arrest






Renal failure



Table 1: the summarized classification of the specimen

While taking care so the resin does not coat the uncovered cortex following the removal of soft tissues, the vertebrae sections were placed in a resin made of polyester. The inferior and superior end plates were placed in a plano-parallel fashion in the polyester resin. The specimens were placed in plastic bags soaked in saline gauzes that help avoid desiccation and were stored at temperatures of -200 C awaiting the tests to be performed. Once the vertebrae were set for the tests to be performed, thawing was done and the surfaces of the cortex prepared by a method formulated by Wright and Hayes together with Cochran. The method they developed uses the principle of a 220-grit sandpaper to sand the cortex followed by surface preparation with the application of ethyl ether, ethanol, and later neutralization with M-Prep Neutralizer in that order. The procedure was repeated thrice followed by air drying. To investigate the strain distribution, the lateral and anterior sections of the cortex were applied with uniaxial strain gauges in four layers by use of cyanoacrylate. The strain gauges were applied parallel to the central axis of the vertebrae sections. To measure the strain, the gauges were soldered to lead wires and the equipment used for signal conditioning connected to by the lead wires (Faulkner, Cann and Hasegawa).

Biomechanical Testing

Detailed below is the testing procedure that was adopted. The Alliance testing machine was used. Custom-made pincers were used to grip the vertebrae while exposing it to axial compressive forces (McBroom, Hayes and Edwards). The experiment was conducted under different loading conditions of forces 200N, 400N, and 600N (Hongo, Abe and Shimada). The rate of displacement was also performed in the sequence of 1, 5, 10 and 25 mm/s. This meant that each section of the vertebrae was tested and data collected twelve times for each section. The vertebrae body and the bottom fixture were separated from each other after the intact test was performed. An electric drill was then used to create a narrow space at the end plate while making sure the trabecular bone is not damaged. The next step involved the removal of the trabecular bone in sequence in the above outlined procedure.

Two methods used in sequence ensured the removal of the proper amount of the trabecular bone (Cochran). The first method involved calculations of the cross sectional areas with the help of a digital photographer and an image scanner with a preinstalled image analysis program that could determine the radius of the section of the spine that was to be removed from the column for analysis (Homminga, Weinans and Gowin). The second method involved the removal of a constant amount of bone from each experiment performed in relation to the previous one. This could only be achieved by weighing the amount of drilled bone in each set up and using a digital weighing meter. The meter has an absolute resolution of 0.01 grams in the weighing scale. In this set up, the accurate amount of the trabecular bone was removed same in all set ups. Following the successful removal of the vertebrae, the conducted tests were similar in the displacement speed s and the applied loading. The sum total of all conducted tests was 72 tests since in each set up, the tests conducted in each vertebra were 12 tests (Bell, Dunbar and Beck).

Collection of Data

The micro strains imminent in each set up were measured and the results tabulated. The loading were in steps outlined in the previous section at a frequency of 50 Hz (Hongo, Abe and Shimada). The measurement system consisted of a scanner, a strain gauge card, and a peripheral connection between the card and the scanner that allowed the data collected to be read.

A personal computer

PCI Interface card model 5101A

Model 5110 Strain Gauge cards

Scanner Model 5100A


Vishay Micro Measurements Group


The decrease in length of the bone, whose sign is negative, was expressed as a fraction of the original length and was the compressive strain. The corresponding increase in length, with a positive sign, was the tensile strain (Kaplan, Dalinka and Karp). A few exceptions yielded the positive sign. However, the compressive strains returned most of the values obtained. The absolute strain value for each set up was defined as the average value between the compressive and the tensile strains from that set up, measured using four sets of gauges (McBroom, Hayes and Edwards). Data for the sixth set of strain values was obtained from the four gauges using the characterization of levels, osteoporosis, age, and the conditions under which the test was conducted (Bell, Dunbar and Beck).

The inferential and descriptive statistics were used in explaining the data collected. A statistical model was used to achieve the overall test results. For the different conditions of the displacement speed and the loading capacity, a general linear model was used for the repetitive data sets for each experiment. Paired T tests were set up and used in the analysis for the differences in the values obtained under the strain gauges and the loading ratios (Genant, Steiger and Block). The mean values obtained from the cortical strain and the loading ratios were moderated using the student’s test. The confidence level of the conducted tests was at 95 % level.


Cortical Strains at the Intact Mode

Table 2 below recorded the average strain values for the lower and the middle sections of the spines under the different loading conditions and displacement speeds. The middle section’s results reveals that the osteopenic vertebrae has an almost doubled value for the strain measurements as compared to the non-osteopenic ones under the loading conditions and the displacement rates (Homminga, Weinans and Gowin). The difference in the strain values recorded for the lower section of the spine showed slight but significant variations. For the normal vertebrae, the inter-region strain variations were slight and the difference between them insignificant. This was the region in the lower and middle sections of the spine. On the contrary, the strain values for the middle spine section were comparably higher than the strain values for the lower section. Strain being linearly proportional to the loading, it increased as the loading capacity increased. The mean computed strain value after the experiment averaged at 1156 ± 578 with an applied force of 200N, a strain value of 2347 ± 964 when the applied loading was at 400N, and strain value of 3376 ± 1408 under the 600N loading capacity (Hongo, Abe and Shimada).

This therefore confirmed the expected results in that the strain values correlate with the applied loading in linear fashion. The displacement rates did not affect the values of the strain gauges in accordance to the linearity of the analysis.

Table 2: The average strain values for the lower and the middle sections of the spines under the different loading conditions and displacement speeds

Load Sharing After Trabecular Bone Removal

Following the systematic removal of the trabecular bone, the corresponding values of the strain gauges increased. This shows a growth in the loading capacity applied to the vertebrae. The strain values were expressed as percentage from the previous section. The differences in the strain values obtained from each consecutive step bear significant comparison (Kaplan, Dalinka and Karp). However, the values have no existing linear correlation with either the level or the osteopenia. The mean deviation of the loading ratio of the experiment was optimal with a displacement rate of 1 mm/s. The loading ratio was sustainable for measurements beyond the second quarter of the spine, the values for the inner two middle vertebrae sections were comparably smaller.

Table 3: Load Sharing After Trabecular Bone Removal

Factors Affecting Load Sharing of Cortical Bone

Data analysis in this section involved specifications for the loading ratio from the previous sections as identifiable to a vertebra in as given location. The loading ratio given in table 4 contains the displacement speed for all vertebrae types investigated in the experiment. Given factors were investigated on their effects on the loading ratio. Such factors included the displacement speeds, level, and loading conditions (Homminga, Weinans and Gowin). Regardless of the loading capacity and the displacement speed used, the loading ratio for the osteopenic set was much higher than the values for the normal set. The averaged mean values for each set were 48.1±7.6 for the osteopenic vertebrae and for the normal vertebrae, the value was 44.3±10.6 giving a statistically indifference of 0.03. Similarly, the loading characteristics of the middle section follow the same criterion with an averaged mean of 49.4 ±10.0 which was much higher in comparison to that for the lower section with an averaged value of 42.4±8.5 with an indifference of p=0.05 (Kaplan, Dalinka and Karp). The displacement speeds and the loading conditions portrayed no significant influence on the loading ratios for higher loading conditions under the general linear model (GLM) analysis program. The figure below shows the established relationship existing under an applied load and the computed loading ratio.

Figure :

Table 4

Table 4: Load Sharing of Cortical Bone


The determination of the structural role played by each of the vertebrae components while they are in position is a difficult task to perform. This is because the weight measurements for the vertebrae cannot be achieved (Goel and Clausen). As a result, the alternative simpler option is to remove the sections of the vertebrae that leave a narrow window that allows for the testing of the set in an intact position and the results are compared to those for the removed section. Past research used the displacement curves or the peak loading to determine the loading ratios of the specific vertebrae.

Compared to the previous tests, this experiment introduces the concept of using the strain gauges to determine the respective strain values from the loading conditions. The concept behind it was that the resultant strain was linearly correlated to the loading conditions. The experiment from the obtained set of data proved that this concept was true and that it applied to this specific experiment. The measured strain values were observed to increment in the range of 1000-1200 for every loading capacity of 200N (Cao, Grimm and Yang). Therefore, the concept of determining the strain values enabled the determination of the load transfer in the series of adjacent sections of the spine. From these results, a second concept was developed and used for analysis in this study. The determination of the loading ratio followed the division of the strain values measured for the hollow to the strain values for the intact section.

Performed experiments in the past reveal that the tests conducted in the determination of the loading ratio involved grinding the cortex to remove it and engaged a study on the trabecular bone. For this experiment, following the decision to measure the strain values of the cortex, the only possible mean to establish the loading ratio was the removal of the trabecular bone.

The initial stage of the experiment involved demonstration tests that were conducted to investigate the best and most efficient means to remove the trabecular bone that would allow the study to continue by not influencing the results that would be obtained from the remaining hollow section (Genant, Steiger and Block). Before settling for this method of conducting the experiment, numerous other test methods were evaluated to mention the division of the lower and the upper sections by transverse cutting of the vertebrae. The obtained two sections were then transferred to the working table and rejoined using sticking glue, cyanoacrylate, to fit their original positions preventing possible slippage, and then the tests were performed. However, the achieved results showed inconsistency and difficulties in comparing the sets of data leading to the abandoning of this method.

The second tried method was the Rockoff. The method compromises the integrity of the spines since it involved drilling the vertebrae. The disruption of the formation made the test difficult to perform and the resulting data set for strain showed a slight increase in the strain depicting that the remaining section of the trabecular bone still exerted some loading conditions on the vertebrae. The surface strains considerably increased rendering the Rochoff method invalid for the required test results. In a conducted Finite Elementary Analysis, the results showed that the inferior sections of the cortex do not undergo bending under loading; considerate the axial loading conditions they are subjected (Bartley, Arnold and Haslam). This analysis revealed that a narrow window created in the middle section of the endplate would not result in significant variations in the strain values obtained because of the loading characteristics. The actual observation was that the consequent improvements made impacted slight changes on the surface strain value. This procedure confirmed that the experimental results could be achieved without any alterations to the loading capacity of the vertebrae.

The variability was discovered as a critical factor that influences the complexity of the prevalent loading conditions. In the review, none other experiment had investigated its influence and hence there was not a single mention of it. Though the variations are wide, the finite experimental analysis confirmed that the lowest range was between 0 % - 34 % with the maximum value achieved within the range of 5 % - 63 % in the mid plane invalidating a single loading ratio (Goel and Clausen). The experimental tests performed earlier therefore aided in the determination of the strain distribution to validate the desired location of the loading ratio based on the formulated hypothesis for the finite element experimentation (Homminga, Weinans and Gowin). Two sets of the level T12, with a large surface allowed the mapping of the strain gages on both the lateral and the anterior positions subject to the testing conditions and the required procedures.

With the data obtained being so limited, detailed results could not be made regarding the test method. The illustrations for the loading ratio are however optimal through this means. The results for the two sets of specimen showed that the surface strain increased slightly upon removal of the trabecular bone. The results confirm with those from the finite element analysis set. The data obtained while the gauge was applied at the bottom section resulted in numerous inconsistencies (Cochran). Therefore, opting for an experimental design bore the conception that the inconsistency would be alleviated. In the experiment, it was discovered that the midsagittal point sustained as much as 45 % of the total axial loading that the spine section could bear. The data recorded also showed certain factors affected the loading ratio with a reported single misleading variable. This followed that the available data and test experiments yielded conflicting results based on the effects of the loading ratio on osteoporosis.

Different authors estimated the contributed strength of the vertebrae on a healthy being, some cited that the trabecular bone together with the cortex based on the loading conditions do not differ in load bearing for an osteoporotic and a normal vertebrae (Bartley, Arnold and Haslam). The experimental data obtained in this study revealed that the loading ratio for the osteoporotic vertebrae was higher than that for the normal. In comparison to previous studies, the differences are however slight more so for the lower section of the vertebrae. An increase in the trabecular bone size produced a corresponding increase in osteoporotic effects observed. The spinal level was found to influence the loading ratio with the results significant for both the osteopenic and the normal vertebrae. The averaged data gave the value of the loading ratio of the cortex at the middle section 7 % higher than the corresponding value obtained for the lower vertebrae section (Kaplan, Dalinka and Karp). As a conclusive remark on this section, the spinal level greatly affected the loading ratio between the trabecular bone and the corresponding section of the cortex. The effects of the osteoporosis were more prominent in the lower sections of the vertebrae.

Conclusive evidence suggests that the vertebral column vitro sets of testing under evenly distributed axial forces tests for fracture patterns in the end plate of the vertebrae column (Mazess). An increase in the resultant measured strain is a hint at the fracture risk of the vertebrae. Therefore, under the experimental conditions in this set up, it was found out that the strain measured was greatly affected by the spinal level and the osteopenia. Under the imposed conditions of physiological loading yielded higher strain values for the osteoporonic vertebrae than for the normal case (Genant, Steiger and Block).

For the non-osteopenic vertebra, the relation between the measured strain and the spinal level shows no major deviations in comparison from that of an osteoporonic vertebra. The imminent differences were recorded in the lower section as well as the middle section. In such conditions, the difference cancels out as a result of the loading distribution and the prevalent contribution of the section of the rib cage in supporting the load more so in the middle section as compared to the lower vertebrae. Similar experiments conducted in biochemical and biomechanical units commonly refer to the 1 mm/s as a reference level for standard experiments (Andresen, Werner and Schober). Repeated experimental set ups at the previously established displacement rates bear no significant effects on the results.

The obtained results bear no significant difference in the deviation of the values in terms of the displacement speed and the loading capacity. This concludes that higher speeds are acceptable when adopted in future experiments. Though the experiment was conducted on given displacement rates, the results are described as valid for all daily applications (Genant, Steiger and Block).


The current experimental data obtained from this study confirm that the process to determine the loading ratio for the spine is an involving activity with numerous prevalent factors influencing it. The established loading characteristics show that an entire 45 % of the total weigh carrying capacity acts on the cortex shell. The spinal level greatly affected the loading ratio that the experiment aimed to investigate. The founded values were between the trabecular bone and the cortex. The established load bearing capacity for the spine based on the trabecular bone showed a decrease by osteoporosis while it increased in the direction of the lower vertebrae.

Works Cited

Andresen R, Werner H.J, and Schober H.C. “Contribution of the Cortical Shell of Vertebrae to Mechanical Behaviour of the Lumbar Vertebrae with Implications for Predicting Fracture Risk.” Br J Radiol, vol.71, no.847, 1998, pp.759-65.

Bartley M.H Jr, Arnold J.S, Haslam R.K, and Jee W.S. “The Relationship of Bone Strength and Bone Quantity in Health, Disease, and Aging. J Gerontol, vol.21, no.4, 1966, pp.517-21.

Bell G.H, Dunbar O, Beck J.S, Gibb A. “Variations in Strength of Vertebrae with Age and Their Relation to Osteoporosis.” Calcif Tissue Res, vol.1, no.1, 1967, pp.75-86.

Cao K.D, Grimm M.J, Yang K.H. “Load Sharing Within a Human Lumbar Vertebral Body Using the Finite Element Method.” Spine, vol.26, no.12, 2001, E253-60.

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Genant H.K, Steiger P, Block J.E, Glueer C.C, Ettinger B, and Harris S.T. “Quantitative Computed Tomography: Update 1987.” Calcif Tissue Int, vol.41, no.4, 1987, pp.179-86.

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Hansson T, and Roos B. “The Relation Between Bone Mineral Content, Experimental Compression Fractures, And Disc Degeneration in Lumbar Vertebrae.” Spine, vol.6, no.2, 1981, pp.147-53.

Homminga J, Weinans H, Gowin W, Felsenberg D, and Huiskes R. “Osteoporosis Changes the Amount of Vertebral Trabecular Bone at Risk of Fracture but Not the Vertebral Load Distribution.” Spine, vol.26, no.14, 2001, pp.1555-61.

Hongo M, Abe E, Shimada Y, Murai H, Ishikawa N, and Sato K. “Surface Strain Distribution On Thoracic and Lumbar Vertebrae Under Axial Compression.” Spine, vol.24, 1999, pp.1197–202.

Kaplan F.S, Dalinka M, Karp J.S, Fallon M.D, Katz M, Boden S, Simpson E, Attie M, and Haddad J.G. “Quantitative Computed Tomography Reflects Vertebral Fracture Morbidity in Osteopenic Patients.” Orthopedics, vol.12, no.7, 1989, pp.949-55.

King A.I, Prasad P, and Ewing C.L. “Mechanism of Spinal Injury Due to Caudocephalad Accleration.” Orthop Clin North Am, vol.6, no.1, 1975, pp.9-31.

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McBroom R.J, Hayes W.C, Edwards W.T, Goldberg R.P, and White A.A. “Prediction of Vertebral Body Compressive Fracture Using Quantitative Computed Tomography.” J Bone Joint Surg Am, vol.67, no.8, 1985, pp.1206-14.

Mizrahi J, Silva M.J, Keaveny T.M, Edwards W.T, Hayes W.C. “Finite-Element Stress Analysis of the Normal and Osteoporotic Lumbar Vertebral Body. Spine, vol.18, no.14, 1993, pp.2088-96.

December 08, 2022

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