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Original Contribution  |   October 2018
Validity of the Rule of Threes and Anatomical Relationships in the Thoracic Spine
Author Notes
  • From the Kansas City University of Medicine and Biosciences in Missouri (Student Doctors Oakley and Pankratz and Drs Janssen, Treffer, and Olinger) and the University of Nebraska Medical Center in Omaha (Dr McCumber). 
  • Financial Disclosures: None reported. 
  • Support: Funding for this project was provided by Kansas City University of Medicine and Biosciences. 
  •  *Address correspondence to Clayton K. Oakley, MS, OMS IV, Kansas City University of Medicine and Biosciences, 1750 Independence Ave, Kansas City, MO 64106-1453. Email: coakley@kcumb.edu
     
Article Information
Neuromusculoskeletal Disorders
Original Contribution   |   October 2018
Validity of the Rule of Threes and Anatomical Relationships in the Thoracic Spine
The Journal of the American Osteopathic Association, October 2018, Vol. 118, 645-653. doi:https://doi.org/10.7556/jaoa.2018.143
The Journal of the American Osteopathic Association, October 2018, Vol. 118, 645-653. doi:https://doi.org/10.7556/jaoa.2018.143
Abstract

Context: The location of the more superficial thoracic spinous processes is used to help osteopathic physicians locate the deeper and more difficult-to-palpate thoracic transverse processes. In 1979, Mitchell et al proposed the thoracic rule of threes to describe the relationship of the spinous processes to the transverse processes in the thoracic spine. This rule is currently taught at osteopathic medical schools. The rule of threes separates the thoracic vertebrae into 3 distinct groups, each with a different relationship between transverse processes and spinous processes. In 2006, Geelhoed et al proposed a new relationship between the spinous processes and transverse processes for all thoracic vertebrae (ie, Geelhoed's rule).

Objective: To determine which anatomical relationship—the rule of threes or Geelhoed's rule—is most accurate in locating the transverse processes and to define anatomical relationships between thoracic spinous and transverse processes.

Methods: The thoracic spinous and transverse processes of 44 formalin-embalmed human cadavers were dissected, marked, and photographed. Six different measurements per vertebra were made between spinous processes and transverse processes in the thoracic spine. Geelhoed's protocol was used to determine the validity of each rule. The measurements were analyzed for additional relationships between thoracic spinous processes and transverse processes. Group 1 consisted of vertebrae T1 to T3 and T12; group 2 consisted of T4 to T6 and T11; and group 3 consisted of T7 to T10.

Results: Of the 528 vertebrae measured, 0% of the first group vertebrae, 10.8% of the second group vertebrae, and 69.3% of the third group vertebrae followed the rule of threes. In total, 26.7% of vertebrae followed the rule of threes, whereas 62.3% of vertebrae followed Geelhoed's rule. Additional relationships worth noting include the distance between the transverse process and the adjacent caudal transverse process on the same side is approximately 25.4 mm (1 inch), and the distance between the transverse processes of the same vertebra is approximately 50.8 mm (2 inches) for male T3-T10 vertebrae and female T1-T12 vertebrae.

Conclusion: According to our findings, the rule of threes is not as accurate anatomically as Geelhoed's rule in locating the transverse processes of the thoracic spine. This study suggests osteopathic medical schools should teach Geelhoed's rule rather than the rule of threes.

Osteopathic physicians (ie, DOs) are unique in their ability to diagnose and manage somatic dysfunction, which is diagnosable throughout the musculoskeletal system, including the thoracic spine.1 To fully examine the thoracic spine for somatic dysfunctions, the thoracic transverse processes (TPs) need to be palpated to check for asymmetries.1 The palpation of the thoracic TPs is also used in the management of thoracic somatic dysfunctions through osteopathic manipulative treatment.1 Hence, it is vital that DOs have the ability to accurately locate and palpate thoracic TPs for the effective practice of osteopathic manipulative medicine. Learning palpation skills to locate TPs can be challenging for some DOs and osteopathic medical students because the thoracic TPs are covered by muscle and connective tissue deep in the back.1,2 Because of this challenge, osteopathic medical schools teach students about the anatomical relationships that occur between the thoracic TPs and other anatomical structures.1,3 The goal of teaching students about these relationships is to improve palpation accuracy by locating a more prominent palpable anatomical landmark that can then be used to locate the TP, which is more difficult to palpate (ie, the more superficial thoracic spinous processes [SPs] can be used to locate the deeper thoracic TPs).1 The relationship between thoracic TPs and SPs that is currently taught at osteopathic medical schools is the thoracic rule of threes, which was proposed by Mitchell et al.1,3,4 However, to our knowledge, the rule of threes has yet to be validated in the literature.5,6 
The rule of threes separates the thoracic vertebrae into 4 sets of 3 vertebrae, each with slightly different relationships between the SPs and TPs.1,3,4 Set 1 consists of vertebrae T1 to T3, where the SPs are located in the same transverse plane as the TPs of the same vertebrae.1,3,4 Set 2 consists of vertebrae T4 to T6, where the SPs are located in a plane that is halfway between its own TPs and the TPs of the adjacent caudal vertebrae.1,3,4 Set 3 consists of vertebrae T7 to T9, and the SPs are located in the same transverse plane as the TPs of the adjacent caudal vertebrae.1,3,4 Set 4 consists of vertebrae T10 to T12, and each of these vertebrae has a different relationship between SPs and TPs.1,3,4 The SP of T10 is located in the same transverse plane as the TPs of the adjacent caudal vertebra.1,3,4 The SP of T11 is located in a plane that is halfway between its own TPs and the TPs of the adjacent caudal vertebra.1,3,4 The SP of T12 is located in the same transverse plane as its own TPs.1,3,4 
In 2006, Geelhoed et al5 proposed a new rule to describe the relationship between the thoracic SPs and TPs. This rule, which we refer to as Geelhoed's rule, states that the SPs of all thoracic vertebrae are located in a transverse plane with the TPs of the adjacent caudal vertebrae.5 This rule and the rule of threes partially contradict each other.1,3-5 Since the findings by Geelhoed et al5 were published in 2006, there have been no additional reports in the literature, to our knowledge, that have tested which rule is more accurate anatomically. Furthermore, reports have described certain measurements of the thoracic SPs and TPs, yet there is a lack of research that describes the relationship between the different processes in the thoracic spine.7-12 The current study was designed to determine whether the rule of threes or Geelhoed's rule more accurately describes the anatomical relationship of the thoracic TPs to the thoracic SPs. 
Methods
Formalin-embalmed human cadavers were included in this study. Exclusion criteria used included cadavers that had known back or spine conditions, scoliosis-exaggerated kyphosis or lordosis, back and spine surgical procedures, or any reported back problems. Any cadavers with postmortem damage to the vertebral column were also excluded. All cadavers were dissected in the prone position by removing skin, muscle, and connective tissue to expose the thoracic TPs and SPs. The thoracic SPs of T1 to T12 and TPs of T1 to L1 were palpated to identify the most prominent posterior part of each process, and the most prominent part of each process was marked with a black dot. All palpation was done by the same investigator (C.K.O.). 
Using a Canon PowerShot digital camera and a tripod, 3 photographs of each thoracic spine in the prone position were taken (Figure 1). Each photograph was used to measure 4 vertebrae. Figure 1A (T1-T4) was taken at an angle of approximately 45° (±15°) to account for the kyphosis of the thoracic spine. This angle was such that the line of sight for the photograph was perpendicular to the spine. Figure 1B and Figure 1C (T5-T8 and T9-T12, respectively) were taken parallel to the spine. Each photograph was taken with a ruler placed parallel to the spine as a reference for future measurements. ImageJ (National Institutes of Health) was used to analyze each photograph. Six measurements per vertebra were collected to define the relationship between TPs and SPs (Figure 2): 
  • ■ Measurement 1: distance between the SP and the TP's level of the same vertebra
  • ■ Measurement 2: distance between the SP and the TP's level of adjacent caudal vertebra
  • ■ Measurement 3 (left and right sides): distance between the TP on one side and the TP on the same side of the adjacent caudal vertebra
  • ■ Measurement 4 (left and right sides): distance between the TP on one side and the SP of the same vertebra
  • ■ Measurement 5 (left and right sides): angle between the TP on one side and the SP of the same vertebra
  • ■ Measurement 6: distance between the TPs of the same vertebra
Figure 1.
Example photographs of the thoracic regions of a cadaver to measure the anatomic locations and relationships of the thoracic transverse and spinous processes. Each photograph was used to measure (A) T1-T4, (B) T5-T8, and (C) T9-T12. Black dots indicate the most palpable posterior portion of each process.
Figure 1.
Example photographs of the thoracic regions of a cadaver to measure the anatomic locations and relationships of the thoracic transverse and spinous processes. Each photograph was used to measure (A) T1-T4, (B) T5-T8, and (C) T9-T12. Black dots indicate the most palpable posterior portion of each process.
Figure 2.
Drawings of each measurement (measurements 1 through 6), as described in the text, used to measure the anatomic locations and relationships of the thoracic transverse and spinous processes. Red lines represent the measured distances. Black lines show how the red lines relate to the spinous and transverse processes.
Figure 2.
Drawings of each measurement (measurements 1 through 6), as described in the text, used to measure the anatomic locations and relationships of the thoracic transverse and spinous processes. Red lines represent the measured distances. Black lines show how the red lines relate to the spinous and transverse processes.
Microsoft Excel was used to analyze the measurements. Each vertebra was tested to determine whether it followed the rule of threes, Geelhoed's rule, or both. All vertebrae were classified into 1 of 3 groups to test the rule of threes, depending on which relationship they followed. Group 1 consisted of T1 to T3 and T12. Group 2 consisted of T4 to T6 and T11. Group 3 consisted of T7 to T10. To determine whether the vertebra followed the rule of threes, the following measurements were used: group 1 used measurement 1, group 2 used measurement 1 minus half of the average of measurement 3 on the left and right, and group 3 used measurement 2. 
To test all vertebrae for Geelhoed's rule, measurement 2 was used. To determine whether a vertebra followed a rule being tested, the distance of 6 mm or less was used, per Geelhoed's protocol.5,13 In other words, if the measurement used to test a vertebra for either the rule of threes or Geelhoed's rule was within 6 mm of 0, that vertebra was recorded as following the rule being tested. If the measurement was greater than 6 mm away from 0, that vertebra was recorded as not following the rule being tested. Van Boven and Johnson15 suggested that the human finger is able to palpate a distance of less than 6 mm; however, we used 6 mm to be consistent with previous studies.5,13-16 
The mean (SD) for each of the measurements was also determined for each thoracic level and all thoracic vertebrae combined. This additional information (ie, measurements 4-6) was collected to better define the relationships between processes in the thoracic spine. Also, all data were analyzed looking at both sex and age of death of the cadaver. t tests were used to identify significant differences between sexes for the mean of each measurement. Statistical significance was set at P<.05. 
Results
Forty-four formalin-embalmed human cadavers were included in this study. Demographic data collected on the cadavers included 19 males and 24 females with ages of death ranging from 44 to 99 years with a mean age of 75.95 years. Five cadavers were younger than 60 years when they died, 9 were between 60 and 69 years, 11 were between 70 and 79 years, 11 were between 80 and 89 years, and 7 were 90 years or older. There was no age of death or sex information recorded for 1 cadaver. 
A total of 528 vertebrae were analyzed. Of the 528 vertebrae, 141 (26.7%) demonstrated the relationship described by the rule of threes. When analyzing each group separately, 0 of 176 vertebrae in group 1, 19 of 176 vertebrae (10.8%) in group 2, and 122 of 176 vertebrae (69.3%) in group 3 demonstrated the relationship described by the rule of threes. Of the 528 total vertebrae, 329 (62.3%) demonstrated the relationship described by Geelhoed's rule. The percentage of vertebrae that demonstrated Geelhoed's rule was approximately 2 times greater than the percentage of vertebrae that followed the rule of threes for all age-of-death ranges and for both sexes. 
Next, each cadaver was tested to determine the number of vertebrae that followed the rule of threes and/or Geelhoed's rule (Figure 3). For the rule of threes, the mean (SD) number of vertebrae that followed the rule per cadaver was 3.2 (1.29). The maximum number of vertebrae that followed the rule of threes for an individual cadaver was 6, and the minimum was 0. For Geelhoed's rule, the mean (SD) number of vertebrae that followed the rule per cadaver was 7.48 (2.36). The maximum number of vertebrae per cadaver that followed the rule was 11, and the minimum was 2. 
Figure 3.
Number of cadavers (N=44) broken down by how many of their vertebrae followed the thoracic rule of threes and Geelhoed's rule.
Figure 3.
Number of cadavers (N=44) broken down by how many of their vertebrae followed the thoracic rule of threes and Geelhoed's rule.
Individual vertebrae were tested to determine whether their measurement 3 values were within ±6 mm of 25.4 mm. Of the 1056 measurements, 865 (81.9%) were within ±6 mm of 25.4 mm. No significant differences were found in measurement 3 values between age of death or sex. The percentage of measurement 3 within ±6 mm of 25.4 mm was greater than 70% for all age-of-death ranges and both sexes. 
Individual vertebrae were also tested to determine whether their measurement 4 values were within ±6 mm of 38.1 mm (1.5 inches). Of the 1056 measurements, 671 (63.5%) were within ±6 mm of 38.1 mm. The mean (SD) of measurement 4 was 37.65 mm (6.73 mm). 
Individual vertebrae were analyzed to determine whether their measurement 6 values were within ±6 mm of 50.8 mm. Of 528 measurement values, 310 (58.7%) were within ±6 mm of 50.8 mm. With the exclusion of T1 and T2, which on average were larger than 50.8 mm, and T11 and T12, which on average were less than 50.8 mm, 270 of 352 (76.7%) measurement 6 values for T3 to T10 were within ±6 mm of 50.8 mm. 
There was no definitive pattern when vertebrae were separated by the cadaver's age of death; however, sex did influence measurement 6 values (Figure 4 and Table). Female cadavers had a higher percentage of measurement 6 values within ±6 mm of 50.8 mm for both T1 to T12 and T3 to T10. Female cadavers also had a higher percentage of vertebrae with their measurement 6 values within ±6 mm of 50.8 mm for T1-T12 than males did for T3-T10. The difference between male and female vertebrae for all measurements was evaluated, and except for measurement 5L (P=.387), male cadavers had statistically significant larger means when compared with female cadavers (Table). 
Figure 4.
Percentage of cadavers with measurement 6 (distance between the transverse processes of the same vertebra) within 6 mm of 2 inches by sex.
Figure 4.
Percentage of cadavers with measurement 6 (distance between the transverse processes of the same vertebra) within 6 mm of 2 inches by sex.
Table.
Mean (SD) Measurements 1 Through 6 in Millimeters for T1 Through T12, All Female (F) and Male (M) Cadavers, and Total of All Thoracic Levelsa
  Image not available

a Measurements in the red box were used to test group 1 for the rule of threes. Measurements in the green boxes were used to test group 2 for the rule of threes. Measurements in the blue box were used to test group 3 for the rule of threes. Measurements in the purple box were used to test Geelhoed's rule. Black boxes highlight other noteworthy measurements not related to either rule.

b Negative values for measurement 2 indicate the spinous process of a vertebra was above the transverse processes of the caudal vertebra.

c Measurement 1 minus half of the average of measurement 3 on the right and left.

d The P value (calculated using the t test) indicates comparisons of male and female means for all measurements (#1 through #6). A significant difference was found between all male and female means except for measurement 5L.

Abbreviations: L, left; NA, not applicable; R, right.

Table.
Mean (SD) Measurements 1 Through 6 in Millimeters for T1 Through T12, All Female (F) and Male (M) Cadavers, and Total of All Thoracic Levelsa
  Image not available

a Measurements in the red box were used to test group 1 for the rule of threes. Measurements in the green boxes were used to test group 2 for the rule of threes. Measurements in the blue box were used to test group 3 for the rule of threes. Measurements in the purple box were used to test Geelhoed's rule. Black boxes highlight other noteworthy measurements not related to either rule.

b Negative values for measurement 2 indicate the spinous process of a vertebra was above the transverse processes of the caudal vertebra.

c Measurement 1 minus half of the average of measurement 3 on the right and left.

d The P value (calculated using the t test) indicates comparisons of male and female means for all measurements (#1 through #6). A significant difference was found between all male and female means except for measurement 5L.

Abbreviations: L, left; NA, not applicable; R, right.

×
Discussion
The ability to accurately locate thoracic TPs is a necessary skill for DOs to confidently diagnose and manage somatic dysfunction in the thoracic spine.1 To help develop confidence as well as palpation and manipulative skills in future DOs, osteopathic medical schools teach anatomical relationships using guidelines such as the rule of threes.1 This study suggests that osteopathic medical schools should teach Geelhoed's rule rather than the rule of threes because it is more accurate anatomically. This study analyzed the data in 3 different ways to determine which rule is more accurate. First, the mean measurement values were used to test the rules. Geelhoed's rule had 11 thoracic levels with a mean value within the 6-mm cutoff. This finding was greater than the 4 thoracic levels with a mean value within the 6-mm cutoff for the rule of threes. Second, each vertebra was tested for both rules. Geelhoed's rule, at 62.3%, had more than twice the percentage of individual vertebra that followed it compared with the rule of threes, at 26.7%. This difference in percentage stayed consistent when vertebrae were separated by sex and age-of-death range. Finally, each cadaver was evaluated as to how many vertebrae followed the rules. 
Geelhoed's rule had more cadavers with 6 to 11 vertebrae that followed its rule compared with the rule of threes. For both rules, no cadaver had all 12 vertebrae follow the rule being tested. All 3 assessments of the data showed that Geelhoed's rule is more accurate than the rule of threes; it is also simpler.3 Geelhoed's rule is one relationship for all thoracic vertebrae compared with 3 different relationships that depend on the vertebral level, making Geelhoed's rule easier to remember and apply in practice.1,3-5 Thus, the present study suggests that osteopathic medical schools should consider teaching Geelhoed's rule instead of the rule of threes. 
Of note, Geelhoed's rule is not perfect anatomically in locating the thoracic TPs—only 62.3% of vertebrae followed Geelhoed's rule. Hence, other measurements were evaluated to determine whether any trends could be identified. Two trends were found that could be applied easily when trying to locate the TPs of the thoracic spine. First, the distance between TP to the TP of the adjacent caudal vertebra on the same side is approximately 25.4 mm (1 in), which can be easily approximated using the distance from the tip of the thumb to the interphalangeal joint of the thumb.17 Once a single TP is located in the thoracic spine, the physician could move up and down 25.4 mm at a time to locate the rest of the TPs in the ipsilateral thoracic spine. This relationship is accurate more than 80% of the time, making it consistent to apply. It is also easily remembered. Because of these reasons, this study suggests that osteopathic medical schools should also teach the distance of 25.4 mm between TPs on the same side in the thoracic spine. The data also showed that there is a distance of approximately 50.8 mm (2 in) between the left and right TPs of the same vertebra. If one TP is identified, this approximation could be used to locate the TPs on the other side of the vertebra. However, there was a difference between the male and female cadavers. In females, the 50.8-mm approximation was accurate more than 60% of the time for T1-T12. This same approximation for T1-T12 in males was accurate less than 50% of the time. To get a percentage higher than 60% in males, T1-T2 and T11-T12 needed to be excluded from the approximation because the distance between TPs of the same vertebra is on average larger than 50.8 mm for T1 and T2 and smaller than 50.8 mm for T11 and T12. Even though there is variation between men and women, this approximation could be easily remembered and applied to help locate TPs. The study suggests that osteopathic medical schools teach a distance of approximately 50.8 mm between TPs of the same vertebra for T1-T12 in females and T3-T10 in males. Using Geelhoed's rule, plus these 2 other approximations, the physician could more easily locate all TPs in the thoracic spine. These guidelines would help osteopathic medical students become more confident in their palpation skills. More confident osteopathic medical students will eventually lead to more confident osteopathic physicians.1,18 
There are some limitations to our study. Formalin-embalmed human cadavers were used instead of living humans for this study. It is not clear what effect the embalming processes has on the measurements taken. Formalin-embalmed cadavers were chosen for the study because of their availability over fresh frozen cadavers. It is also not clear what effect the postmortem state of the cadaver had on the measurements. However, research19 suggests that human cadavers are an accurate representation of the living when it comes to angle and curvature measurements of the spine. Thus, the argument that human cadavers are accurate representatives of living humans can be made. Another potential limitation is the removal of the musculature and connective tissue in the back to expose the thoracic TPs and SPs. It is unknown how the removal of this tissue affected the relationships that were described in this study. The minimum amount of tissue necessary to expose the TPs and SPs was removed and did not result in any appreciable movement of the spine. Also, measurements were only collected in the prone position and not the seated position. Positioning a formalin-embalmed cadaver in a seated posture is not possible because of the rigidity of the cadaver. An additional limitation is the ages of death of our cadavers. The average age of death of the cadavers in this study was approximately 75 years, with the youngest cadaver being 44 years. Thus, these findings cannot be extrapolated to all age ranges. 
Possible future directions include testing both rules and the anatomical relationships described in this study on live patients. A second option would be to use computed tomography or magnetic resonance imaging of live study participants instead of dissection of cadavers to measure and verify these relationships. Imaging modalities could also be used to determine whether these relationships change if an individual is in the seated position. These data would provide further evidence as to which rule is more accurate and should be taught in osteopathic medical schools. 
Conclusion
The findings of this study suggest that Geelhoed's rule is more anatomically accurate than the rule of threes at locating the TPs in the thoracic spine. Furthermore, this study shows that the distance from TP to the adjacent caudal TP on the same side is approximately 25.4 mm (1 inch). Finally, this study shows that the distance between TPs of the same vertebra is approximately 50.8 mm (2 inches) for male vertebrae T3-T10 and female vertebrae T1-T12. In the osteopathic community, these rules could aid osteopathic medical students and DOs as they work toward improving their palpation abilities. For anatomists, the raw numbers add data to the literature about the relationship between the TPs and SPs in the thoracic spine. 
Acknowledgments
We thank the Department of Anatomy at the Kansas City University of Medicine and Biosciences and the Department of Genetics, Cell Biology, and Anatomy at the University of Nebraska Medical Center for the use of their laboratories and donors. We also thank the donors, without whom this research could not be accomplished. 
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Figure 1.
Example photographs of the thoracic regions of a cadaver to measure the anatomic locations and relationships of the thoracic transverse and spinous processes. Each photograph was used to measure (A) T1-T4, (B) T5-T8, and (C) T9-T12. Black dots indicate the most palpable posterior portion of each process.
Figure 1.
Example photographs of the thoracic regions of a cadaver to measure the anatomic locations and relationships of the thoracic transverse and spinous processes. Each photograph was used to measure (A) T1-T4, (B) T5-T8, and (C) T9-T12. Black dots indicate the most palpable posterior portion of each process.
Figure 2.
Drawings of each measurement (measurements 1 through 6), as described in the text, used to measure the anatomic locations and relationships of the thoracic transverse and spinous processes. Red lines represent the measured distances. Black lines show how the red lines relate to the spinous and transverse processes.
Figure 2.
Drawings of each measurement (measurements 1 through 6), as described in the text, used to measure the anatomic locations and relationships of the thoracic transverse and spinous processes. Red lines represent the measured distances. Black lines show how the red lines relate to the spinous and transverse processes.
Figure 3.
Number of cadavers (N=44) broken down by how many of their vertebrae followed the thoracic rule of threes and Geelhoed's rule.
Figure 3.
Number of cadavers (N=44) broken down by how many of their vertebrae followed the thoracic rule of threes and Geelhoed's rule.
Figure 4.
Percentage of cadavers with measurement 6 (distance between the transverse processes of the same vertebra) within 6 mm of 2 inches by sex.
Figure 4.
Percentage of cadavers with measurement 6 (distance between the transverse processes of the same vertebra) within 6 mm of 2 inches by sex.
Table.
Mean (SD) Measurements 1 Through 6 in Millimeters for T1 Through T12, All Female (F) and Male (M) Cadavers, and Total of All Thoracic Levelsa
  Image not available

a Measurements in the red box were used to test group 1 for the rule of threes. Measurements in the green boxes were used to test group 2 for the rule of threes. Measurements in the blue box were used to test group 3 for the rule of threes. Measurements in the purple box were used to test Geelhoed's rule. Black boxes highlight other noteworthy measurements not related to either rule.

b Negative values for measurement 2 indicate the spinous process of a vertebra was above the transverse processes of the caudal vertebra.

c Measurement 1 minus half of the average of measurement 3 on the right and left.

d The P value (calculated using the t test) indicates comparisons of male and female means for all measurements (#1 through #6). A significant difference was found between all male and female means except for measurement 5L.

Abbreviations: L, left; NA, not applicable; R, right.

Table.
Mean (SD) Measurements 1 Through 6 in Millimeters for T1 Through T12, All Female (F) and Male (M) Cadavers, and Total of All Thoracic Levelsa
  Image not available

a Measurements in the red box were used to test group 1 for the rule of threes. Measurements in the green boxes were used to test group 2 for the rule of threes. Measurements in the blue box were used to test group 3 for the rule of threes. Measurements in the purple box were used to test Geelhoed's rule. Black boxes highlight other noteworthy measurements not related to either rule.

b Negative values for measurement 2 indicate the spinous process of a vertebra was above the transverse processes of the caudal vertebra.

c Measurement 1 minus half of the average of measurement 3 on the right and left.

d The P value (calculated using the t test) indicates comparisons of male and female means for all measurements (#1 through #6). A significant difference was found between all male and female means except for measurement 5L.

Abbreviations: L, left; NA, not applicable; R, right.

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