EDITORIALS
Metaanalysis in Wound Healing Joseph LoCicero 111, MD Section of General Thoracic Surgery, the Feinberg Cardiovascular Research Institute of Northwestern University Medical School, Chicago, Illinois, and New England Deaconess Hospital, Harvard Medical School, Boston, Massachusetts
M
edical researchers use tensile strength testing as one of the methods to determine wound healing characteristics of an incision [l]. All surgical disciplines accept this technique and report it regularly in the journals [24]. The usual test method involves cutting strips containing the anastomosis and then pulling it apart. The force applied is known as the stress on the anastomosis. When the suture line breaks, the recorded stress is reported as the ultimate strength or tensile strength of the anastomosis. See also page 80.
In the past few years, attempts have been made to simplify experimental design and achieve comparable data. One of these techniques is to measure the bursting pressure obtained by injecting an incompressible liquid (such as colored saline solution) into a closed tube that contains the anastomosis being evaluated. These data are reported as wound strength. Such an evaluation may be described as metaanalysis. Webster’s lists among the definitions of “meta” a transformation often added to a name of a discipline designed to deal critically with the original one [5]. Auteri and associates [6] used metaanal-
ysis to evaluate bronchial anastomosis in canine lung transplants. However, such transformed information is confusing and misleading. To understand the forces at work in a particular strength application, one must understand the basic concepts of experimental stress analysis [7]. A blood vessel, trachea or bronchus, or a segment of bowel can be represented as a thin-walled cylinder (Fig 1). Stress analysis theory can represent this tube using polar coordinates to define any force (P) applied to this segment in three primary directions. These forces act along the long axis (Z) direction (stretching the length of the cylinder); the angular (a)direction (stretching the circle wider); and the radial (R) direction (compressing the thickness of the wall). In addition to the three primary directions through which a force acts, there is an interrelation of any two coordinates known as the shearing force ( 7 ) . All five of these forces are mathematically represented by the Airy stress function, which comprises five simultaneous equations. Such a solution, although ideal, is impractical for a biologic system unless complex measurements can be taken. Most researchers therefore assume that the changes in the radial direction-the ones that alter wall thickness-are negligible. This decreases the Airy stress
Fig 1 . Schematic representation of a thin-walled cylinder with an anastomosis being stressed by an internal force (P). The cylinder has length 0) and radius (r). The primary stresses are represented by the longitudinal stress Z , the angular stress a, and the compressive stress R.
o(
Address reprint requests to Dr LoCicero, Department of Surgery, New England Deaconess Hospital, 110 Francis St, Suite ZC, Boston, MA 02215. 0 1992 by The Society of Thoracic Surgeons
Ann Thorac Surg 1992;53:5-6
OOO3-4975/92/$3.50
6
Ann Thorac Surg 1992;5354
EDITORIAL LoCICERO METAANALYSIS IN WOUND HEALING
function to two directions and only three simultaneous equations. Additionally, most investigators limit their evaluation to one dimension, the one at right angles to the anastomosis in question, because this force exerts all of its effect to pull apart the anastomosis. Thus, the stress (u)in that direction can truly define the ultimate tensile strength. When bursting strength is used to analyze an end-toend anastomosis, investigators report only one number (P). However, this represents two-dimensional stress: the stress in the Z direction acting along the entire length of the segment and the stress in the a or angular direction acting along the circle. Moreover, the interrelationship between these two primary directions produces a shearing force (7).This yields three simultaneous equations with only one overall force P known and no information available to break it into the two component stresses or vectors and their interrelationship (7). Thus, it is not possible to accurately determine the force in the Z direction that primarily pulled apart the anastomosis. The answer obtained is far removed from the actual tensile strength or ultimate stress value desired. This also holds true for a longitudinal anastomosis. It would be impossible to separate out the angular stress from the longitudinal stress or the interactive shear force. The use of bursting pressure, even for comparison, is problematic. Wound healing is a three dimensional process including the minor direction (angular for end-to-end anastomosis, and Z for longitudinal anastomoses). These
changes are not characterized or evaluated in bursting pressure techniques. Yet, despite these major shortcomings, such metaanalysis will continue to appear in the journals. The reader is cautioned to interpret these data strictly as relative. They reflect only the overall strength of the entire object being tested and not the incision.
References 1. Peacock EE, NanWinkle. Wound repair. 2nd ed. Philadelphia: W.B. Saunders, 1970. 2. Mustoe TA, Landes A, Cromacic DT, Griffin A, Deuel TF, Pierce GF. Differential acceleration of healing of surgical incisions in the rabbit gastrointestinaltract by platelet-derived growth factor and transforming growth factor, type beta. Surgery 1990;108:324-9. 3. Donovan DL, Schmidt SP, Townshend SP, Njus GO, Sharp WV. Material and structural characterization of human saphenous vein. J Vasc Surg 1990;12531-7. 4. Lima 0,Cooper JD, Peters WJ,et al. Effects of methylprednisolone and azathioprine on bronchial healing following lung autotransplantation. J Thorac Cardiovasc Surg 1981;82211-5. 5. Webster's ninth new collegiate dictionary. Springfield: Merriam-Webster, 1989. 6. Auteri JS, JeevanandamV, Sanchez JA, Marboe CC, Kirby TJ, Smith CR. Normal bronchial healing without bronchial wrapping in canine lung transplantation. Ann Thorac Surg 1992; 53S0-4. 7. Dally JW, Riley WF. Experimental stress analysis. New York: McGraw Hill, 1965.
Metaanalysis in Wound Healing Joseph LoCicero 111, MD Section of General Thoracic Surgery, the Feinberg Cardiovascular Research Institute of Northwestern University Medical School, Chicago, Illinois, and New England Deaconess Hospital, Harvard Medical School, Boston, Massachusetts
M
edical researchers use tensile strength testing as one of the methods to determine wound healing characteristics of an incision [l]. All surgical disciplines accept this technique and report it regularly in the journals [24]. The usual test method involves cutting strips containing the anastomosis and then pulling it apart. The force applied is known as the stress on the anastomosis. When the suture line breaks, the recorded stress is reported as the ultimate strength or tensile strength of the anastomosis. See also page 80.
In the past few years, attempts have been made to simplify experimental design and achieve comparable data. One of these techniques is to measure the bursting pressure obtained by injecting an incompressible liquid (such as colored saline solution) into a closed tube that contains the anastomosis being evaluated. These data are reported as wound strength. Such an evaluation may be described as metaanalysis. Webster’s lists among the definitions of “meta” a transformation often added to a name of a discipline designed to deal critically with the original one [5]. Auteri and associates [6] used metaanal-
ysis to evaluate bronchial anastomosis in canine lung transplants. However, such transformed information is confusing and misleading. To understand the forces at work in a particular strength application, one must understand the basic concepts of experimental stress analysis [7]. A blood vessel, trachea or bronchus, or a segment of bowel can be represented as a thin-walled cylinder (Fig 1). Stress analysis theory can represent this tube using polar coordinates to define any force (P) applied to this segment in three primary directions. These forces act along the long axis (Z) direction (stretching the length of the cylinder); the angular (a)direction (stretching the circle wider); and the radial (R) direction (compressing the thickness of the wall). In addition to the three primary directions through which a force acts, there is an interrelation of any two coordinates known as the shearing force ( 7 ) . All five of these forces are mathematically represented by the Airy stress function, which comprises five simultaneous equations. Such a solution, although ideal, is impractical for a biologic system unless complex measurements can be taken. Most researchers therefore assume that the changes in the radial direction-the ones that alter wall thickness-are negligible. This decreases the Airy stress
Fig 1 . Schematic representation of a thin-walled cylinder with an anastomosis being stressed by an internal force (P). The cylinder has length 0) and radius (r). The primary stresses are represented by the longitudinal stress Z , the angular stress a, and the compressive stress R.
o(
Address reprint requests to Dr LoCicero, Department of Surgery, New England Deaconess Hospital, 110 Francis St, Suite ZC, Boston, MA 02215. 0 1992 by The Society of Thoracic Surgeons
Ann Thorac Surg 1992;53:5-6
OOO3-4975/92/$3.50
6
Ann Thorac Surg 1992;5354
EDITORIAL LoCICERO METAANALYSIS IN WOUND HEALING
function to two directions and only three simultaneous equations. Additionally, most investigators limit their evaluation to one dimension, the one at right angles to the anastomosis in question, because this force exerts all of its effect to pull apart the anastomosis. Thus, the stress (u)in that direction can truly define the ultimate tensile strength. When bursting strength is used to analyze an end-toend anastomosis, investigators report only one number (P). However, this represents two-dimensional stress: the stress in the Z direction acting along the entire length of the segment and the stress in the a or angular direction acting along the circle. Moreover, the interrelationship between these two primary directions produces a shearing force (7).This yields three simultaneous equations with only one overall force P known and no information available to break it into the two component stresses or vectors and their interrelationship (7). Thus, it is not possible to accurately determine the force in the Z direction that primarily pulled apart the anastomosis. The answer obtained is far removed from the actual tensile strength or ultimate stress value desired. This also holds true for a longitudinal anastomosis. It would be impossible to separate out the angular stress from the longitudinal stress or the interactive shear force. The use of bursting pressure, even for comparison, is problematic. Wound healing is a three dimensional process including the minor direction (angular for end-to-end anastomosis, and Z for longitudinal anastomoses). These
changes are not characterized or evaluated in bursting pressure techniques. Yet, despite these major shortcomings, such metaanalysis will continue to appear in the journals. The reader is cautioned to interpret these data strictly as relative. They reflect only the overall strength of the entire object being tested and not the incision.
References 1. Peacock EE, NanWinkle. Wound repair. 2nd ed. Philadelphia: W.B. Saunders, 1970. 2. Mustoe TA, Landes A, Cromacic DT, Griffin A, Deuel TF, Pierce GF. Differential acceleration of healing of surgical incisions in the rabbit gastrointestinaltract by platelet-derived growth factor and transforming growth factor, type beta. Surgery 1990;108:324-9. 3. Donovan DL, Schmidt SP, Townshend SP, Njus GO, Sharp WV. Material and structural characterization of human saphenous vein. J Vasc Surg 1990;12531-7. 4. Lima 0,Cooper JD, Peters WJ,et al. Effects of methylprednisolone and azathioprine on bronchial healing following lung autotransplantation. J Thorac Cardiovasc Surg 1981;82211-5. 5. Webster's ninth new collegiate dictionary. Springfield: Merriam-Webster, 1989. 6. Auteri JS, JeevanandamV, Sanchez JA, Marboe CC, Kirby TJ, Smith CR. Normal bronchial healing without bronchial wrapping in canine lung transplantation. Ann Thorac Surg 1992; 53S0-4. 7. Dally JW, Riley WF. Experimental stress analysis. New York: McGraw Hill, 1965.
