J Forensic Sci, March 2014, Vol. 59, No. 2 doi: 10.1111/1556-4029.12349 Available online at: onlinelibrary.wiley.com
PAPER ENGINEERING SCIENCES
Kevin Tang,1 H.S.D.; Wyatt Sharpe,1 H.S.D.; Alexandra Schulz,1 H.S.D.; Edric Tam,1 H.S.D.; Ian Grosse,2 Ph.D.; John Tis,3 M.D.; and Dennis Cullinane,1 Ph.D.
Determining Bruise Etiology in Muscle Tissue Using Finite Element Analysis
ABSTRACT: Bruising, the result of capillary failure, is a common physical exam finding due to blunt trauma and, depending on location
and severity, a potential indicator of abuse. Despite its clinical relevance, few studies have investigated the etiology of capillary failure. The goal of this study was to determine whether capillaries primarily fail under shear stress or hydraulic-induced tensile stress. An arteriole bifurcating into four capillaries was modeled using ANSYS 14.0 â. The capillaries were embedded in muscle tissue and a pressure of 20.4 kPa was applied. Any tensile stress exceeding 8.4 9 104 Pa was considered failure. Results showed that failure occurred directly under the impact zone and where capillaries bifurcated, rather than along the line of greatest shear stress, indicating that internal tensile stress is likely the primary mode of capillary failure in bruising. These results are supported by the concept that bruising can occur via blunt trauma in which no shearing lacerations occur.
KEYWORDS: forensic science, bruising, capillary failure, finite element analysis, hydraulic tensile stress, shear stress
A bruise is an area of skin discoloration created when a stress caused by blunt trauma exceeds the ultimate strength of capillaries. During bruising, the blood in the capillaries leaks into the surrounding soft tissue, resulting in swelling and pain (1,2). Bruising can occur in the skin and adipose layers (subcutaneous), within the belly of the underlying muscle (intramuscular), or on bone (periosteal). Bruising is also a common clinical indicator of abuse (3–5). Because of the clinical relevance of bruising, it would be beneficial to determine the mechanism of capillary failure and the load threshold at which bruising occurs. When a force is applied to soft tissue, the tissue deforms (strain) based on the tissue’s architecture and mechanical properties, as well as the force magnitude, direction, and loading rate. The tissue will eventually fail when the stress induced by the loading reaches the ultimate strength of the tissue. Thus, the failure of capillaries depends upon both their architecture and material properties. Capillaries are composed of two layers, the intima and the media (6). The intima is a 2-lm-thick endothelial layer with a 1-lm-thick basal lamina of collagen. The media is a thicker layer of smooth muscle cells with elastic laminae and a minor amount of collagen. Although capillary failure is known to be the cause of bruising, very little is known regarding the etiology of capillary failure. The goal of this study is to determine the mode of capillary failure in bruising and thus the etiology of bruising.
1
Biomechanics Laboratory, Deerfield Academy, 7 Boyden Lane Deerfield, Deerfield, MA 01342. 2 Department of Mechanical and Industrial Engineering, University of Massachusetts, 130 Natural Resources Road, Amherst, MA 01003. 3 Department of Orthopaedic Surgery, Johns Hopkins University School of Medicine, 1800 Orleans St, Suite 7356, Baltimore, MD 21287. Received 21 Aug. 2012; and in revised form 7 Jan. 2013; accepted 3 Feb. 2013. © 2013 American Academy of Forensic Sciences
Studies have demonstrated that finite element analysis (FEA) software has an application in soft tissue modeling (7). Finite element analysis is a numerical method to approximate the mechanical behavior of a structure when a force is applied. The structure’s geometry, material properties, and loading characteristics are defined in the model. The model is then divided into a finite number of subelements with the mechanical behavior of each element characterized by a set of algebraic equations that are directly related to governing differential equations of equilibrium. The shape of each element is defined by vertices (four vertices for a tetrahedron element and eight vertices for a hexahedron element), which are called nodes, and assigned appropriate material properties, such as Young’s modulus and Poisson’s ratio for linear elastic, isotropic material behavior. Together, the contiguous set of elements form what is called a mesh. When a load is applied to the model, the FEA software is able to solve for the displacement at each node, in each coordinate direction, and the resulting strain and stress fields throughout the model, providing an accurate simulation of the mechanical behavior of the structure. Because capillaries are microscopic, past studies have approximated their elastic properties through mathematical equations (8) and FEA (7). The goal of these studies was to model how capillaries would react to different types of stresses; however, neither study investigated the potential modes of capillary failure, as is the case in bruising. Shear stress and tensile stress (due to internal hydraulic pressure) are two possible modes of capillary failure. In shear stress, as the force is applied over an area of tissue containing capillaries, the inertia of the adjacent tissue resists motion in the direction of the force, creating two adjoining planes moving in opposite directions relative to each other (shear). If the shear stress exceeds the shear strength of the capillary wall, the capillary fails, resulting in blood flowing into 371
372
JOURNAL OF FORENSIC SCIENCES
surrounding tissue and bruising. Tensile stress due to hydraulic pressure occurs when the capillaries are deformed within the compression zone of the impact, forcing blood at high pressure into regions of the capillary outside the compression zone. These portions of the capillary outside the compression zone then dilate due to the high-pressure pulse of the blood, creating a circumferential tensile stress (hoop stress) in the capillary wall. If this tensile stress exceeds the ultimate tensile strength of the capillary wall, the capillary bursts. Using FEA, the goal of this study is to characterize capillary failure mode by simulating a traumatic impact on muscle tissue containing capillaries. Methods A geometry model of a branching capillary bed in human muscle tissue was created using ANSYS Workbench Design Modeler 14.0 â (ANSYS, Inc. / Southpointe / 275 Technology Drive / Canonsburg, PA). An arteriole with four branching capillaries was created with circular cross-sections (Fig. 1). Two circles were swept tangentially to four spline paths to model the capillary walls and blood-filled lumens. The diameters of the inner and outer cross-sections at the proximal end were defined to be 12 lm and 20 lm, respectively. The profiles were diminished along the sweep to half their original diameters, producing a capillary with a 10 lm diameter and a 2 lm wall thickness at the distal end of each path, dimensions used by Fung and Liu (6). To simulate the muscle tissue that surrounds the capillaries, a 64 lm by 215 lm rectangle was sketched and extruded 182 lm; accordingly, the distal end of the rectangular extrusion was flushed with the distal ends of the four capillary extrusions. The capillaries ran through the mid depth of the muscle tissue block. The volumetric regions representing the blood within the capillary, the capillary wall, and the surrounding muscle tissue were combined into one global structure in a manner that enabled different material properties to be assigned to each volumetric region. To specify an area over which the load would be applied, an imprint area was created on the proximal half of the dorsal face. The total area of the impact zone was 1.9565 9 104 lm2 (Fig. 1). Once the geometry of the model was completed, the biomechanical properties of muscle (9–13), blood, and capillaries
FIG. 1––Muscle tissue (pink) with embedded branching capillary geometry (purple). The green area on the dorsal face of the muscle tissue block represents the area over which the impact force was applied.
obtained from the literature were entered for each specific tissue type. While muscle and capillary tissue have complex viscoelastic material behavior, they were treated as linear elastic isotropic materials and assigned mechanical properties of Poisson’s ratio and Young’s modulus. A mesh was inserted in the static structural model window of the ANSYS Workbench. Blood was modeled as an incompressible solid, a technique used to simulate fluid dynamics (14). To ensure that the thickness of the 2 lm capillary wall could be adequately represented, a sizing control of 1 lm was applied to the capillary wall in the ANSYS automatic mesh generator module. Displacement constraints were added to the lateral and proximal faces, and a fixed support was applied to the ventral face. Trials were conducted to estimate a physiologically realistic trauma event – a grabbing force. Four adult male subjects maximally squeezed a Vernier HD-BTA Hand Dynamometer between their index fingers and thumbs. The average of the peak forces was divided by the area of two finger pads, which was calculated to be 12.56 cm2, resulting in an average pressure of 101,911 Pa. The area of the model’s impact zone was then multiplied by that pressure to obtain force of 2.0 9 10 3 N, which caused global capillary failure, according to our threshold criteria. The force was then reduced to 4.0 9 10-4 N; a force magnitude that reduced trauma to nearer the bruise threshold. The model was solved using static structural analysis, because all elastic properties used in this study were isotropic and not timedependent. Thus, the peak static load applied to the model was 4.0 9 10 4 N. Capillaries have the potential to fail as a result of tensile stress or shear strain. The value used for the ultimate tensile stress of the capillary wall was 8.4 9 104 Pa (15), while that for ultimate shear strain was 0.6 (16). Any stresses or strains that exceed their respective thresholds were considered to result in capillary failure, and thus bruising. Results A finite element model of four branching capillaries embedded in muscle tissue was successfully created and solved in ANSYS Workbench Design Modeler 14.0 â. The model was solved for both maximum principal stress and maximum shear strain. Any principal stress values that exceeded the threshold for failure (8.4 9 104 Pa) appear in orange, red, and deep blue (Fig. 2). Principal stress values appear to peak at two locations: stress failure occurred more directly under the impact zone and on the lateral faces of capillary walls at bifurcations (Fig. 3). The maximum principal stress recorded on the capillary geometry was 5.181 9 105 Pa. The shear strain results can be seen in Fig. 4. Any maximum shear strain values that exceed the threshold for capillary failure (0.6) would have appeared in yellow, orange, and red, but minimal values of maximum shear strain were observed on the geometry. Furthermore, peak shear values were not observed on the plane conjoining the loaded and nonloaded portions of the model (the presumed location of highest shear). Although the block of muscle tissue experienced relatively large amounts of compressive deformation under the area of impact, the capillaries embedded in the muscle tissue did not experience significant shear. The nominal maximum shear strains in the capillary wall are less than 0.3 and typically in the range from 0.1 to 0.2. Values above 0.3 occur only at the perfectly sharp edges of capillary junctions, which reflect an artifact of the model construction process, rather than anatomical reality.
TANG ET AL.
FIG. 2––Maximum principal stress (Pa) with muscle tissue and blood absent for viewing purposes. Peak stress values resulting in capillary failure are tagged. Values in orange, red, and deep blue indicate capillary failure. Failure occurs at bifurcations.
FIG. 3––Longitudinal cross-section of maximum principal stress (Pa). As a reference, the area of loading includes the topmost bifurcation and the entire area below that point. Peak stress values resulting in capillary failure are tagged. Values in orange, red, and deep blue indicate capillary failure. Note bifurcations and lateral walls are the primary principle locations of failure.
Discussion Based on the distribution of stress, capillaries primarily fail due to tensile stress in two locations: directly under the impact zone and at bifurcations. The shear strain results show no failure on the plane between loaded and unloaded tissues; therefore, shear strain is not likely a primary mode of failure. Under the impact zone, the capillaries failed at their lateral margins where the circular cross-sections were compressed into an ellipse. This pattern of deformation and local failure indicates that capillaries fail due to internal tensile stress. The increased stress and resulting strains at bifurcations are a result of the capillary geometry, with some strain augmentation due to modeling artifact. The increased surface area per volume at bifurcations (diminishing wall diameters) results in high stress values local to these
.
THE ETIOLOGY OF BRUISING
373
FIG. 4––Maximum shear strain (yellow, orange, and red values indicate failure levels). No areas experienced strain levels indicative of failure via shear strain.
junctions. As there is no ballooning effect visible in the images (even at exaggerated amounts of deformation), hydraulic stress does not seem to be a likely mode of capillary failure in this model. Instead, the deformation of the capillary wall into an ellipsoid reinforces that tensile stress is likely the primary mode of capillary failure. That direct shear strain is not necessary to initiate bruising is supported by the clinical practice of cupping, where simple pressure differentials cause bruising (17). Our model results are promising, considering that ocular petechia resulting from chocking, or shaken baby syndrome can only be initiated by internally derived pressure differentials, rather than shearing via direct mechanical trauma. An additional factor that influences the mechanical properties of soft connective tissues is genetic variation between individuals (18). For example, polyallelic variation in collagen necessarily results in variations in the mechanical properties of connective tissues between individuals (19), and thus the load threshold of bruising may vary somewhat from subject to subject due to amino acid sequence differences in the protein. A final recommendation for future studies investigating capillary failure and bruising would be the evaluation of loading rate, as well as determining load and pressure thresholds. References 1. Kumar V, Abbas A, Fausta N, Richard N. Robbins pathological basis of disease, 8th edn. Philadelphia, PA: Saunders Elsevier, 2007, p. 86. 2. Di Maio V, Di Maio D. Blunt trauma wounds: contusions. In: Geberth VJ, editor. Forensic pathology, 2nd edn. New York, NY: CRC, 2001; 98–101. 3. Akbarnia BA, Campbell R. The role of the orthopaedic surgeon in child abuse. In: Morrissy RT, Weinstein SL, editors. Pediatric orthopaedics, 5th edn. Philadelphia, PA: Lippincott Williams & Wilkins, 2000; 1423–45. 4. Blair L, Clauss E, Meredith M. Child abuse: discovering the horrifying yruth. J Emerg Med Serv 2011;36(10):62–7. 5. Mimasaka S, Oshima T, Ohtani M. Characterization of bruises using ultrasonography for potential application in diagnosis of child abuse. Leg Med (Tokyo) 2012;14(1):6–10. 6. Fung YC, Liu SQ. Determination of the mechanical properties of the different layers of blood vessels in vivo. Proc Natl Acad Sci U S A 1995; 92:2169–73. 7. Shilo M, Gefen A. Identification of capillary blood pressure levels at which capillary collapse is likely in a tissue subjected to large compres-
374
8. 9. 10. 11. 12. 13. 14.
JOURNAL OF FORENSIC SCIENCES
sive and shear deformations. Comput Methods Biomech Biomed Engin 2010;15(1):59–71. Fung YC. Structure and stress-strain relationship of soft tissues. Am Zoo 1984;24(1):13–22. Chen EJ, Novakofski J, Jenkens WK, O’Brien WD. Young’s modulus measurements of soft tissues with application to elasticity imaging. IEEE Trans Ultrason Perroelec Freq Con 1996;43(1):191–4. Livarinen JT, Korhonen RK, Julkunen P, Jurvelin JS. Experimental and computational analysis of soft tissue stiffness in forearm using a manual indentation device. Med Eng Phys 2011;33(10):1245–53. Meier P, Blickhan R. FEM-simulation of skeletal muscle: the influence of inertia during activation and deactivation. Skelet Muscle Mech 2000;1 (12):207–24. Morrow DA. Haut Donahue TL, Odegard GM, Kaufman KR. Transversely isotropic tensile material properties of skeletal muscle tissue. J Mech Behav Biomed Mater 2010;3(1):124–9. Nordez A, Hug F. Muscle shear elastic modulus measured using supersonic shear imaging is highly related to muscle activity level. J Appl Physiol 2010;108(5):1389–94. Ross JW, Miller WA, Weatherly GC. Dynamic computer simulation of viscous flow sintering kinetics. J Appl Physics 1981;52(6):3884–8.
15. Stemper BD, Yoganandan N, Sinson GP, Gennarelli TA, Stineman MR, Pintar FA. Biomechanical characterization of internal layer subfailure in blunt arterial injury. Ann Biomed Eng 2007;35(2):285–91. 16. West JB, Tsukimoto K, Mathieu-Costello O, Prediletto R. Stress failure in pulmonary capillaries. J Appl Physiol 1991;70(4):1731–42. 17. Tham LM, Lee HP, Lu C. Cupping: from a biomechanical perspective. J Biomech 2006;39(12):2183–93. 18. Puthucheary Z, Skipworth JR, Rawal J, Loosemore M, Van Someren K, Montgomery HE. Genetic influences in sport and physical performance. Sports Med 2011;41(10):845–59. 19. Nose M. A polygene network model for the complex pathological phenotypes of collagen disease. Pathol Int 2011;61(11):619–29. Additional information and reprint requests: Dennis Cullinane, Ph.D. Biomechanics Laboratory Deerfield Academy 7 Boyden Lane Deerfield MA 01342 E-mail: [email protected]
PAPER ENGINEERING SCIENCES
Kevin Tang,1 H.S.D.; Wyatt Sharpe,1 H.S.D.; Alexandra Schulz,1 H.S.D.; Edric Tam,1 H.S.D.; Ian Grosse,2 Ph.D.; John Tis,3 M.D.; and Dennis Cullinane,1 Ph.D.
Determining Bruise Etiology in Muscle Tissue Using Finite Element Analysis
ABSTRACT: Bruising, the result of capillary failure, is a common physical exam finding due to blunt trauma and, depending on location
and severity, a potential indicator of abuse. Despite its clinical relevance, few studies have investigated the etiology of capillary failure. The goal of this study was to determine whether capillaries primarily fail under shear stress or hydraulic-induced tensile stress. An arteriole bifurcating into four capillaries was modeled using ANSYS 14.0 â. The capillaries were embedded in muscle tissue and a pressure of 20.4 kPa was applied. Any tensile stress exceeding 8.4 9 104 Pa was considered failure. Results showed that failure occurred directly under the impact zone and where capillaries bifurcated, rather than along the line of greatest shear stress, indicating that internal tensile stress is likely the primary mode of capillary failure in bruising. These results are supported by the concept that bruising can occur via blunt trauma in which no shearing lacerations occur.
KEYWORDS: forensic science, bruising, capillary failure, finite element analysis, hydraulic tensile stress, shear stress
A bruise is an area of skin discoloration created when a stress caused by blunt trauma exceeds the ultimate strength of capillaries. During bruising, the blood in the capillaries leaks into the surrounding soft tissue, resulting in swelling and pain (1,2). Bruising can occur in the skin and adipose layers (subcutaneous), within the belly of the underlying muscle (intramuscular), or on bone (periosteal). Bruising is also a common clinical indicator of abuse (3–5). Because of the clinical relevance of bruising, it would be beneficial to determine the mechanism of capillary failure and the load threshold at which bruising occurs. When a force is applied to soft tissue, the tissue deforms (strain) based on the tissue’s architecture and mechanical properties, as well as the force magnitude, direction, and loading rate. The tissue will eventually fail when the stress induced by the loading reaches the ultimate strength of the tissue. Thus, the failure of capillaries depends upon both their architecture and material properties. Capillaries are composed of two layers, the intima and the media (6). The intima is a 2-lm-thick endothelial layer with a 1-lm-thick basal lamina of collagen. The media is a thicker layer of smooth muscle cells with elastic laminae and a minor amount of collagen. Although capillary failure is known to be the cause of bruising, very little is known regarding the etiology of capillary failure. The goal of this study is to determine the mode of capillary failure in bruising and thus the etiology of bruising.
1
Biomechanics Laboratory, Deerfield Academy, 7 Boyden Lane Deerfield, Deerfield, MA 01342. 2 Department of Mechanical and Industrial Engineering, University of Massachusetts, 130 Natural Resources Road, Amherst, MA 01003. 3 Department of Orthopaedic Surgery, Johns Hopkins University School of Medicine, 1800 Orleans St, Suite 7356, Baltimore, MD 21287. Received 21 Aug. 2012; and in revised form 7 Jan. 2013; accepted 3 Feb. 2013. © 2013 American Academy of Forensic Sciences
Studies have demonstrated that finite element analysis (FEA) software has an application in soft tissue modeling (7). Finite element analysis is a numerical method to approximate the mechanical behavior of a structure when a force is applied. The structure’s geometry, material properties, and loading characteristics are defined in the model. The model is then divided into a finite number of subelements with the mechanical behavior of each element characterized by a set of algebraic equations that are directly related to governing differential equations of equilibrium. The shape of each element is defined by vertices (four vertices for a tetrahedron element and eight vertices for a hexahedron element), which are called nodes, and assigned appropriate material properties, such as Young’s modulus and Poisson’s ratio for linear elastic, isotropic material behavior. Together, the contiguous set of elements form what is called a mesh. When a load is applied to the model, the FEA software is able to solve for the displacement at each node, in each coordinate direction, and the resulting strain and stress fields throughout the model, providing an accurate simulation of the mechanical behavior of the structure. Because capillaries are microscopic, past studies have approximated their elastic properties through mathematical equations (8) and FEA (7). The goal of these studies was to model how capillaries would react to different types of stresses; however, neither study investigated the potential modes of capillary failure, as is the case in bruising. Shear stress and tensile stress (due to internal hydraulic pressure) are two possible modes of capillary failure. In shear stress, as the force is applied over an area of tissue containing capillaries, the inertia of the adjacent tissue resists motion in the direction of the force, creating two adjoining planes moving in opposite directions relative to each other (shear). If the shear stress exceeds the shear strength of the capillary wall, the capillary fails, resulting in blood flowing into 371
372
JOURNAL OF FORENSIC SCIENCES
surrounding tissue and bruising. Tensile stress due to hydraulic pressure occurs when the capillaries are deformed within the compression zone of the impact, forcing blood at high pressure into regions of the capillary outside the compression zone. These portions of the capillary outside the compression zone then dilate due to the high-pressure pulse of the blood, creating a circumferential tensile stress (hoop stress) in the capillary wall. If this tensile stress exceeds the ultimate tensile strength of the capillary wall, the capillary bursts. Using FEA, the goal of this study is to characterize capillary failure mode by simulating a traumatic impact on muscle tissue containing capillaries. Methods A geometry model of a branching capillary bed in human muscle tissue was created using ANSYS Workbench Design Modeler 14.0 â (ANSYS, Inc. / Southpointe / 275 Technology Drive / Canonsburg, PA). An arteriole with four branching capillaries was created with circular cross-sections (Fig. 1). Two circles were swept tangentially to four spline paths to model the capillary walls and blood-filled lumens. The diameters of the inner and outer cross-sections at the proximal end were defined to be 12 lm and 20 lm, respectively. The profiles were diminished along the sweep to half their original diameters, producing a capillary with a 10 lm diameter and a 2 lm wall thickness at the distal end of each path, dimensions used by Fung and Liu (6). To simulate the muscle tissue that surrounds the capillaries, a 64 lm by 215 lm rectangle was sketched and extruded 182 lm; accordingly, the distal end of the rectangular extrusion was flushed with the distal ends of the four capillary extrusions. The capillaries ran through the mid depth of the muscle tissue block. The volumetric regions representing the blood within the capillary, the capillary wall, and the surrounding muscle tissue were combined into one global structure in a manner that enabled different material properties to be assigned to each volumetric region. To specify an area over which the load would be applied, an imprint area was created on the proximal half of the dorsal face. The total area of the impact zone was 1.9565 9 104 lm2 (Fig. 1). Once the geometry of the model was completed, the biomechanical properties of muscle (9–13), blood, and capillaries
FIG. 1––Muscle tissue (pink) with embedded branching capillary geometry (purple). The green area on the dorsal face of the muscle tissue block represents the area over which the impact force was applied.
obtained from the literature were entered for each specific tissue type. While muscle and capillary tissue have complex viscoelastic material behavior, they were treated as linear elastic isotropic materials and assigned mechanical properties of Poisson’s ratio and Young’s modulus. A mesh was inserted in the static structural model window of the ANSYS Workbench. Blood was modeled as an incompressible solid, a technique used to simulate fluid dynamics (14). To ensure that the thickness of the 2 lm capillary wall could be adequately represented, a sizing control of 1 lm was applied to the capillary wall in the ANSYS automatic mesh generator module. Displacement constraints were added to the lateral and proximal faces, and a fixed support was applied to the ventral face. Trials were conducted to estimate a physiologically realistic trauma event – a grabbing force. Four adult male subjects maximally squeezed a Vernier HD-BTA Hand Dynamometer between their index fingers and thumbs. The average of the peak forces was divided by the area of two finger pads, which was calculated to be 12.56 cm2, resulting in an average pressure of 101,911 Pa. The area of the model’s impact zone was then multiplied by that pressure to obtain force of 2.0 9 10 3 N, which caused global capillary failure, according to our threshold criteria. The force was then reduced to 4.0 9 10-4 N; a force magnitude that reduced trauma to nearer the bruise threshold. The model was solved using static structural analysis, because all elastic properties used in this study were isotropic and not timedependent. Thus, the peak static load applied to the model was 4.0 9 10 4 N. Capillaries have the potential to fail as a result of tensile stress or shear strain. The value used for the ultimate tensile stress of the capillary wall was 8.4 9 104 Pa (15), while that for ultimate shear strain was 0.6 (16). Any stresses or strains that exceed their respective thresholds were considered to result in capillary failure, and thus bruising. Results A finite element model of four branching capillaries embedded in muscle tissue was successfully created and solved in ANSYS Workbench Design Modeler 14.0 â. The model was solved for both maximum principal stress and maximum shear strain. Any principal stress values that exceeded the threshold for failure (8.4 9 104 Pa) appear in orange, red, and deep blue (Fig. 2). Principal stress values appear to peak at two locations: stress failure occurred more directly under the impact zone and on the lateral faces of capillary walls at bifurcations (Fig. 3). The maximum principal stress recorded on the capillary geometry was 5.181 9 105 Pa. The shear strain results can be seen in Fig. 4. Any maximum shear strain values that exceed the threshold for capillary failure (0.6) would have appeared in yellow, orange, and red, but minimal values of maximum shear strain were observed on the geometry. Furthermore, peak shear values were not observed on the plane conjoining the loaded and nonloaded portions of the model (the presumed location of highest shear). Although the block of muscle tissue experienced relatively large amounts of compressive deformation under the area of impact, the capillaries embedded in the muscle tissue did not experience significant shear. The nominal maximum shear strains in the capillary wall are less than 0.3 and typically in the range from 0.1 to 0.2. Values above 0.3 occur only at the perfectly sharp edges of capillary junctions, which reflect an artifact of the model construction process, rather than anatomical reality.
TANG ET AL.
FIG. 2––Maximum principal stress (Pa) with muscle tissue and blood absent for viewing purposes. Peak stress values resulting in capillary failure are tagged. Values in orange, red, and deep blue indicate capillary failure. Failure occurs at bifurcations.
FIG. 3––Longitudinal cross-section of maximum principal stress (Pa). As a reference, the area of loading includes the topmost bifurcation and the entire area below that point. Peak stress values resulting in capillary failure are tagged. Values in orange, red, and deep blue indicate capillary failure. Note bifurcations and lateral walls are the primary principle locations of failure.
Discussion Based on the distribution of stress, capillaries primarily fail due to tensile stress in two locations: directly under the impact zone and at bifurcations. The shear strain results show no failure on the plane between loaded and unloaded tissues; therefore, shear strain is not likely a primary mode of failure. Under the impact zone, the capillaries failed at their lateral margins where the circular cross-sections were compressed into an ellipse. This pattern of deformation and local failure indicates that capillaries fail due to internal tensile stress. The increased stress and resulting strains at bifurcations are a result of the capillary geometry, with some strain augmentation due to modeling artifact. The increased surface area per volume at bifurcations (diminishing wall diameters) results in high stress values local to these
.
THE ETIOLOGY OF BRUISING
373
FIG. 4––Maximum shear strain (yellow, orange, and red values indicate failure levels). No areas experienced strain levels indicative of failure via shear strain.
junctions. As there is no ballooning effect visible in the images (even at exaggerated amounts of deformation), hydraulic stress does not seem to be a likely mode of capillary failure in this model. Instead, the deformation of the capillary wall into an ellipsoid reinforces that tensile stress is likely the primary mode of capillary failure. That direct shear strain is not necessary to initiate bruising is supported by the clinical practice of cupping, where simple pressure differentials cause bruising (17). Our model results are promising, considering that ocular petechia resulting from chocking, or shaken baby syndrome can only be initiated by internally derived pressure differentials, rather than shearing via direct mechanical trauma. An additional factor that influences the mechanical properties of soft connective tissues is genetic variation between individuals (18). For example, polyallelic variation in collagen necessarily results in variations in the mechanical properties of connective tissues between individuals (19), and thus the load threshold of bruising may vary somewhat from subject to subject due to amino acid sequence differences in the protein. A final recommendation for future studies investigating capillary failure and bruising would be the evaluation of loading rate, as well as determining load and pressure thresholds. References 1. Kumar V, Abbas A, Fausta N, Richard N. Robbins pathological basis of disease, 8th edn. Philadelphia, PA: Saunders Elsevier, 2007, p. 86. 2. Di Maio V, Di Maio D. Blunt trauma wounds: contusions. In: Geberth VJ, editor. Forensic pathology, 2nd edn. New York, NY: CRC, 2001; 98–101. 3. Akbarnia BA, Campbell R. The role of the orthopaedic surgeon in child abuse. In: Morrissy RT, Weinstein SL, editors. Pediatric orthopaedics, 5th edn. Philadelphia, PA: Lippincott Williams & Wilkins, 2000; 1423–45. 4. Blair L, Clauss E, Meredith M. Child abuse: discovering the horrifying yruth. J Emerg Med Serv 2011;36(10):62–7. 5. Mimasaka S, Oshima T, Ohtani M. Characterization of bruises using ultrasonography for potential application in diagnosis of child abuse. Leg Med (Tokyo) 2012;14(1):6–10. 6. Fung YC, Liu SQ. Determination of the mechanical properties of the different layers of blood vessels in vivo. Proc Natl Acad Sci U S A 1995; 92:2169–73. 7. Shilo M, Gefen A. Identification of capillary blood pressure levels at which capillary collapse is likely in a tissue subjected to large compres-
374
8. 9. 10. 11. 12. 13. 14.
JOURNAL OF FORENSIC SCIENCES
sive and shear deformations. Comput Methods Biomech Biomed Engin 2010;15(1):59–71. Fung YC. Structure and stress-strain relationship of soft tissues. Am Zoo 1984;24(1):13–22. Chen EJ, Novakofski J, Jenkens WK, O’Brien WD. Young’s modulus measurements of soft tissues with application to elasticity imaging. IEEE Trans Ultrason Perroelec Freq Con 1996;43(1):191–4. Livarinen JT, Korhonen RK, Julkunen P, Jurvelin JS. Experimental and computational analysis of soft tissue stiffness in forearm using a manual indentation device. Med Eng Phys 2011;33(10):1245–53. Meier P, Blickhan R. FEM-simulation of skeletal muscle: the influence of inertia during activation and deactivation. Skelet Muscle Mech 2000;1 (12):207–24. Morrow DA. Haut Donahue TL, Odegard GM, Kaufman KR. Transversely isotropic tensile material properties of skeletal muscle tissue. J Mech Behav Biomed Mater 2010;3(1):124–9. Nordez A, Hug F. Muscle shear elastic modulus measured using supersonic shear imaging is highly related to muscle activity level. J Appl Physiol 2010;108(5):1389–94. Ross JW, Miller WA, Weatherly GC. Dynamic computer simulation of viscous flow sintering kinetics. J Appl Physics 1981;52(6):3884–8.
15. Stemper BD, Yoganandan N, Sinson GP, Gennarelli TA, Stineman MR, Pintar FA. Biomechanical characterization of internal layer subfailure in blunt arterial injury. Ann Biomed Eng 2007;35(2):285–91. 16. West JB, Tsukimoto K, Mathieu-Costello O, Prediletto R. Stress failure in pulmonary capillaries. J Appl Physiol 1991;70(4):1731–42. 17. Tham LM, Lee HP, Lu C. Cupping: from a biomechanical perspective. J Biomech 2006;39(12):2183–93. 18. Puthucheary Z, Skipworth JR, Rawal J, Loosemore M, Van Someren K, Montgomery HE. Genetic influences in sport and physical performance. Sports Med 2011;41(10):845–59. 19. Nose M. A polygene network model for the complex pathological phenotypes of collagen disease. Pathol Int 2011;61(11):619–29. Additional information and reprint requests: Dennis Cullinane, Ph.D. Biomechanics Laboratory Deerfield Academy 7 Boyden Lane Deerfield MA 01342 E-mail: [email protected]
