Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics

Summary

This protocol uses multi-view stereo to generate three-dimensional (3D) models out of uncalibrated sequences of photographs, making it affordable and adjustable to a surgical setting. Strain maps between the 3D models are quantified with spline-based isogeometric kinematics, which facilitate representation of smooth surfaces over coarse meshes sharing the same parameterization.

Abstract

Tissue expansion is a popular technique in plastic and reconstructive surgery that grows skin in vivo for correction of large defects such as burns and giant congenital nevi. Despite its widespread use, planning and executing an expansion protocol is challenging due to the difficulty in measuring the deformation imposed at each inflation step and over the length of the procedure. Quantifying the deformation fields is crucial, as the distribution of stretch over time determines the rate and amount of skin grown at the end of the treatment. In this manuscript, we present a method to study tissue expansion in order to gain quantitative knowledge of the deformations induced during an expansion process. This experimental protocol incorporates multi-view stereo and isogeometric kinematic analysis in a porcine model of tissue expansion. Multi-view stereo allows three-dimensional geometric reconstruction from uncalibrated sequences of images. The isogeometric kinematic analysis uses splines to describe the regional deformations between smooth surfaces with few mesh points. Our protocol has the potential to bridge the gap between basic scientific inquiry regarding the mechanics of skin expansion and the clinical setting. Eventually, we expect that the knowledge gained with our methodology will enable treatment planning using computational simulations of skin deformation in a personalized manner.

Introduction

Tissue expansion is a common technique in plastic and reconstructive surgery that grows skin in vivo for the correction of large cutaneous defects ¹. Neumann, in 1957, was the first surgeon to document this procedure. He implanted a balloon below the skin of a patient and inflated it gradually over a period of several weeks to grow new tissue and resurface an ear ². Skin, like most biological tissues, adapts to applied forces and deformations in order to reach mechanical homeostasis. When stretched beyond the physiological regime, skin grows ^3,4. One of the central advantages of tissue expansion is the production of skin with proper vascularization and the same hair bearing, mechanical properties, color, and texture as the surrounding tissue ⁵.

After its introduction six decades ago, skin expansion has been widely adopted by plastic and reconstructive surgeons and is presently used to correct burns, large congenital defects, and for breast reconstruction after mastectomy ^6,7. Yet, despite its widespread use, skin expansion procedures can lead to complications ⁸. This is partly due to the lack of sufficient quantitative evidence needed to understand the fundamental mechanobiology of the procedure and to guide the surgeon during preoperative planning ^9,10. Key parameters in this technique are the filling rate, filling volume per inflation, the selection of the shape and size of the expander, and the placement of the device ^11,12. Current preoperative planning relies largely on the physician's experience, resulting in a wide variety of arbitrary protocols that often differ greatly ^13,14,15.

To address the current knowledge gaps, we present an experimental protocol to quantify expansion-induced deformation in a porcine animal model of tissue expansion. The protocol relies on the use of multi-view stereo (MVS) to reconstruct three-dimensional (3D) geometries out of sequences of two-dimensional (2D) images with unknown camera positions. Employing splines, representation of smooth surfaces leads to the calculation of the corresponding deformation maps by means of an isogeometric (IGA) description. The analysis of the geometry is based on the theoretical framework of continuum mechanics of membranes having an explicit parameterization ¹⁶.

Characterizing physiologically relevant deformations of living materials over long periods of time still remains a challenging problem. Common strategies for imaging of biological tissues include stereoscopic digital image correlation, commercial motion capture systems with reflective markers, and biplane video fluoroscopy ^17,18,19. However, these techniques require a restrictive experimental setup, are generally expensive, and have been primarily used for ex vivo or acute in vivo settings. Skin has the advantage of being a thin structure. Even though it consists of several layers, the dermis is largely responsible for the mechanical properties of the tissue and thus the surface deformation is of primary importance ²⁰; reasonable kinematical assumptions can be made regarding the out of plane deformation ^21,22. Moreover, skin is already exposed to the outside environment, making it possible to use conventional imaging tools to capture its geometry. Here we propose the use of MVS as an affordable and flexible approach to monitor in vivo deformations of skin over several weeks without interfering majorly with a tissue expansion protocol. MVS is a technique that extracts 3D representations of objects or scenes from a collection of 2D images with unknown camera angles ²³. Only in the last three years, several commercial codes have appeared (see list of materials for examples). The high accuracy of the model reconstruction with MVS, with errors as low as 2% ²⁴, makes this approach suitable for the kinematic characterization of skin in vivo over long periods of time.

To obtain the corresponding deformation maps of skin during tissue expansion, points between any two geometric configurations are matched. Conventionally, researchers in computational biomechanics have used finite element meshes and inverse analysis to retrieve the deformation map ^25,26. The IGA approach employed here uses spline basis functions which offer several advantages for the analysis of thin membranes ^27,28. Namely, the availability of high degree polynomials facilitates representations of smooth geometries even with very coarse meshes ^29,30. Additionally, it is possible to fit the same underlying parameterization to all the surface patches, which circumvents the need for an inverse problem to account for non-matching discretizations.

The method described here opens new avenues to study skin mechanics in relevant in vivo settings over long periods of time. In addition, we are hopeful that our methodology is an enabling step towards the ultimate goal of developing computational tools for personalized treatment planning in the clinical setting.

Protocol

This protocol involves animal experiments. The protocol was approved by the IRB of Ann and Robert H. Lurie Children's Hospital of Chicago Research Center Animal Care and Use Committee to guarantee humane treatment of animals. The results for two expansion studies using this protocol have been published elsewhere ^16,31.

Execution of this protocol requires a team with complementary expertise. The first part of the protocol describes the surgical procedure on the animal model, requiring personnel with the appropriate medical training. The subsequent analysis, particularly sections 4 and 5, involve basic computer programming skills in C++ and Python, and use of a command line shell.

1. Surgical Procedure for Expander Placement

NOTE: Personnel involved in the operation must be scrubbed and gowned in a sterile fashion. Sterile towels and drapes are applied around the surgical field to maintain sterility. All instruments, sutures, and tissue expanders are received in sterile packaging and handled only by sterile personnel. Sterility of the operative site must not be violated until the procedure is complete.

1. Acclimate one-month-old male Yucatan mini pigs to standard housing for one week, and feed ad libitum.
2. On the day of surgery, anesthetize the animal using ketamine/acepromazine for induction (4 - 6 mg/kg), then isoflurane for maintenance. Evaluate depth of anesthesia by monitoring the palpebral reflex. Also, monitor vital signs (heart rate, body temperature, respiratory rate, and/or response to pinch by tissue forceps). Apply ophthalmic ointment to the eyes to protect against corneal abrasions.
3. Administer pre-procedural antibiotics and clean the dorsal skin with chlorhexidine-based surgical soap. Transfer four 10 x 10 cm² grids, two on each side of the animal, with 1 cm line markings to the pig skin using tattoo transfer medium. The grids correspond to the following four regions: left rostral, right rostral, left caudal, and right caudal. Use a template with a midline reference to ensure symmetric placement of the grid patterns.
   1. Create the grids on paper by tracing the grid outlines heavily with a ballpoint pen. Wash the area on the animal where the grid is to be placed with isopropyl rubbing alcohol.
   2. Apply the grid (pen-ink side down) directly onto the skin. The alcohol serves to leech some of the ink off of the paper, transferring the grid to the animal's skin.
4. Inject local anesthetic (1% lidocaine with 1:100,000 epinephrine) subcutaneously at the site of each planned incision.
5. Make an incision on either side of the animal in the midpoint between the two grids.
   NOTE: The incisions are placed on the left and right side of the animal between the 2 grids on that side. There is a left sided incision and a right sided incision
6. Use a hemostat to develop a subcutaneous tunnel beneath the grid of interest. After developing a tunnel, insert the expander beneath the grid.
   NOTE: Tunnels are placed under any grid that will have a tissue expander.
7. Place the port for expander inflation remotely through a subcutaneous tunnel developed in a similar fashion along the dorsal midline of the animal. Repair wounds by suturing.
8. Postoperatively, treat the animal with prophylactic antibiotics (Ceftiofur 5 mg/kg IM once) as well as analgesics (Buprenorphine 0.05 - 0.1 mg/kg) via intramuscular injection every 12 h for 4 doses, with additional doses available for evidence of animal distress.
9. Observe animals continuously for 2 h postoperatively, including routine measurement of vital signs until they have resumed ambulation and are able to maintain normothermia. House the animal in a separate cage and monitor until it is able to walk independently on all 4 legs before transferring it back to its normal housing area and leaving it unattended.
10. Following the immediate post anesthesia recovery period, check animals daily to evaluate wound healing. Remove the sutures 14 days postoperatively. These incisions do not require dressings. Leave the incisions to heal for 3 - 4 weeks before beginning expansion

2. Inflation Protocol

NOTE: The timing of the inflations and amount of solution used in each expander depends on the specific question being studied. To characterize the effect of different expander geometries, a suitable protocol is to perform five inflation steps at 0, 2, 7, 10, and 15 days to achieve filling volumes of 50, 75, 105, 165, and 225 cc respectively.

1. Before each inflation step, sedate the animal administering ketamine (4 - 6 mg/kg) and dexmedetomidine at 20 - 80 µg/kg.
   NOTE: Dexmedetomidine is an alpha-adrenergic agonist that can be reversed with atipamezole (1:1 volume:volume) to facilitate faster recovery; however, this level of sedation may not be adequate for the animal to tolerate expansion without undue risk of harm to the animal or handlers. If this is the case, administer general anesthesia by delivering isoflurane via mask ventilation following ketamine/acepromazine induction.
2. Attach two plastic flexible tape measures to the skin of the animal using surgical tape. Place the tape measures between the grids on the left and right sides.
3. Place the animal on one side and acquire 30 photographs of the scene from as many different angles as possible.
   NOTE: The objective is to capture the geometry of the two grids visible when the animal is laying down on one side.
   1. First, position the camera above the animal and leaning towards the caudal side, to capture a shot where the tattooed grids are fully visible and fill the frame.
   2. Move in a circular pattern around the animal in an arch from the caudal to the rostral direction, taking photographs along the way, ensuring that, for every photograph, the tattooed grids that are visible appear entirely in the frame.
      1. At the same time, try to maximize the space that the grids occupy in the frame. An ideal shot would capture the back of the animal with the tattooed grids and only small regions of background.
   3. Next, position the camera towards the ventral side to capture a shot angle that is approximately parallel to the ground and take photographs in an arch from the ventral to the dorsal region.
      NOTE: The amount of photographs is not a fixed value. For a good reconstruction, every point on the tattooed grid should be in at least 3 photographs; 30 photographs in total is an adequate amount for successful geometry reconstruction.
4. Place the animal on the opposite side and take 30 photographs of the two remaining grids following the same steps outlined above.
5. Perform the inflation step by finding the remote filling port and injecting the required amount of saline solution corresponding to the expansion protocol of interest. Use sterile 0.9% injectable saline.
   1. Locate the ports and prep over the skin of the animal with isopropyl alcohol wipes. Access the port with a sterile 25-gauge butterfly needle attached to a syringe filled with sterile injectable saline.
      NOTE: As described above, the ports are tunneled subcutaneously to a position on the anterior midline dorsum during expander placement.
   2. Inject the desired amount of saline solution. Please refer to the note at the beginning of this section for the inflation volumes injected at each step of the expansion process.
6. Repeat the photo acquisition steps after inflation.
7. Once the inflation protocol is complete, euthanize the animals.
   1. Administer general anesthesia by delivering isoflurane via mask ventilation following ketamine/acepromazine induction. Evaluate depth of anesthesia by monitoring the palpebral reflex. Also, monitor vital signs (heart rate, body temperature, respiratory rate, and/or response to pinch with tissue forceps).
   2. Euthanize the animal by intravenous overdose of pentobarbital 90 - 100 mg/kg. Following pentobarbital overdose for euthanasia, confirm death by the absence of detectable heartbeat using a pulse oximeter and pulse palpation as well as the absence of spontaneous respirations.

3. Multi-view Stereo Reconstruction

1. Use commercially available software to upload the image files and reconstruct the geometric models.
   1. Launch the MVS software on the browser and log in.
   2. Select Photo to 3D on the top left corner.
   3. Click add photos, browse to the location of the images and manually select the 30 photographs corresponding to a single model.
   4. Name the model and click create
   5. Wait for the model to be created. This can take several minutes. Click dashboard on the right to go back to the original landing page of the software.
      NOTE: The dashboard shows representative images of the geometric models that have been created by the user.
   6. Place the cursor on the model that has just been created. Place the cursor on the bottom right corner of the model image. Click downloads and select obj.

4. Spline Surface Fit

1. Use open source software to process the geometric models.
2. Click File->Import->obj to import the file generated from the MVS software. On the bottom of the 3D View click on Viewport Shading and select Texture. Look for a tab on the right of the 3D View with the submenus: Transform, Grease Pencil, View, 3D Pencil, etc. Click on Shading and select Shadeless.
3. Right click on the geometry to select it. On the bottom of the 3D View select Edit Mode to visualize the triangular mesh.
4. Select one by one the nodes on the 1 cm markings of the tape measure.
   1. To select a point, right click on it, and highlight the point. Coordinates for the point appear on the tab on the right-hand side of the 3D View. Select and copy the coordinates of the selected point to a text file.
   2. Repeat this operation for all the points on the 1 cm markings of the tape measure.
   3. Do this for both tape measures. Examples of coordinate text files are provided: tape1.txt, tape2.txt.
      NOTE: If there are no nodes of the mesh on the point of interest, subdivide the mesh until there is a node on the point of interest. To subdivide the mesh select the three vertices of a triangle by pressing Shift key and right-clicking on the vertices. Then click on the button Subdivide on the tab appearing on the left-hand side of the 3D View. This operation adds three more nodes inside the selected triangle.
5. Select the 11 x 11 points of the grid and save the coordinates of the 121 points to a text file in the pattern shown in Figure 1.
   1. Analogously to what was done for the tape measures, to select a point of the grid, right click on it, the point will be highlighted. Coordinates for the point will appear on the tab on the right-hand side of the 3D View. Select and copy the coordinates of the selected point to a text file
      NOTE: The numbering of the grid points is always caudal to rostral and from the dorsal midline towards the ventral region. This ordering guarantees that the parameter space is consistent for any two patches. As an example, the file gridReference.txt which contains the coordinates of 121 points of a skin patch is provided.
6. Download, compile and install C++ spline libraries. The file splineLibraryInstallation.txt contains the link to the source code of the spline libraries and instructions for installation.
7. Compile the source code generateCurve.cpp to generate the executable generateCurve
   NOTE: The program generateCurve only needs to be compiled once. To compile this C++ source code and generate an executable follow the instructions at the top of the source code file generateCurve.cpp.
8. Use the program generateCurve to fit splines to the tape measures and to the grid points. To run the executable in a Bash shell, type
   directory$ ./generateCurve
   1. Upon running the program, it will ask the user to type in the path to the file containing the coordinates of the tape measure. Then the program will ask for a name for the output file. Add the termination .g2 to the filename.
      NOTE: The termination .g2 stands for go tools, and is associated to the spline libraries. Two examples of spline files corresponding to the tape measures are available with this protocol (tape1.g2, tape2.g2).
9. Use the Python script scalePoints.py to scale the grid points. Run the program in a Bash shell prompt with three arguments: the filename of the grid points and the file names of the splines corresponding to the tape measures
   directory$ python scalePoints.py gridReference.txt tape1.g2 tape2.g2
   NOTE: The script scalePoints.py imports the scripts B_spline.py and NURBS_Curve.py, therefore all three scripts must be in the same folder.
10. Compile the source code generateSurface.cpp to generate the executable generateSurface.
    NOTE: This step only needs to be done once. More detailed instructions are available at the beginning of the source code file generateSurface.cpp.
11. Use the program generateSurface to fit a spline surface to the grid points. Run the executable generateSurface on the Bash shell
    directory$ ./generateSurface
    1. Running the program in a shell will ask for the filename containing the scaled points. Then it will ask for the name of the output file. Add the termination .g2 to the output filename.
       NOTE: The termination .g2 is suggested by the spline libraries and stands for go tools. The files gridReference.g2 and gridDeformed.g2 are provided as examples.

5. Quantification of Expansion-induced Deformation

1. Start Python in the Bash shell prompt
   directory$ python
   NOTE: Python initializes the interpreter, which is an interface similar to the shell that will show a new command line environment >>>
2. Import the script expansionIGA.py which contains a function called evaluateMembraneIGA
   >>> from expansionIGA import evaluateMembraneIGA
3. Call the function evaluateMembraneIGA to calculate the deformation maps.
   NOTE: This function takes as arguments:
   Filename of the reference surface
   Filename of the deformed surface
   Resolution of the evaluation (how many points are evaluated in each direction)
   Minimum value of area stretch used to scale the contour plot
   Maximum value of area stretch used to scale the contour plot
   Minimum value of stretch in longitudinal direction used to scale the contours
   Maximum value of stretch in longitudinal direction used to scale the contours
   Minimum value of stretch in transverse direction used to scale the contours
   Maximum value of stretch in transverse direction used to scale the contours
   Spacing between grid lines in the contour plot
   Output filename
   1. For example, run
      >>> evaluateMembraneIGA('gridReference.g2', 'gridDeformed.g2', 250, 3, 0.5, 2, 0.5, 2, 0.5, 25, 'deformation')
      NOTE: This command will generate and save six output files. Note that the last argument in the example above is the output filename deformation, thus, the files that will be generated are:
      deformation_theta.png: contour plot of the area stretch
      deformation_theta.txt: table of values corresponding to the contour plot of area stretch
      deformation_G1.png: contour plot of the stretch along the longitudinal axis of the animal
      deformation_G1.txt: table of values corresponding to the contour plot of stretches along the longitudinal axis of the animal
      deformation_G2.png: contour plot of the stretch component in the transverse axis of the animal
      deformation_G2.txt: table of values corresponding to the contour plot of the component of the stretch in the transverse axis of the animal
      NOTE: Do not confuse the termination of the spline files, .g2, with the vector G2. The spline files have ending .g2 following the naming conventions of the spline library. On the other hand, the vectors G1 and G2 denote the longitudinal and transverse directions with respect to the animal.
      NOTE: The contour files are generated with distinct features at the four corners to facilitate interpretation of the parameter space: Black pixel: most caudal, most dorsal point; Red pixel corner: most rostral, most dorsal point; Green pixel corner: most caudal, most ventral point; Blue pixel corner: most rostral, most ventral point.

Results

This methodology has been successfully employed to study the deformation induced by different expander geometries: rectangle, sphere and crescent expanders ^31,32. The results corresponding to the sphere and crescent expanders are discussed next. Figure 2 illustrates the three steps of MVS model reconstruction. The starting point is a collection of photographs from a static scene. The animal with the tattooed grids...

Discussion

Here we presented a protocol to characterize the deformations induced during a tissue expansion procedure in a porcine model using multi-view stereo (MVS) and isogeometric kinematics (IGA kinematics). During tissue expansion, skin undergoes large deformations going from a smooth and relatively flat surface to a dome-like 3D shape. Skin, like other biological membranes ³⁴, responds to stretch by producing new material, increasing in area that can be then used for reconstructive purposes

Materials

Name	Company	Catalog Number	Comments
Yucatan miniature swine	Sinclair Bioresources, Windham, ME	N/A
Antibiotics	Santa Cruz Animal Health, Paso Robles, CA	sc-362931Rx	Ceftiofur, dosage 5 mg/kg intramuscular
Chlorhexidine-based surgical soap	Cardinal Health, Dublin, OH	AS-4CHGL(4-32)	4% chlorhexidine gluconate surgical hand scrub
Tattoo transfer medium	Hildbrandt Tattoo Supply, Point Roberts, WA	TRANSF	Stencil thermal tattoo transfer paper
Lidocaine with epinephrine	ACE Surgical Supply Co, Brockton, MA	001-1423	Lidocaine Hcl 1% (Xylocaine) - Epinephrine 1:100,000, 20 mL
Buprenorphine	ZooPharm, Windsor, CO		1 mg/mL sustained release, dosage 0.01 mg/kg intramuscular
Digital camera	Sony	Alpha33	Standard digital camera with 18 - 35 mm lens, 3.5 - 5.6 aperture. Used in automatic mode, no flash
Tape measure	Medline, Mundelein, Illinois	NON171330	Retractable tape measure, cloth, plastic case, 72 inches
Tissue expanders	PMT, Chanhassen, MN	03610-06-02	4 cm x 6 cm, rectangular, 120 cc, 3610 series 2 stage tissue expander with standard port
ReCap360	Autodesk	N/A	MVS Software, Web application: recap360.autodesk.com
Blender	Blender Foundation	N/A	Computer Graphics Software, open source: blender.org
SISL	SINTEF	N/A	C++ spline libraries, open source: https://www.sintef.no/projectweb/geometry-toolkits/sisl/