Research Papers

A Potential Tool for the Study of Venous Ulcers: Blood Flow Responses to Load

[+] Author and Article Information
Wu Pan

Fellow ASME
Department of Mechanical Engineering,
Michigan State University,
2555 Engineering Building,
East Lansing, MI 48824-1226
e-mail: panwu@egr.msu.edu

Joshua P. Drost

Fellow ASME
Department of Mechanical Engineering,
Michigan State University,
2555 Engineering Building,
East Lansing, MI 48824-1226
e-mail: drostjos@msu.edu

Sara Roccabianca

Fellow ASME
Department of Mechanical Engineering,
Michigan State University,
2555 Engineering Building,
East Lansing, MI 48824-1226
e-mail: roccabis@egr.msu.edu

Seungik Baek

Fellow ASME
Department of Mechanical Engineering,
Michigan State University,
2555 Engineering Building,
East Lansing, MI 48824-1226
e-mail: sbaek@egr.msu.edu

Tamara Reid Bush

Fellow ASME
Chair of the Dynamics,
Design and Rehabilitation (DDR) Committee,
Bioengineering Technical Division,
Department of Mechanical Engineering,
Michigan State University,
2555 Engineering Building,
East Lansing, MI 48824-1226
e-mail: reidtama@msu.edu

1Corresponding author.

Manuscript received December 20, 2016; final manuscript received December 11, 2017; published online January 18, 2018. Assoc. Editor: Jonathan Vande Geest.

J Biomech Eng 140(3), 031009 (Jan 18, 2018) (7 pages) Paper No: BIO-16-1529; doi: 10.1115/1.4038742 History: Received December 20, 2016; Revised December 11, 2017

Venous ulcers are deep wounds that are located predominantly on the lower leg. They are prone to infection and once healed have a high probability of recurrence. Currently, there are no effective measures to predict and prevent venous ulcers from formation. Hence, the goal of this work was to develop a Windkessel-based model that can be used to identify hemodynamic parameters that change between healthy individuals and those with wounds. Once identified, these parameters have the potential to be used as indicators of when internal conditions change, putting the patient at higher risk for wound formation. In order to achieve this goal, blood flow responses in lower legs were measured experimentally by a laser Doppler perfusion monitor (LDPM) and simulated with a modeling approach. A circuit model was developed on the basis of the Windkessel theory. The hemodynamic parameters were extracted for three groups: legs with ulcers (“wounded”), legs without ulcers but from ulcer patients (“nonwounded”), and legs without vascular disease (“healthy”). The model was executed by two independent operators, and both operators reported significant differences between wounded and healthy legs in localized vascular resistance and compliance. The model successfully replicated the experimental blood flow profile. The global and local vascular resistances and compliance parameters rendered quantifiable differences between a population with venous ulcers and healthy individuals. This work supports that the Windkessel modeling approach has the potential to determine patient specific parameters that can be used to identify when conditions change making venous ulcer formation more likely.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


Cleveland Clinic, 2015, “ Lower Extremity Ulcers,” Cleveland Clinic, Cleveland, OH, accessed Dec. 12, 2017, https://my.clevelandclinic.org/health/diseases/17169-leg-and-foot-ulcers?view=print
Snyder, R. J. , 2005, “ Treatment of Nonhealing Ulcers With Allografts,” Clin. Dermatol., 23(4), pp. 388–395. [CrossRef] [PubMed]
Kolluri, R. , 2014, “ Management of Venous Ulcers,” Tech. Vasc. Interv. Radiol., 17(2), pp. 132–138. [CrossRef] [PubMed]
Lamel, S. A. , and Kirsner, R. S. , 2013, “ New Approaches to Enhanced Wound Healing: Future Modalities for Chronic Venous Ulcers,” Drug Discov. Today Dis. Mech., 10(3–4), pp. e71–e77. [CrossRef]
Lazarus, G. , Valle, M. F. , Malas, M. , Qazi, U. , Maruthur, N. M. , Doggett, D. , Fawole, O. , Bass, E. , and Zenilman, J. , 2014, “ Chronic Venous Leg Ulcer Treatment: Future Research Needs,” Wound Repair Regen., 22(1), pp. 34–42. [CrossRef] [PubMed]
Johnson, S. , 2002, “ Compression Hosiery in the Prevention and Treatment of Venous Leg Ulcers,” J. Tissue Viability, 12(2), pp. 67–74. [CrossRef] [PubMed]
Simka, M. , and Majewski, E. , 2003, “ The Social and Economic Burden of Venous Leg Ulcers: Focus on the Role of Micronized Purified Flavonoid Fraction Adjuvant Therapy,” Am. J. Clin. Dermatol., 4(8), pp. 573–581. [CrossRef] [PubMed]
Valencia, I. C. , Falabella, A. , Kirsner, R. S. , and Eaglstein, W. H. , 2001, “ Chronic Venous Insufficiency and Venous Leg Ulceration,” J. Am. Acad. Dermatol., 44(3), pp. 401–424. [CrossRef] [PubMed]
Milic, D. J. , Zivic, S. S. , Bogdanovic, D. C. , Karanovic, N. D. , and Golubovic, Z. V. , 2009, “ Risk Factors Related to the Failure of Venous Leg Ulcers to Heal With Compression Treatment,” J. Vasc. Surg., 49(5), pp. 1242–1247. [CrossRef] [PubMed]
Collins, L. , and Seraj, S. , 2010, “ Diagnosis and Treatment of Venous Ulcers,” Am. Fam. Physician, 81(8), pp. 989–996. https://www.aafp.org/afp/2010/0415/p989.html [PubMed]
Ontario, H. Q. , 2010, “ Endovascular Laser Therapy for Varicose Veins an Evidence-Based Analysis,” Ont. Health Technol. Assess Ser., 10(6), pp. 1–92. https://www.ncbi.nlm.nih.gov/pubmed/23074409
Herrman, E. C. , Knapp, C. F. , Donofrio, J. C. , and Salcido, R. , 1999, “ Skin Perfusion Responses to Surface Pressure-Induced Ischemia: Implication for the Developing Pressure Ulcer,” J. Rehabil. Res. Dev., 36(2), pp. 109–120. https://www.ncbi.nlm.nih.gov/pubmed/10661527 [PubMed]
Jan, Y. K. , Liao, F. , Rice, L. A. , and Woods, J. A. , 2013, “ Using Reactive Hyperemia to Assess the Efficacy of Local Cooling on Reducing Sacral Skin Ischemia Under Surface Pressure in People With Spinal Cord Injury: A Preliminary Report,” Arch. Phys. Med. Rehabil., 94(10), pp. 1982–1989. [CrossRef] [PubMed]
Rendell, M. S. , and Wells, J. M. , 1998, “ Ischemic and Pressure-Induced Hyperemia: A Comparison,” Arch. Phys. Med. Rehabil., 79, pp. 1451–1455. [CrossRef] [PubMed]
Mollison, H. L. , McKay, W. P. S. , Patel, R. H. , Kriegler, S. , and Negraeff, O. E. , 2006, “ Reactive Hyperemia Increases Forearm Vein Area,” Can. J. Anaesth., 53, pp. 759–763. [CrossRef] [PubMed]
Langemo, D. K. , 1999, “ Venous Ulcers: Etiology and Care of Patients Treated With Human Skin Equivalent Grafts,” J. Vasc. Nurs., 17(1), pp. 6–11. [CrossRef] [PubMed]
Mlacak, B. , Blinc, A. , Gale, N. , and Ivka, B. , 2005, “ Microcirculation Disturbances in Patients With Venous Ulcer before and after Healing as Assessed by Laser Doppler Flux-Metry,” Arch. Med. Res., 36(5), pp. 480–484. [CrossRef] [PubMed]
Heit, J. A. , Rooke, T. W. , Silverstein, M. D. , Mohr, D. N. , Lohse, C. M. , Petterson, T. M. , O'Fallon, W. , and Melton, J. , 2001, “ Trends in the Incidence of Venous Stasis Syndrome and Venous Ulcer: A 25-Year Population-Based Study,” J. Vasc. Surg., 33(5), pp. 1022–1027. [CrossRef] [PubMed]
Sagawa, K. , Lie, R. K. , and Schaefer, J. , 1990, “ Translation of Otto Frank's Paper ‘Die Grundform Des Arteriellen Pulses’ Zeitschrift Fur Biologie 37: 483–526 (1899),” J. Mol. Cell. Cardiol., 22(3), pp. 253–277. [CrossRef] [PubMed]
Westerhof, N. , Lankhaar, J. W. , and Westerhof, B. E. , 2009, “ The Arterial Windkessel,” Med. Biol. Eng. Comput., 47(2), pp. 131–141. [CrossRef] [PubMed]
Zheng, Y. , and Mayhew, J. , 2009, “ A Time-Invariant Visco-Elastic Windkessel Model Relating Blood Flow and Blood Volume,” Neuroimage, 47(4), pp. 1371–1380. [CrossRef] [PubMed]
Abdolrazaghi, M. , Navidbakhsh, M. , and Hassani, K. , 2010, “ Mathematical Modelling and Electrical Analog Equivalent of the Human Cardiovascular System,” Cardiovasc. Eng., 10(2), pp. 45–51. [CrossRef] [PubMed]
Segers, P. , Stergiopulos, N. , Verdonck, P. , and Verhoeven, R. , 1997, “ Assessment of Distributed Arterial Network Models,” Med. Biol. Eng. Comput., 35(6), pp. 729–736. [CrossRef] [PubMed]
Vo, T. V. , Hammer, P. E. , Hoimes, M. L. , Nadgir, S. , and Fantini, S. , 2007, “ Mathematical Model for the Hemodynamic Response to Venous Occlusion Measured With Near-Infrared Spectroscopy in the Human Forearm,” IEEE Trans. Biomed. Eng., 54(4), pp. 573–584. [CrossRef] [PubMed]
de Mul, F. F. M. , Morales, F. , Smit, A. J. , and Graaff, R. , 2005, “ A Model for Post-Occlusive Reactive Hyperemia as Measured With Laser-Doppler Perfusion Monitoring,” IEEE Trans. Biomed. Eng., 52(2), pp. 184–190. [CrossRef] [PubMed]
de Mul, F. F. M. , Blaauw, J. , Smit, R. J. , Rakhorst, G. , and Aarnoudse, J. G. , 2009, “ Time Development Models for Perfusion Provocations Studied With Laser-Doppler Flowmetry, Applied to Iontophoresis and PORH,” Microcirculation, 16(7), pp. 559–571. [CrossRef] [PubMed]
Humeau, M. , Saumet, J. , and L’huillier, J. , 2000, “ Simplified Model of Laser Doppler Signals During Reactive Hyperaemia,” Med. Biol. Eng. Comput., 38(1), pp. 80–87. [CrossRef] [PubMed]
Solovyev, A. , Mi, Q. , Tzen, Y. T. , Brienza, D. , and Vodovotz, Y. , 2013, “ Hybrid Equation/Agent-Based Model of Ischemia-Induced Hyperemia and Pressure Ulcer Formation Predicts Greater Propensity to Ulcerate in Subjects With Spinal Cord Injury,” PLoS Comput. Biol., 9(5), p. e1003070. [CrossRef] [PubMed]
Smye, S. , and Bloor, M. , 1990, “ A Single-Tube Mathematical Model of Reactive Hyperaemia,” Phys. Med. Biol., 35(1), pp. 103–113. [CrossRef] [PubMed]
Wilkin, J. K. , 1987, “ Cutaneous Reactive Hyperemia: Viscoelasticity Determines Response,” J. Invest. Dermatol., 89, pp. 197–200. https://www.ncbi.nlm.nih.gov/pubmed/2955056 [PubMed]
Grace, P. A. , 1994, “ Ischemia-Reperfusion Injury,” Br. J. Surg., 81(5), pp. 637–647. [CrossRef] [PubMed]
Mak, A. F. T. , Zhang, M. , and Tam, E. W. C. , 2010, “ Biomechanics of Pressure Ulcer in Body Tissues Interacting With External Forces During Locomotion,” Annu. Rev. Biomed. Eng., 12, pp. 29–53. [CrossRef] [PubMed]
Hagisawa, S. , Ferguson-Pell, M. , Cardi, M. , and Miller, D. , 1994, “ Assessment of Skin Blood Content and Oxygenation in Spinal Cord Injured Subjects During Reactive Hyperemia,” J. Rehabil. Res. Dev., 31(1), pp. 1–14. https://www.ncbi.nlm.nih.gov/pubmed/8035356 [PubMed]
Pan, W. , Drost, J. P. , Basson, M. D. , and Bush, T. R. , 2015, “ Skin Perfusion Responses Under Normal and Combined Loadings: Comparisons Between Legs With Venous Stasis Ulcers and Healthy Legs,” Clin. Biomech., 30(10), pp. 1218–1224. [CrossRef]
Manorama, A. , Meyer, R. , Wiseman, R. , and Bush, T. R. , 2013, “ Quantifying the Effects of External Shear Loads on Arterial and Venous Blood Flow: Implications for Pressure Ulcer Development,” Clin. Biomech., 28(5), pp. 574–578. [CrossRef]
Zhang, M. , and Roberts, V. C. , 1993, “ The Effect of Shear Forces Externally Applied to Skin Surface on Underlying Tissues,” J. Biomed. Eng., 15(6), pp. 451–456. [CrossRef] [PubMed]
Bennett, L. , Kavner, D. , Lee, B. K. , and Trainor, F. A. , 1979, “ Shear Vs Pressure as Causative Factors in Skin Blood Flow Occlusion,” Arch. Phys. Med. Rahbil., 60(7), pp. 309–314. https://www.ncbi.nlm.nih.gov/pubmed/454129
Burton, A. C. , 1972, Physiology and Biophysics of Circulation, Year Book Medical Publishers, Chicago, IL.
Cooney, D. O. , 1973, Biomedical Engineering Principles: An Introduction to Fluid, Heat, and Mass Transport Processes, M. Dekker, New York.
Ohm, G. S. , 1827, Die Galvanische Kette, Mathematisch, Bei T H Riemann, Berlin, pp. 1–244. [CrossRef]
Kutner, M. H. , Nachtsheim, C. J. , Neter, J. , and Li, W. , 2013, “ Analysis of Factor Level Means,” Applied Linear Statistics Model, 5th ed., McGraw-Hill Education, New York, pp. 733–774.
Sherratt, J. A. , and Dallon, J. C. , 2002, “ Theoretical Models of Wound Healing: Past Successes and Future Challenges,” C. R. Biol., 325(5), pp. 557–564. [CrossRef] [PubMed]
Geris, L. , Gerisch, A. , and Schugart, R. C. , 2010, “ Mathematical Modeling in Wound Healing, Bone Regeneration and Tissue Engineering,” Acta Biotheor., 58(4), pp. 355–367. [CrossRef] [PubMed]
Gefen, A. , 2009, Bioengineering Research of Chronic Wounds a Multidisciplinary Study Approach, Vol. 1, Springer, Berlin. [CrossRef]
Bennett, S. P. , Griffiths, G. D. , Schor, A. M. , Leese, G. P. , and Schor, S. L. , 2003, “ Growth Factors in the Treatment of Diabetic Foot Ulcers,” Br. J. Surg., 90(2), pp. 133–146. [CrossRef] [PubMed]
Casavola, C. , Paunescu, L. A. , Fantini, S. , and Gratton, E. , 2000, “ Blood Flow and Oxygen Consumption With Near-Infrared Spectroscopy and Venous Occlusion: Spatial Maps and the Effect of Time and Pressure of Inflation,” J. Biomed. Opt., 5(3), pp. 269–276. [CrossRef] [PubMed]
Suehiro, K. , Morikage, N. , Murakami, M. , Yamashita, O. , Ueda, K. , Samura, M. , and Hamano, K. , 2014, “ A Study of Leg Edema in Immobile Patients,” Circ. J., 78(7), pp. 1733–1739. [CrossRef] [PubMed]
Gelman, S. , 2008, “ Venous Function and Central Venous Pressure,” Am. Soc. Anestesiol, 108(4), pp. 735–748 [CrossRef]
Goldoozian, L. S. , and Zahedi, E. , 2011, “ Electrical Analog Model of Arterial Compliance During Reactive Hyperemia,” First Middle East Conference on Biomedical Engineering (MECBME), Sharjah, United Arab Emirates, Feb. 21–24, pp. 49–53.


Grahic Jump Location
Fig. 1

Leg perfusion test setup (a) front view of the test setup with perfusion sensor attached to the participant's lateral lower calf, the customized load applicator can slide in the medial/lateral and vertical directions to apply normal and shear loadings, respectively; (b) noninvasive perfusion sensor attached to the skin; (c) load applicator with the contact platform [34]. (a) Front view of the test, (b) sensor attachment, and (c) load applicator.

Grahic Jump Location
Fig. 2

A typical last Doppler output of perfusion during testing in which the (1) baseline period is prior to loading, (2) the ischemia period is under loading, and (3) the reperfusion is the blood flow recovery after loading. Two loading conditions occurred during one testing with similar LDPM output. This figure represents one loading scenario. The reactive hyperemia is the spike in the blood flow upon the release of the loading. PU refers to perfusion unit, which is defined as the relative number and velocity of blood cells in the tissue (Perimed).

Grahic Jump Location
Fig. 3

Model to simulate the blood flow of the lower leg under external loadings. R1 and R2 are global and local vessel resistances, respectively, C is the local vessel compliance, V0 is the hydrostatic pressure at the testing site, and Vext is the pressure induced by locally applied external loadings.

Grahic Jump Location
Fig. 4

Vext as a rectangular wave function

Grahic Jump Location
Fig. 5

Flowchart for simulation and RCR iteration process

Grahic Jump Location
Fig. 6

Comparison between the model output (smooth line, or red if in color) and experimental data (wavy line, or blue if in color). Left (a): operator 1, R1 = 12, R2 = 2.5, C = 2, NRMSE = 6.0%; Right (b): operator 2, R1=10, R2=3, C = 2, NRMSE = 6.4%.

Grahic Jump Location
Fig. 7

Comparison R1, R2, C between wounded, nonwounded, and healthy legs from operator 1 (left) and operator 2 (right) (* indicates statistical significant difference, p < 0.05)



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In