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Methods

Using the Drake-Laine and Starling-Landis equations [2], a system of equations was created that can be algebraically solved for and used to model the lymphatics system and its response to subatmospheric pressure from NPWT. In this model it is assumed that the patient has no underlying health issues [9] and that flow into the interstitium is equal to flow out.

Discussion

-Limitations: conservation of mass in terms of flow into and out of the interstitium; Pout must be a value within the range 25-200 mmHg; values for a, Pcap, Psv, Pout, and 𝜋cap are assumed to be constant

-Relevance and Future Studies: This model characterizes the relationship between VAC therapy and lymphatic behavior, something that hasn’t been attempted before. It’s intended uses include: the population optimization of VAC therapy, the study of the physiological effects of VAC therapy, comparison between the efficiency of VAC therapy amongst different wound types, and the production of exclusion criteria for large scale random trials, all areas of study that have not been focused on in previously done clinical trials [1, 4, 6, 7, 8, 12, 13, 14, 15].

The diagram above shows a simplified version of the model that uses Drake-Lane and Starling-Landis equations to relate membrane permeability, flows, and pressures to determine how Negative Pressure Wound Therapy (NPWT) treatment affects lymphatic regeneration and general wound healing.

Negative Pressure Wound Therapy’s Effect on the Lymphatic System

Rosemary H. Garrett, Amanda Benavides, Kimberly A. Chancellor, Kassandra L. Elizondo, Hannah N. Nicosia, and Christopher M. Quick

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Introduction

  • Medical vacuum uses negative pressure to promote wound healing
  • Fluid/macromolecule transport in lymphatics in relation to a medical vacuum has yet to be studied
  • Current research is more focused on optimizing the materials used to increase area of wound affected through microdeformations
  • No mathematical model currently exists for the vacuum-lymphatic interaction
  • The purpose of the present work is to develop a model of VAC device-tissue interaction to derive general algebraic formulas for flow into and out of interstitium and flow into the VAC device in terms of the mechanical properties of the system characterizing the device and tissue.

Mathematical Equations and Variables

Capillary Filtration constant

Kfc

Interstitial osmotic pressure

𝝅int

Interstitial Filtration Constant

Kfint

Capillary Pressure

Pcap

Resistance of Lymphatics

RL

Interstitial pressure/ hydrostatic pressure difference

Pint

Pump Pressure

PP

Capillary Osmotic Pressure

𝝿cap

Negative Pressure applied to system by Wound VAC

Pout

Osmotic Pressure of Wound VAC

𝝿out

Capillary Reflection coefficient

𝝈cap

Interstitial Reflection coefficient

𝝈int

Systemic Venous Pressure

Psv

Initial Volume

V0

Interstitial compliance

Cint

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Fmf = Kfc(Pcap - Pint - σcap(πcap - πint))

This equation calculates the microvascular filtration from the capillaries to the interstitium

Fout = Kfint(Pint - Pout - σint(πint - πout))

Calculates the flow of fluid out of the system into the VAC

FL = (Pint - Psv + PP)/RL

Calculates flow from the interstitium into the systemic veins. Expressed by Drake-Laine

Fmf = FL + Fout

Conservation of mass

Vint = V0 + Cint ∙ Pint

Calculates the initial volume of the interstitium

Fig.2 depicts a graph of Pout vs Flow Out showing that the less negative the pressure out becomes, less flow out is occuring.

Pressure Out (mmHg)

Flow Out (mL/min)

Fig 2.

Jsmf == Fmf (1 - \[Sigma]cap) \[Pi]cap/a +

PScap (\[Pi]cap - \[Pi]int)/a

Calculates the protein flow with microvascular filtration

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Jsout == Fout (1 - \[Sigma]out) \[Pi]int/a +

PSint (\[Pi]int - ((1 - \[Sigma]out)*\[Pi]int))/a

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References

[1]Babic S, Tanaskovic S, Lozuk B, Samardzic D, Popov P, Gajin P, Matic P, Maric V, Radak D. Treatment of stump complications after above-knee amputation using negative-pressure wound therapy. Srpski arhiv za celokupno lekarstvo 144: 503–506, 2016.

[2]Dongaonkar RM, Laine GA, Stewart RH, Quick CM. Balance point characterization of interstitial fluid volume regulation. American Journal of Physiology-Regulatory, Integrative and Comparative Physiology297, 2009.

[3]Jacobs S, Simhaee DA, Marsano A, Fomovsky GM, Niedt G, Wu JK. Efficacy and mechanisms of vacuum-assisted closure (VAC) therapy in promoting wound healing: a rodent model. Journal of Plastic, Reconstructive & Aesthetic Surgery 62: 1331–1338, 2009.

[4] Kamamoto F, Lima A, Rezende M, Mattar-Junior R, Leonhardt M, Kojima K, Santos C. A new low-cost negative-pressure wound therapy versus a commercially available therapy device widely used to treat complex traumatic injuries: a prospective, randomized, non-inferiority trial. Clinics72: 737–742, 2017

[6] Laimer J, Steinmassl O, Hechenberger M, Rasse M, Pikula R, Bruckmoser E. Intraoral Vacuum-Assisted Closure Therapy—A Pilot Study in Medication-Related Osteonecrosis of the Jaw. Journal of Oral and Maxillofacial Surgery 75: 2154–2161, 2017.

[7]Leclercq A, Labeille B, Perrot J-L, Vercherin P, Cambazard F. Skin graft secured by VAC (vacuum-assisted closure) therapy in chronic leg ulcers: A controlled randomized study. Annales de Dermatologie et de Vénéréologie 143: 3–8, 2016.

[8] Liu, Zhenmi, Jo C. Dumville, Robert Hinchliffe, Nicky Cullum, Nicky Stubbs, Michael Sweeting, and Frank Peinemann. "Negative Pressure Wound Therapy for Treating Foot Wounds in People with Diabetes Mellitus." Health Education Research. August 31, 2018. Accessed November 30, 2018. https://research-information.bristol.ac.uk/en/publications/negative-pressure-wound-therapy-for-treating-foot-wounds-in-people-with-diabetes-mellitus(2e72273f-2d22-446b-a4fd-3a38b26f3d5f).html.

[9]Mendez-Eastman S. Guidelines for Using Negative Pressure Wound Therapy. Advances in Skin & Wound Care14: 314–323, 2001.

[12]Saxena, V., Hwang, C. W., Huang, S., Eichbaum, Q., Ingber, D., and Orgill, D. P., 2004, “Vacuum-Assisted Closure: Microdeformations of Wounds and Cell Proliferation,� Plast. Reconstr. Surg., 1145, pp. 1086–1096.

[13]Uğurlar M, Sönmez MM, Armağan R, Eren OT. Comparison of two different vacuum-assisted closure (VAC) treatments of multiple chronic diabetic foot wounds in the same extremity. Foot and Ankle Surgery 23: 173–178, 2017.

[14]Wilkes R, Zhao Y, Kieswetter K, Haridas B. Effects of Dressing Type on 3D Tissue Microdeformations During Negative Pressure Wound Therapy: A Computational Study [Online]. Journal of Biomechanical Engineering American Society of Mechanical Engineers: 2009. http://biomechanical.asmedigitalcollection.asme.org/article.aspx?articleid=1475658 [31 Oct. 2018].

[15]Zhou Z-Y, Liu Y-K, Chen H-L, Liu F. Prevention of Surgical Site Infection After Ankle Surgery Using Vacuum-Assisted Closure Therapy in High-Risk Patients With Diabetes. The Journal of Foot and Ankle Surgery 55: 129–131, 2016.

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Pcap

𝞹cap

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