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Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 1 / 33
Modeling interaction between micro-climatefactors and moisture-related skin-supportfriction during patient repositioning in bedDelft University of Technology
Thyrza Jagt 1509489
April 9, 2015
Table of Contents
1 Topic and goal
2 The problem
3 Solution Method
4 The Model
5 Results
6 Conclusions
7 Sources
Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 2 / 33
Topic and Goal
Risk of pressure ulcers
• Bedbound patients
• Repositioning in bed
• Effects of microclimate factors
Goal
To create a combined model from two models created by Amit Gefen,in which a patients risk of pressure ulcers can be assessed whenconsidering not only the contact between the body and the bed, butalso including the effects of microclimate factors.
Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 3 / 33
Pressure Ulcers (a.k.a. bedsores or pressuresores)
European Pressure Ulcer Advisory Panel: EPUAP
”A pressure ulcer is localized injury to the skin and/orunderlying tissue usually over a bony prominence, as a resultof pressure, or pressure in combination with shear. Anumber of contributing or confounding factors are alsoassociated with pressure ulcers; the significance of thesefactors is yet to be elucidated.” – http://www.epuap.org
Can occur after application of
• a large pressure for a short period of time,
• or a small pressure for a long period of time.
Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 4 / 33
The basis
1 ”Modeling the effects of moisture-related skin-support friction onthe risk for superficial pressure ulcers during patient repositioningin bed” by Eliav Shaked and Amit Gefen [4]
2 ”How do microclimate factors affect the risk for superficialpressure ulcers: A mathematical modeling study” by AmitGefen [2]
Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 5 / 33
Modeling the effects of moisture-relatedskin-support friction on the risk for superficialpressure ulcers during patient repositioning inbed
Figure: Source: [4].
• Body exists of skin andsubcutaneous tissue
• Body comes into contact withthe bed
• Body is repositioned: movedacross the bed
Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 6 / 33
How do microclimate factors affect the risk forsuperficial pressure ulcers: A mathematicalmodeling study
∆V (t)
V=
[α
Ta − 30 C
Tmaxa − Tmin
s
− βTa − Ts
Tmaxa − Tmin
s
(1 − RH) − γ
]·t
µ = 0.5∆V (t)
V+ 0.4
τ =
(0.5
∆V (t)
V+ 0.4
)· P
τ sw =
(1− 0.8
∆V (t)
V
)τ s0
• Patient produces sweat• Dependent on ambient
and skin temperature
• Coefficient of frictionchanges due to sweatproduction
• Stress levels increase
• Strength of the skindecreases due to sweatproduction
Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 7 / 33
How do microclimate factors affect the risk forsuperficial pressure ulcers: A mathematicalmodeling study
∆V (t)
V=
[α
Ta − 30 C
Tmaxa − Tmin
s
− βTa − Ts
Tmaxa − Tmin
s
(1 − RH) − γ
]·t
µ = 0.5∆V (t)
V+ 0.4
τ =
(0.5
∆V (t)
V+ 0.4
)· P
τ sw =
(1− 0.8
∆V (t)
V
)τ s0
• Patient produces sweat• Dependent on ambient
and skin temperature
• Coefficient of frictionchanges due to sweatproduction
• Stress levels increase
• Strength of the skindecreases due to sweatproduction
Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 7 / 33
How do microclimate factors affect the risk forsuperficial pressure ulcers: A mathematicalmodeling study
∆V (t)
V=
[α
Ta − 30 C
Tmaxa − Tmin
s
− βTa − Ts
Tmaxa − Tmin
s
(1 − RH) − γ
]·t
µ = 0.5∆V (t)
V+ 0.4
τ =
(0.5
∆V (t)
V+ 0.4
)· P
τ sw =
(1− 0.8
∆V (t)
V
)τ s0
• Patient produces sweat• Dependent on ambient
and skin temperature
• Coefficient of frictionchanges due to sweatproduction
• Stress levels increase
• Strength of the skindecreases due to sweatproduction
Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 7 / 33
How do microclimate factors affect the risk forsuperficial pressure ulcers: A mathematicalmodeling study
∆V (t)
V=
[α
Ta − 30 C
Tmaxa − Tmin
s
− βTa − Ts
Tmaxa − Tmin
s
(1 − RH) − γ
]·t
µ = 0.5∆V (t)
V+ 0.4
τ =
(0.5
∆V (t)
V+ 0.4
)· P
τ sw =
(1− 0.8
∆V (t)
V
)τ s0
• Patient produces sweat• Dependent on ambient
and skin temperature
• Coefficient of frictionchanges due to sweatproduction
• Stress levels increase
• Strength of the skindecreases due to sweatproduction
Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 7 / 33
How do microclimate factors affect the risk forsuperficial pressure ulcers: A mathematicalmodeling study
Figure: Skin fails when stress exceeds strength. Source: [2].
Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 8 / 33
The difficulties of the problem
Patient lies in a bed:
• Body is in contact with the bed
• Both the body and the mattress will deform due to the contact
Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 9 / 33
Deformation
Figure: Many quantities change in thedeformation of a body. Source: [1].
• Two configurations:reference and current.
• Need different notation forboth configurations.
Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 10 / 33
Contact
1 Contact area is unknown, only conditions are known:
• Gap function g(X, t) = −v(ϕ
(1)t (X)−ϕ
(2)t (Y(X))
)≤ 0.
• Contact pressure tN ≥ 0.• tNg = 0.
2 Friction is present: frictional traction force tT ≤ µtN .
Figure: The two body contact problem. Source: [3].
Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 11 / 33
Complete problem
Searching for an equilibrium configuration ϕ→ virtual work should be zero for each body i .
δW (i)(ϕ(i),ω(i)) =
∫Ω(i)
∇ω(i) : P(i) dΩ︸ ︷︷ ︸Internal stresses
−∫
Ω(i)
ω(i) · B(i) dΩ︸ ︷︷ ︸Body forces
−∫
Γ(i)σ
ω(i) · T(i) dΓ︸ ︷︷ ︸External surface forces
−∫
Γ(i)c
ω(i) · T(i) dΓ︸ ︷︷ ︸Contact tractions
= 0
Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 12 / 33
Complete problem
δW (i)(ϕ(i),ω
(i)) =
∫Ω(i)
∇ω(i) : P(i)dΩ−
∫Ω(i)
ω(i) ·B(i)dΩ−
∫Γ
(i)σ
ω(i) ·T(i)dΓ−
∫Γ
(i)c
ω(i) ·T(i)dΓ = 0
The summation of the virtual work over the two bodies should be zero.
δW (ϕ,ω) :=2∑
i=1
δW (i)(ϕ(i),ω
(i))
=2∑
i=1
∫Ω(i)
∇ω(i) : P(i) dΩ −
∫Ω(i)
ω(i) · B(i) dΩ −
∫Γ
(i)σ
ω(i) · T(i) dΓ
︸ ︷︷ ︸
δWint,ext (ϕ,ω)
−2∑
i=1
∫Γ
(i)c
ω(i) · T(i) dΓ
︸ ︷︷ ︸δWc (ϕ,ω)
= 0.
Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 13 / 33
Solution Method
Newton-Raphson Method
Figure: The Newton-Raphsonmethod for aone-degree-of-freedomproblem. Source: [3].
Solving f (x) = 0.
• Iterative method
• Initial guess x0
• Update the guess
Solving δW (ϕ,ω) = 0.
• SolveδW (ϕk ,ω) = −DδW (ϕk ,ω)[u],with
• ϕk+1 = ϕk + u.
Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 14 / 33
Finite Element Method
• Divide the volumes into elements.
• Solve the problem as a summation over the elements instead ofan integral over the volume.
Figure: Discretization of the volume. Source: [1].
Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 15 / 33
The basic model
• Body exists ofsubcutaneous tissue andskin
• Two steps:
1 Body moves downwardstowards the bed
2 Body is repositioned;moved across the bed
Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 16 / 33
Including Micro-Climate factors
While the body is at rest the effects of the microclimate factors areapplied
• Perspiration is accumulated
• The coefficient of friction changes as an effect of the productionof perspiration.
time (s)0 0.5 1 1.5 2 2.5 3
0
0.2
0.4
0.6
0.8
1The accumulation of perspiration
Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 17 / 33
Including Micro-Climate factors
While the body is at rest the effects of the microclimate factors areapplied
• Perspiration is accumulated
• The coefficient of friction changes as an effect of the productionof perspiration.
time (s)0 0.5 1 1.5 2 2.5 3
CO
F
0.4
0.5
0.6
0.7
0.8
0.9The COF against the time
Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 17 / 33
Further improvements
• The Young’s modulus (stiffness) of the skin changes
• Additional weight is added
• A different value of the skin temperature is used
time (s)0 0.5 1 1.5 2 2.5 3
You
ngs
mod
ulus
(kP
a)
0
20
40
60
80
100The Youngs modulus against the time
Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 18 / 33
Further improvements
• The Young’s modulus (stiffness) of the skin changes
• Additional weight is added
• A different value of the skin temperature is used
→
Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 18 / 33
Further improvements
• The Young’s modulus (stiffness) of the skin changes
• Additional weight is added
• A different value of the skin temperature is used
time (s)0 0.5 1 1.5 2 2.5 3
0
0.2
0.4
0.6
0.8
1The accumulation of perspiration
Ts =30
Ts =35
Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 18 / 33
Further improvements
• The Young’s modulus (stiffness) of the skin changes
• Additional weight is added
• A different value of the skin temperature is used
Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 18 / 33
Further improvements
• The Young’s modulus (stiffness) of the skin changes
• Additional weight is added
• A different value of the skin temperature is used
Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 18 / 33
The final model
• Body exists of only skin
• Three steps:
1 Body is subject to gravityand hence movesdownwards
2 The body is at rest andthe effects of themicroclimate factors areapplied
3 Body is moved across thebed
Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 19 / 33
Results
Skin breakdown: skin ’fails’ if stress exceeds strength
• Look at the strength of the skin
• Look at the stress levels of the skin
Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 20 / 33
Results basic model
The Basic model
Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 21 / 33
Results basic model
The maximum, minimum and average stress
Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 22 / 33
Results basic model
The stress compared to the strength
Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 23 / 33
Results model with microclimate factors
The Microclimate model
Coefficient of friction is time dependent
Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 24 / 33
Results microclimate model
The maximum, minimum and average stress
Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 25 / 33
Results microclimate model
The stress compared to the strength
Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 26 / 33
Results changing stiffness
Changing the stiffness
Both the COF and the stiffness of the skin change in time.
Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 27 / 33
Results changing stiffness
The movement in the z-direction
Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 28 / 33
Results changing stiffness
The maximum, minimum and average stress
Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 29 / 33
Overall Results
The stress levels of the different models
Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 30 / 33
Conclusions
• The two models are combined : a model now exists including theeffect of the microclimate factors
• Stress increases:• Microclimate factors (changing friction)• Changing stiffness• Adding of weight• Increasing skin temperature
• No skin failure is noted
• Improvements are still necessary
Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 31 / 33
Remarks and Recommendations
• The model should be increased.
• The geometry of human body should be improved.
• It should be noted that the different body parts of the patient areconnected.
• Constants such as the temperature should be time-dependent.
• More timesteps could be added to see what happens when thepatient is at rest for a longer period of time.
• More realistic values for the changing stiffness should be used.
Once improved the model can be used for special cases.
• An unresponsive patient lies on top of a tube.
• A patient whose head or legs need to be elevated.
Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 32 / 33
Sources
[1] Javier Bonet and Richard D. Wood. Nonlinear Continuum Mechanics for Finite Element Analysis. CambridgeUniversity Press, Cambridge, United Kingdom, 1997.
[2] Amit Gefen. How do microclimate factors affect the risk for superficial pressure ulcers: A mathematical modelingstudy. Journal of tissueviability, 20:81–88, 2011.
[3] Tod A. Laursen. Computational Contact and Impact Mechanics. Springer, Durham,USA, 2002.
[4] Eliav Shaked and Amit Gefen. Modeling the effects of moisture-related skin-support friction on the risk forsuperficial pressure ulcers during patient repositioning in bed. frontiers in bioengineering and biotechnology, 1, 2013.
Thyrza Jagt 1509489 (TU Delft) Modeling the risk at Pressure Ulcers April 9, 2015 33 / 33