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Kristen Windoloski & Mette OlufsenNorth Carolina State University
Collaborator: Ronan BergRigshospitalet, Copenhagen, Denmark
June 2021
Modeling the inflammatory-cardiovascular response during sepsis
Sepsis Background
Bacteria enters the body and causes an infection
The infection spreads and enters the bloodstream, allowing it to travel to different parts of the body
Uncontrolled inflammation can result in major organ dysfunction and even death
Immune cells and cytokines work to fight the infection throughout the body, leading to unregulated inflammation
Neurological System
Respiratory System
Hematological System
Cardiovascular System
Renal System
Hepatic System
Macrophages
Granulocyte
Fibroblast
Endothelial Cells
Mast Cell
Lymphocyte
Sepsis Symptoms
Low blood pressure
High heart rate
𝑑𝐸𝑑𝑡 = −𝑘'𝐸
𝑑𝑀)
𝑑𝑡 = 𝐾+)𝑀) 1 −𝑀)
𝑀-− 𝐻+/ 𝐸 𝑘+ + 𝑘+123𝐻+/ 𝑇𝑁𝐹 𝐻+7 𝐼𝐿10 𝑀)
𝑑𝑀;𝑑𝑡
= 𝐻+/ 𝐸 𝑘+ + 𝑘+123𝐻+/ 𝑇𝑁𝐹 𝐻+7 𝐼𝐿10 𝑀) − 𝐾+;𝑀;
𝑑𝑇𝑁𝐹𝑑𝑡
= 𝑘123+𝐻1237 𝐼𝐿6 𝐻1237 𝐼𝐿10 𝑀; − 𝑘123 𝑇𝑁𝐹 − 𝑤123
𝑑𝐼𝐿6𝑑𝑡
= 𝑘>+ + 𝑘>123𝐻?@>/ 𝑇𝑁𝐹 𝐻?@>7 𝐼𝐿6 𝐻?@>7 𝐼𝐿10 𝑀; − 𝑘> 𝐼𝐿6 − 𝑤?@>
𝑑𝐼𝐿8𝑑𝑡 = 𝑘B+ + 𝑘B123𝐻?@B/ 𝑇𝑁𝐹 𝐻?@B7 𝐼𝐿10 𝑀; − 𝑘B 𝐼𝐿8 − 𝑤?@B
𝑑𝐼𝐿10𝑑𝑡
= 𝑘CD+ + 𝑘CD>𝐻?@CD/ 𝐼𝐿6 𝑀; − 𝑘CD 𝐼𝐿10 − 𝑤?@CD
Bolus Dose Inflammation Model
Monocytes
Cytokines
Endotoxin
E1EF= C
GH(−𝑇 + 𝑇J + 𝑘1 𝑇+ − 𝑇J (𝑘123𝐻/ TNF − 𝑞123 + 𝑘1>𝐻/ IL6 − 𝑞?@> )−𝑘1CD(1 − 𝐻7 IL10 − 𝑞?@CD )Temperature
𝑑𝑃1𝑑𝑡 = −𝑘S1S 𝐸 𝑃1 + 𝑘S1 𝑃1,+ − 𝑃1Pain
𝑑𝑁𝑑𝑡
=𝑘2+𝑀;)TNF(t − κ WX,YZ[
)TNF(t − κ WX,YZ[ + 𝜂2,]^_WX,YZ[
𝜂2CDWXH`
)IL10(t − κ WXH` + 𝜂2CDWXH`
− 𝑘2𝑁Nitric Oxide
Blood Flow & Volume
𝑄 ≈ 𝐻𝑉dFe = 𝐻(𝑉f7 − 𝑉fg)
𝑑𝑉h𝑑𝑡 = 𝑞hi − 𝑞jkF
𝑞h=𝑝jkF − 𝑝hi
𝑅h
Peripheral Vascular Resistance & Heart Rate
𝑑𝑅d𝑑𝑡
= 𝑘)S1𝛤o
𝛤o + 𝜂o)S1− 𝑘)2𝑁 − 𝑘) 𝑅d − 𝑅p , 𝛤 =
𝑑𝑃1𝑑𝑡
𝑑𝐻𝑑𝑡
=−𝐻 + 𝑘q 𝐻+ − 𝐻p 𝐻q/ 𝑇 − 𝑇p 𝑓 𝐵𝑃, 𝐵𝑃p + 𝐻p
𝜏o
Cardiovascular-Pain-Thermal Model
Inflammatory-Cardiovascular-Pain-Thermal Model
Mean Bolus Data & Model
Source: Dobreva, A., Brady-Nicholls, R., Larripa, K., Puelz, C., Mehlsen, J., & Olufsen, M. S. (2021). A physiological model of the inflammatory-thermal-pain-cardiovascular interactions during an endotoxin challenge. The Journal of Physiology, 599(5), 1459-1485.
Patient Specific Bolus Data & Model
0
400
800
TNF-
(p
g/m
L)
0
500
1000
1500
IL-6
(pg/
mL)
Time (hr)
36
38
40
Tem
p (o
C)
Time (hr)
840
880
920
PP
T (k
Pa)
Time (hr)
115
120
125
130
BP (m
mH
g)
0
40
80
0
200
400
0
20
40
0
400
800
37
38
39
40
600
700
800
110
120
130
60
80
100
0
20
40
60
IL-1
0 (p
g/m
L)
Time (hr)
60
80
100
HR
(bpm
)
200
600
1000
IL-8
(pg/
mL)
0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8
0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8
A
B
Patient 6
Patient 19
Time (hr) Time (hr) Time (hr)0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8
Time (hr)
TNF-
(p
g/m
L)Te
mp
(o C
)
IL-6
(pg/
mL)
PP
T (k
Pa)
BP (m
mH
g)IL
-10
(pg/
mL)
HR
(bpm
)IL
-8 (p
g/m
L)
R = 0.962
R = 0.972 R = 1.002
R = 0.992 R = 0.802
R = 0.832 R = 0.932
R = 0.932
R = 0.972
R = 0.962 R = 1.002
R = 0.862 R = 0.902
R = 0.902 R = 0.972
R = 0.972
a
a
R = 0.842
R = 0.792 R = 0.972
R = 0.982 R = 0.882
R = 0.882 R = 0.952
R = 0.942
R = 0.922
R = 0.952 R = 0.892
R = 0.902 R = 0.892
R = 0.902 R = 0.822
R = 0.832
0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8
Source: Dobreva, A., Brady-Nicholls, R., Larripa, K., Puelz, C., Mehlsen, J., & Olufsen, M. S. (2021). A physiological model of the inflammatory-thermal-pain-cardiovascular interactions during an endotoxin challenge. The Journal of Physiology, 599(5), 1459-1485.
18 patient-specific parameters
12 patient specific parameters, and 6 population parameters
𝑑𝐸𝑑𝑡 = −𝑘'𝐸
𝑑𝐸𝑑𝑡
=𝐿𝑃𝑆1
𝑡fiE − 𝑡gFveF− 𝑘'𝐸 if 𝑡 ≤ 𝑡fiE
−𝑘'𝐸 if 𝑡 > 𝑡fiE
where
𝑡gFveF = infusion start time
𝑡fiE = infusion end time
𝐿𝑃𝑆1 = total dose ng/kg
Transition from Bolus to Continuous Dose
Continuous Infusion Inflammation Model
= Bolus= Continuous= Optimized
Volunteer 7
Begin with bolus dose inflammation model
Adapt bolus dose inflammation model to become a continuous dose inflammation model
Investigate the transition from 1) recovery to chronic inflammation2) chronic inflammation to sepsis
Investigate immune response to continuous infusion
Connect continuous dose inflammation model to cardiovascular model
Estimate cardiac biomarkers and study sepsis treatments
Current & Future Work
References & Acknowledgments
Funding: The National Science Foundation NSF/DMS(RTG) #1246991
Image References:1. https://wp.math.ncsu.edu/cdg/2. https://www.rigshospitalet.dk/english/Pages/default.aspx3. https://en.wikipedia.org/wiki/North_Carolina_State_University4. https://online.seterra.com/en-an/vgp/38015. http://www.iemoji.com/view/emoji/2742/objects/microbe6. https://patientsafetymovement.org/blog/uci-health-spotlight-on-central-line-
associated-bloodstream-infections/7. https://www.nature.com/articles/s41581-018-0005-
7?WT.feed_name=subjects_acute-kidney-injury8. https://www.news-medical.net/health/What-are-Cytokines.aspx9. https://www.worldsepsisday.org/sepsis10. https://www.health.harvard.edu/blog/increase-in-resting-heart-rate-is-a-signal-
worth-watching-20111221401311. https://time.com/4630345/systolic-blood-pressure-hypertension/12. https://www.boundtree.com/IV-Drug-Delivery/Syringes/Syringes-with-Needle-
Luer-lock-Tip-3cc/p/group00261413. https://www.ocrevus.com/patient/infusion-experience.html14. https://en.wikipedia.org/wiki/National_Science_Foundation
Publications:1. A Dobreva, R Brady-Nicholls, K Larripa, C Puelz, J Mehlsen,
MS Olufsen (2021). A physiological model of the inflammatory-thermal-pain-cardiovascular interactions during an endotoxin challenge. J Physiol,
2. R Brady, DO Frank-Ito, HT Tran, S Janum, SB Pedersen, JT Ottesen, J Mehlsen, MS Olufsen (2018.) Mathematical modeling of endotoxin-induced inflammatory response in young men. Math Modeling Natural Phenomena