Modeling the inflammatory-cardiovascular response during

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