Chemical Power for Microscopic Robots in Capillaries

1. Chemical Power for Microscopic Robots in Capillaries Tad Hogg Institute for Molecular Manufacturing with Robert A. Freitas Jr. preprint: http://arxiv.org/abs/0906.5022

2. Sensors for Medicine and Science (SMSI) implantable glucose monitor Given Imaging’s PillCam photos inside GI tract Aarhus University targeting drugs to cells microscopic robots for medicine • extending today’s implanted devices • to much smaller sizes • enhancing today’s in vivo nanoparticles • with computation & communication

3. challenges formicroscopic robots • fabricate • control • power • identify applications

4. power • short operation: • fuel inside robots • extended operation: • power from environment, e.g., • acoustics (ultrasound) • chemical fuels from environment see R. Freitas, Nanomedicine Vol. I, chap. 6, 1999

5. example: glucose + oxygen C6H12O6 + 6O2 6CO2 + 6H2O energy released: 4x10-18 Joule per reaction e.g,: react a million O2/second = about a pico watt

6. How much power can glucose + oxygen provide?

7. Is power generation safe for nearby tissue?

8. method • pick medical application context • identify key constraints on power • evaluate quantitatively

9. application: robots in bloodstream • useful for diagnosis and treatment • devices pass near cells throughout body • examples • passive motion with fluid • active motion • self-assembled groups on vessel wall • for long term monitoring

10. glucose and oxygen in blood • blood plasma • glucose concentration ~100x that of oxygen • hence: oxygen is rate-limiting chemical • most oxygen carried in red cells • bound to hemoglobin • ~100x higher concentration than in plasma

11. chemical power in capillaries • modeling chemical transport • results • robot power • effect on surrounding tissue

12. modeling challenges • complex geometry • distorting cells • kinetics of oxygen release from cells

13. geometry • simplify to axial symmetric • vessel, robots and tissue

14. Krogh cylinder model tissue cylinder capillary venous end flow arterial end A. Krogh, J. of Physiology 52:409 (1919)

15. numerical model domain 100μm capillary radius 4 μm 40 μm model a portion of ~1mm capillary length

16. robots inside vessel 10μm 8μm static robot scenario: robots attached to wall fluid moves past the robots example robot group: each robot about 1μm3 20 robots in each ring 10 rings group of 200 robots

17. modeling challenges • complex geometry • distorting cells • kinetics of oxygen release from cells

18. cells distort to go through capillaries “single file” cell maintains volume and surface area as it distorts typical values: surface area 135 μm2 volume 90 μm3

19. approximation for cell distortion group of robots vessel wall plasma gap direction of flow vessel wall distorted cells based on Secomb et al., American J. of Physiology: Heart and Circulatory Physiology 281:H629 (2001) instead of modeling individual cells, use “smeared out” average fluid with mix of cells and plasma

20. modeling challenges • complex geometry • distorting cells • kinetics of oxygen release from cells

21. oxygen transport oxygen diffuses out of cell into plasma from plasma into tissue O2 cell O2 flow diffusion: from higher to lower concentrations hence cell still has substantial oxygen at end of vessel

22. cell oxygen release & robots • robots have high power densities • larger concentration gradients than tissue • cells may pass before releasing oxygen • model must include kinetics

23. cell oxygen release kinetics • depends on • concentration in surrounding plasma • amount of oxygen bound within cell • approximate model Clark et al., Biophysical Journal 47:171 (1985)

24. numerical model • fluid flow • oxygen transport • from cells • diffusion in plasma and tissue • power generation • in robots and tissue • Michaelis-Menten kinetics • heating • conduction and convection

25. chemical power in capillaries • modeling chemical transport • results • robot power • effect on surrounding tissue

26. scenarios • low demand • resting tissue • slow flow • avg. speed 0.2mm/s • high demand • active tissue • fast flow • avg. speed 1mm/s typical situation for nanomedicine

27. oxygen transport to robots and tissue

28. section through vessel and tissue tissue vessel wall flow streamlines of fluid flow tissue distance (μm)

29. low demand scenario

30. no robots (1022 molecule/m3 ) flow distance (μm)

31. 10-micron group (1022 molecule/m3 ) flow distance (μm)

32. high demand scenario

33. no robots (1022 molecule/m3 ) flow distance (μm)

34. 10-micron group (1022 molecule/m3 ) flow distance (μm)

35. power for the robots

36. power comparisons • robots ~10s of pW • cells use 10-1000pW • cell size ~10mm • i.e., ~103 x robot volume • person at rest uses ~100 watts

37. What can a picowatt do? • compute: ~105 logic operations/sec • near-term molecular electronics • 103 kT/operation • communicate: ~104 bits/sec over 100mm • with ultrasound • move: ~1mm/sec through water • overcoming viscous drag see R. Freitas, Nanomedicine Vol. I, chap. 6, 1999 www.nanomedicine.com

38. effects on nearby tissue

39. effects of robots • less oxygen for tissues • local heating • waste products • forces on vessel wall • …

40. oxygen for tissue • robots • compete with tissue for oxygen • block diffusion out of vessel • is this a problem for nearby tissue?

41. (1022 molecule/m3 ) examine tissue power next to vessel wall flow distance (μm)

42. power drop ~ 10% power in tissue next to vessel flow compare no robots 10-micron group power decrease much less than oxygen concentration decrease due to Michaelis-Menten kinetics parameters in tissue (oxygen must get very low to cause significant power decrease)

43. heating • robots have high power density ~107 watt/m3 • tissue cells ~104 watt/m3 • possible significant local heating

44. temperature increase by robots high demand 10-4 degrees C flow

45. heating not significant • about 10-4 degree C • for a group of 100s of robots • heating would be significant if: • much larger groups • many groups in nearby capillaries

46. summary • ~10s of pW per robot on capillary walls • for group of ~100s of robots • oxygen: mainly from passing cells • small reduction in tissue power • especially for low demand scenario (resting tissue) • insignificant local heating • in spite of high power density

47. additional biology questions effects on robots and surrounding tissue

48. local effects • white blood cells • block oxygen transport as they pass • additional forces on robots • other functions of blood • e.g., immune response, clotting • response of cells in vessel wall to • forces from robots clinging to wall • blocked chemical transport

49. long-range effects • lower cell oxygen downstream of robots • response to partially blocked vessel • increase pressure? • time scale of response • systemic effects of many robot groups

50. further info • T. Hogg, Designing Microscopic Robots for Medical Diagnosis and Treatment, • Nanotechnology Perceptions3:63-73 (2007) • preprint: http://arxiv.org/abs/0906.5022 • R. Freitas Jr.,www.nanomedicine.com