{Eqn. 6.52}
Nanomedicine, Volume I: Basic Capabilities
© 1999 Robert A. Freitas Jr. All Rights Reserved.
Robert A. Freitas Jr., Nanomedicine, Volume I: Basic Capabilities, Landes Bioscience, Georgetown, TX, 1999
6.5.2 Thermogenic Limits In Vivo
Consider nanorobots at work inside a single biological cell of size Lcell, volume Vcell = Lcell3, and thermal conductivity Kt = 0.623 watts/m-K (water) immersed in a large isothermal heat sink. The maximum temperature differential DTn between core and periphery caused by the intracellular release of Pcell (watts) due to nanorobot activity is:
where Dcell is total cellular energy density (watts/m3). A typical ~20 micron diameter human tissue cell produces 30-480 pW, giving DTcell = 0.3-6.0 microkelvins. The data in Table 6.8 indicates that individual cells appear to safely tolerate internal energy releases up to Dcell ~ 106 watts/m3, which leads to the following proposed thermogenic limit for in cyto operations:
Thus, for example, using the proposed limit an isolated 20 micron tissue cell can safely host in its interior a set of active nanorobotic machinery that in total generates Pcell ~ 8000 pW and raises cell temperature by DTcell ~ 100 microkelvins, which seems extremely conservative.
If many cells in a given block of tissue contain active nanomachinery, as will often be the case, then the assumption of an isothermal heat sink no longer holds because the nanorobots will collectively warm up their operating environment. In the limit of an entire human body, a 100-watt total nanorobot power expenditure giving a whole-body 1000 watt/m3 incremental power density (Table 6.8) seems quite conservative since 50,000-100,000 watts/m3 is considered the safe therapeutic range for medical diathermy. 819 A temperature rise in the tissues triggers an increase in blood flow, which in turn produces a cooling effect. The maximum thermal load that an adult can dissipate under room temperature conditions without an increase in body temperature is a whole-body exposure of 100 watts/m2,822 or ~2000 watts/m3. Thus a 100-watt whole-body nanorobot power budget normally will produce no measurable increase in body temperature.
Operated at its peak output of 1600 watts,780,865 the human body's core temperature rises ~3.5 K.821 Even assuming a simple linear relation, a whole-body 100-watt nanorobot power budget would correspond to an increase in core body temperature of at most ~0.2 K, far smaller than the mean normal diurnal variation of ~1 K (Section 6.3.1) and less than the ~0.2-0.5 K load error in the human thermoregulatory control system.865 Since glucose-powered nanorobots may compete with tissues for fuel, a 100-watt total withdrawal also represents ~2000 Kcal/day, near the limit of what can be conveniently replaced dietetically on a long-term basis.
A proper comprehensive analysis of energy flows818 requires a detailed model of body geometry, incident radiation, skin emissivity, convection currents, heat exchange by conduction, evaporative cooling, respiratory heat losses, physiological and behavioral thermoregulatory responses, work done by the patient, and the precise distribution, clumping patterns and activities of in vivo nanorobots, all of which is very complex and quite beyond the scope of this book. However, a simple log-linear interpolative relation with correct endpoints (Dtiss = 106 watts/m3 at Ltiss = 20 microns and Dtiss = 103 watts/m3 at Ltiss = 0.5 meters) suggests the following proposed crude maximum thermogenic limits for nanorobot operations in human soft tissue:
where Vtiss = Ltiss3 for the total volume of soft tissue in which all deployed nanorobots are active. (Eqns. 6.52 through 6.56 are summarized in Figs. 6.14 and 6.15). Thus, for example, medical nanorobots deployed solely in the thyroid gland (Ltiss ~ 2.6 cm; Table 8.9) should be restricted to a maximum total power budget Ptiss ~ 0.1 watt which elevates thyroid temperature by DTtiss ~ 0.02 K. Higher in vivo power densities may sometimes be justified in hospital or emergency medical situations (Chapter 24), and a few other special circumstances (e.g., Chapter 21).
Last updated on 18 February 2003
{Eqn. 6.53}
{Eqn. 6.54}
{Eqn. 6.55}
{Eqn. 6.56}