Strong correlation between specific heat capacity and water content in human tissues suggests preferred heat deposition in malignant tumors upon electromagnetic irradiation

Figures & data

Figure 1. Spectral absorption coefficient of liquid water as a function of wavelengths within the spectral range of infrared radiation with sub-ranges infrared-A (IR-A), infrared-B (IR-B) and infrared-C (IR-C) [51–53]. Spectral peaks and their extents are caused by basic vibrations of water molecules (v₁: symmetric O-H stretching, v₂: H-O-H bending, v₃: asymmetric O-H stretching, L₁: minor libration, L₂: major libration) and by their superposition and overtones (IR-A and IR-B), as well as by cluster/collective vibrations due to H-O ··· O stretching/bending (IR-C) [54–57]. Extents of horizontal boxes mark wavelength ranges of respective vibration types (Dashed line supplements data of the spectral absorption coefficient within 0.5 μm and 0.78 μm of the spectral range of visible radiation (VIS) for additional information).

Figure 2. Dielectric loss ε" of pure liquid water at temperatures of 2 °C (curve 1), 37 °C (curve 2) and 47 °C (curve 3), and of intracellular water at 1 °C (curve 4, open circles) as a function of frequency between 300 MHz and 20 THz [59,63]. Relaxation times decreased in pure water from τ ≈ 18 ps at 2 °C to τ ≈ 6 ps at 37 °C, and to τ ≈ 5.3 ps at T = 47 °C [59]. Debye Peak frequencies at ν_p ≈ 9 GHz (2 °C), at ν_p ≈ 26 GHz (37 °C) and at ν_p ≈ 30 GHz (47 °C), and extents of peak maxima of dielectric loss at ε'' ≈ 40% (2 °C), at ε'' ≈ 36% (37 °C) and at ε'' ≈ 34 (47 °C) [59]. Respective data for intracellular water at 1 °C: τ  ≈  20 ps, ν_p ≈ 8 GHz, and ε'' ≈ 27 (at maximum) [63].

Figure 3. Dielectric loss ε" in splenic hematoma (curve 1, squares), intestinal leiomyosarcoma (curve 2, dots), hemangiopericytoma (curve 3, stars)) and in NaCl solution of different salinity: 0.9% w/v (curve 4, open triangles), 0.5% w/v (curve 5, solid triangles) as a function of frequency between 10 MHz and 20 GHz. Data for NaCl solutions were measured by Gadani DH et al. [60]. Data for splenic hematoma and for both tumor tissues were calculated using data of conductivity measurements performed by Schepps and Foster [64] according to Equation (3)(3) $$\sigma \left(\omega \right)=\omega {\epsilon }_0{\epsilon }_r″\left(\omega \right),$$(3) .

Figure 4. Dielectric loss ε" in normal tissues (blue symbols: fat (triangles, upward), bone (triangles (downward), lung (dots), muscle (stars)) and in NaCl solution (salinity = 0.4% w/v, black hexagon) at frequencies of 13.56 MHz (curve 1, solid symbols) and of 434 MHz (curve 2, open symbols) as a function of water content of tissues. Data for dielectric loss were calculated using data of conductivity measurements by Kok and Crezee [65] according to Eq. 3(3) $$\sigma \left(\omega \right)=\omega {\epsilon }_0{\epsilon }_r″\left(\omega \right),$$(3) . Data for water content according to Pethig and Kell [61].

Table 1. Mean water content (C_w) and specific heat capacity (c_p) of liquid water, body fluids, normal human tissues (selection) and biological media*.

Tissues etc.	Cw [wt.%]	cp [J·g^–1·K^–1]
Water (33–43 °C)	100	4.18
Agar (2.5% w/v)	97	4.13
Blood, plasma	91	3.9
Whole	80	3.6
Placenta	87	3.8
Egg white	85	3.8
Testis	85	3.8
Brain, gray matter	83	3.7
Whole brain	78	3.65
White matter	70	3.6
Kidney	79	3.7
Prostate	79	3.65
Lung, parenchymal	79	3.9
Spleen	78	3.6
Uterus	79	3.65
Eye, cornea	77	3.6
Lens	66	3.2
Cartilage	75	3.6
Myocard	75	3.7
Liver	74	3.6
Skeletal muscle	73	3.6
Pancreas	73	3.55
Mammary, gland	60	3.0
Adipose	50	2.3
Skin**	63	3.4
Stratum corneum	20	2.0
Epidermis	75	3.6
Hypodermis	30	2.7
Body, whole	61	3.3
Connective tissues	60	3.4
Tense	33	2.4
Lysozyme solution	28	2.3
Adipose tissue	22	2.35
Breast (postmen.)	21	2.2
Bone, cortical	13	1.65
Yellow marrow	15	2.0
Red marrow	40	2.65
Tooth, dentin	10	1.5
Enamel	1–2	0.7

*References describing the water content of individual tissues and biological media are listed in Section 3.2, references for specific heat capacities are listed in Section 3.3.

For standard deviations and ranges of water contents see [35] (number of studies: 1–6). For standard deviations and ranges of c_p-values see [35,66,67] (number of studies: 1–6).

**Water content rises in the epithelium from the stratum cornea to the basal layer (15–70 wt.% [68]).

Table 2. Mean water content (C_w) and specific heat capacity (c_p) of normal human tissues vs. corresponding tumor tissues (selection).

Tissues [References]		Cw [wt.%]	cp [J·g^–1·K^–1]
Breast	Normal (whole breast)	53	3.0
[69–83]	Cancers	≈ 80	3.85
Brain	Normal (whole brain)	78	3.65
[84–89]	Primary malignancies, metastases	88	3.95
Skin	Normal	61	3.4
[68,90–98]	Cancers	82	3.75
Lung	Normal	79	3.5
[66,82,99]	Cancers (primary, metastatic)	85	3.8
Liver	Normal	74	3.6
[100–104]	Hepatomas	≈ 80	3.8
Pancreas	Normal	73	3.55
[103,105,106]	Cancers	84	3.8
Prostate	Normal	79	3.65
[107–111]	Cancers (Gleason 1)	80	3.65
	Cancers (Gleason 2–5)	76	3.5
[103]	Cancers (all)	84	3.8
Kidney	Normal	79	3.7
[103]	Cancers	84	3.8

Values are averaged means.

Table 3. Water contents (C_w) and specific heat capacities (c_p) of the multilayer tissue structures exposed in hyperthermia treatment of breast cancers.

Tissue layer	Cw [wt.%]	cp [J· g^–1· K^–1]
Skin
Stratum corneum	20	2.0
Epidermis	75	3.6
Dermis	60	3.3
Subcutis	30	2.7
Breast, gland	60	3.0
Adipose tissue	50	2.3
Muscle	73	3.6
Breast cancer	80	3.85

Values are averaged means, see data in Table 2 [68,83].

Figure 5. Specific heat capacity c_p of liquid pure water, body fluids, normal human tissues (selection), and biological media as a function of mean water content within the ranges C_w = 10–100 wt.% (5A), C_w = 70–100 wt.% (5 B), and C_w < 70 wt.% (5C) according to data listed in Table 1.

Figure 6. Specific heat capacity c_p of liquid pure water, body fluids, normal human tissues (selection), biological media (blue circles), and of tumor tissues (selection, red dots) as a function of mean water content within the range C_w = 70–100 wt.% according to data listed in Tables 1 and 2.

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