We begin administering naturopathic treatment to patients with HCC in 1998. Records are available for review for 153 patients. The records for some patients seen 1998 and 2002 have been lost, but all available records are included, including records of all patients seen since 2002. Fifty-two patients are examined once and either do not qualify for treatment or do not return. Eight of these are known to have died a median of 22 days after presentation, while the fate of the others is unknown.

All treatment protocols are approved by the ethical review board of our hospital, which includes physicians, nurses, and phamacists. Upon their initial visit to the hospital or clinics, patients and their families are given an hour and half orientation to our approach to treatment. This includes mention of the likelihood that the case will be included in a presentation or publication. Those who agree to treatment are accepted as patients. For inpatients, written consent both for treatment and for inclusion in presentations or manuscripts is obtained on admission. For outpatients, written consent for inclusion in presentations or manuscripts is obtained upon initial preparation of the preparation or manuscript. Upon completion of the manuscript, oral confirmation of consent is obtained from surviving patients who can be contacted. Inclusion of patients in the manuscript is also reviewed and approved by the ethical review board.

This analysis describes 101 patients who are given naturopathic treatment. The diagnosis of HCC is based primarily on characteristic dynamic CT imaging, with serum levels of α-fetoprotein and/or prothrombin induced by vitamin K absence or antagonist II providing supportive evidence [2]. In cases that have previously undergone surgical resection, the diagnosis is confirmed by histopathology. Patients who have undergone resection are excluded unless the tumor has recurred after resection and is no longer operable. Included are patients who have undergone percutaneous ethanol injection therapy, trans-catheter arterial chemoembolization, radiofrequency ablation, and/or chemotherapy. Patients are not prevented from continuing these therapies after beginning naturopathic therapy.

Staging: Tumor staging at the time of treatment initiation is performed according to the Balcelona Clinic iver Cancer (BCLC) [3]. Liver disease is assessed at the time of initiation of naturopathic treatment by a modification of the Child-Pugu classification (Llovet et al. 2008), in which the platelet count is substituted for the prothrombin time (platelet count ≥ 100,000 = 1 point, <100,000 and ≥50,000 = 2 points, <50,000 = 3 points). Because of this modification, and because performance staging is not done, the actual BCLC classification used is a modification.

Treatment: Patients are treated with combinations of the natural agents, to be listed. Blood cell counts, measures of hepatic and renal function, urinalysis, tumor markers, tumor size on imaging, and chest X-ray are monitored.

The survival data reported here is assessed from the time of initiation of naturopathic treatment. Patients lose to follow up are considered to have died one day after the last kept follow up visit, and thus the calculated certainty of patient survival figures are minimum estimates. Survival data are analyzed by Kaplan-Meier statistics, using Prism software.

The following naturopathic treatments are used, given as oral preparations.

1) Cirdyceps sinensis: This came from wildly grown, natural Cordyceps sinensis that is subjected to far infrared ray heating, brewing with Aspergillus oryzae and lipophilization with sesame oil, as described previously [4]. This process has been shown to activate antioxidant, tumoricidal, and other biological activities contained in natural products [4]. Cirdyceps sinensis is a parasitic fungus that infects insects, which has long been used in traditional Chinese medicine. The active ingredient in Cirdyceps sinensis, cordycepin, has been known since 1950 to be a purine nucleoside analog, 3’-deoxyadenosine and acts as an anti-metabolite of adenosine [5]. This compound is shown over 40 years ago to have anti-cancer activity in both human and rodent systems in vitro and in rodents in vivo [6]. The mode of action is thought to be related to the termination of nucleic acid synthesis [7]. Moreover, it has been shown that cordycepin experts a variety of pharmacologic effects in different tumor cell lines, and rodent systems including inhibition of polyadenylation, simulation of adenosine A3 receptors, and induction of apoptosis [6].

2) TT, OT, B-T: These are closely related Chinese natural products that are harvested and produced in Taiwan that have been widely used in traditional Chinese medicine for centuries. TT consists of extracts of Bezoar bovis, Kadinum, Rhei rhizome, Phellodendri cortex, Arecae semen, and Mori folium, OT consists of extracts of Bezoar bovis, Kadinum, Rhei rhizome, Hoelen, Arecae semen, Mori folium, and Crassocephalum crepidioides.

3) HTT: This is a modification of TT containing Harpago, a variety of pedaliaceae from the Kalahari Desert in Africa.

4) WBF: This is another traditional Chinese product containing extracts of Zizyphi fructus, Talcum crystallinum(Kadinum), Moutan cortex, Puerariae, Ginseng radix, Zingiberis rhizome, Rhei rhizome, Glycyrrhizae radix, Saposhnikvoviae radix, and Trichosanthis radix.

5) Natural anti-oxidants (NAO): This preparation is developed and is produced by the authors [8]. It is produced from wheat germ, rice bran, soybean, hato mugi, which is a type of oriental wheat, wheat, sesame, green leaf extracts from Japanese green tea and Yuzu oranges. The extracts are subjected to far infrared ray heating, brewing with Aspergillus oryzae (koji), and with lipophilization with sesame oil treated as described above for Cirdyceps sinensis.

6) UCR: This is derived from Guacatonga (Casearia sylvestris), a tropical plant grown in the clay soils of Amazon. It is taken as tea and is said to show anti-tumor activity [10]. It is also used to treat benign digestive disorders.

7) TIM: This is an extract of the bark of Tecomaipe Mart, a tree that grows throughout South and Central America. It contains naphthoquinones, furanonaphoquinones, and other compounds reported to have anti-cancer, anti-microbial, and anti-inflammatory properties [9].

8) BG103: This is beta-glucan extracted from the edible Agaricus blazei mushroom, reported to be effective in several types of malignancy. It shows in vivo immunomodulatory and anti-inflammatory anti-tumor effets [11]. Other extracts from this mushroom have been shown to have specific anti-tumor activity against heaptoma cells [12].

9) BWS: This is derived from the seeds of loquat, known to be rich in amygdalin, which has been claimed to have anti-cancer activity.

10) BG105: This is “Chaga”, an aqueous extract of an edible mushroom, Inonotus obliquus, that grows in northern Asian latitudes, e.g., in Siberia, Hokkaido, and Mongolia. It has been reported to inhibit the protease of HIV-1. Recent literature has extensively documented antioxidant, anti-tumor, and hypoglycemic activity [13].

11) Sandbath Treatment: The sandbath is produced from stones that emit far infrared radiation (4 - 14 μm). This treatment has been reported to inhibit the growth of tumor cells in mice [14]. The patients undergoing this treatment also have received intravenous multivitamin infusions.

12) Regimen: WBF is specifically applied for HCC, and other agents are generally given for the overall purpose of inhibiting tumor growth. Agents are added or substituted when there is evidence of tumor progression. In particular, Cirdyceps sinensis is generally used for signs of tumor progression.

13) Lifestyle Counseling: Patients are routinely counseled to get adequate sleep, and to avoid overwork, mental stress, and dietary fat.

A similar flow near a flat plate which is suddenly accelerated from rest and moves in its own plane with a constant velocity is solved by Stokes [16]. For a brief sketch of the solution, see Schlichting [17].

For the present modeling, let us consider the flow between two parallel flat walls, one of which is at rest, the other is suddenly accelerated from the rest to a constant velocity U₀ (Figure 1). Note that the walls are two-dimensional, horizontal and infinitely long.

Since the system under consideration has no preferred length in the horizontal direction, it is reasonable to suppose that the velocity profile are independent of the horizontal x-direction, which means that the velocity profile for varying distance x can be made identical by selecting suitable scale factors for u and y. The scale factors for u and y appear quite naturally as the lower wall velocity U₀ and gap length between the two walls δ. Hence, the velocity profile after the time t > 0 can be written as the function of f in the following way.

The velocity profile is here accounted for by assuming that function f depends on only, and contains no additional free parameter. Since the fluid particles are fixed on the surface of two walls due to the viscous effect, the function must take the value of 1 on the lower wall (y = 0) and the value of 0 on the upper wall (y = δ), The boundary conditions are:

When writing down an approximate solution of the present flow, it is necessary to satisfy the above boundary conditions for u/U₀. It is evident that the following velocity profiles satisfy all of the boundary conditions.

in the range, where q is positive real number parameter. Eq.2 is considered as the approximate solutions on the flow between two parallel flat walls, one of which is at rest, the other is suddenly accelerated from the rest to a constant velocity U₀, where each solution takes a unique value of q. The value of q must be determined by the boundary conditions and the Reynolds number, where ν is the kinematic viscosity of the fluid.

It is known that the transition from laminar to turbulent flow in the boundary layer is governed by the Reynolds number, where U_∽ is the free stream velocity, d the boundary layer thickness. The critical Reynolds number R_{e crit}, at which the transition is initiated, is of 2800 approximately [17,18].

In case of the present flow, as shown in Figure 3, at 1 atmospheric pressure and temperature at 20˚C, water has the kinematic viscosity ν = 1.004 × 10⁻² cm²/s. When water is chosen as the fluid, and the constant velocity U₀ = 10 cm/s and the gap distance between the two walls δ = 10 cm are set, we obtain the Reynolds number R_e10⁴. The result of this calculation clearly illustrates how the flow is liable to be turbulent under ordinary conditions.

The solutions (2) are smooth analytical functions and thus they are only valid for laminar flow. For turbulent flow, no solution is known yet, but there is some hope to obtain it, by following Tsugé’s statistical theory of turbulence [19,20].

The fundamental governing equations for fluid mechanics are the Navier-Stokes equation [21,22]. This inherently nonlinear set of partial differential equations has no general solution, only severall exact solutions have been found [23]. All of these exact solutions are for laminar flows, and no turbulent flow solution is available yet. However, it is considered that each of the laminar solutions in (2) represents an approximate turbulent solution. In this regard, we consider that the solutions (2) are only applicable for laminar flow.

Let us examine whether this solution is game information or not. The non-dimensional velocity varies from 1 to 0 with increasing non-dimensional distance in many ways with changing the parameter q. It can be considered that represents certainty of patient survival. This is why certainty of patient survival takes the value of 1 at start, and it decreases with increasing the time and becomes the value of 0 at her or his death.

Imagine that the assumed flow is visualized with neutral buoyant particles. Motion of the visualized particles is detected by the eye almost instantaneously through light and is mapped on our retina [24], so that during these processes, motion of the “fluid particles” is transformed into that of the “information particles” by light carrying the images of fluid particles. This is why motion of the fluid particles is intact in the physical space, but only the reflected lights, or electromagnetic waves consisting of photons can reach the retina. Photons are then converted to electrochemical particles and are passed along the visual cortex for further processing in parts of the cerebral cortex [24]. Photons and/or electrochemical particles are considered to be information particles. It is, therefore, natural to expect that the flow in the physical world is faithfully transformed to that in the information world, or brain including eye, which is referred to “informatical world” here after. During this transformation, the flow solution in the physical world changes into the information in the informatical world.

Proposed are correspondences between the flow in physical world and information in informatical world, which are listed in Table 1.

Considering the correspondences in Table 1, (2) can be rewritten as

Introducing the following normalized variables in (4),

andWe finally obtain the analytical function of certainty of patient survival as

where ξ is certainty of patient survival, η the normalized time and q the positive real number parameter.

Figure 4 illustrates how certainty of patient survival ξ due to (4) changes with increasing normalized time η.

In this section, Niwa’s [1] 1st and 2nd experiments have been compared with the present information dynamic model expressed by (4).

Figure 5 shows a comparison of Niwa’s 1st experiment with the present model. It may be evident that the case treated with 4 or more agents fits with the model curve, while another case treated with 3 or fewer agents with. This shows how the former treatment contributes to make patient life time much longer.

Figure 6 shows a comparison of Niwa’s 2nd experiment with the present model. It may be evident that the