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Stem Cells, Vol. 17, No. 1, 25-30, January 1999
© 1999 AlphaMed Press

Bone Marrow as Multidimensional Orbit Oscillator after Autologous Bone Marrow Transplantation

Dobroslav Hajeka, Hana Kubesovab, Rostislav Vyzulac, Jiri Mayerb, Miloslav Druckmuellerd, Miroslav Tomiskab, Anna Vaskua

a Institute of Pathophysiology, Medical Faculty, Masaryk University;
b Department of Hematooncology, Masaryk University Hospital;
c Department of Medical Oncology, Masaryk University Hospital;
d Department of Mathematics, Technical University, Brno, Czech Republic

Key Words. Bone marrow transplantation • Multidimensional oscillator • Granulocytes • Sodium and potassium in urine

Dr. Dobroslav Hajek, Department of Hematooncology, Masaryk University Hospital, Jihlavska 20, CZ 639 00, Brno, Czech Republic.


   Abstract
Top
 Abstract
Introduction
 Patients and Procedures
 Method
 Results
 Discussion
 Conclusions
 References
 
The local renin-angiotensin system (RAS) in bone marrow is probably involved in the control of hematopoiesis. Earlier observations suggest the relationship between the frequency of sodium and potassium concentration changes in urine and bone marrow recovery after chemotherapy. The purpose of this study was to prove the relationship between sodium and potassium excretion changes in urine and granulocyte counts in peripheral blood after autologous bone marrow and peripheral blood stem cell transplantation.

The correlation between amplitude maximum FFmax of F=d[Na]/d[K], where d[Na] and d[K] are changes of sodium and potassium excretions in 24 h, and granulocytes, recorded k days later, was found in 12 patients with autologous bone marrow transplantation (BMT) and/or PBSCT. In patients with successful engraftment, k ranged from 4 to 7 days. In the patient with unsuccessful BMT, k was 12 days.

The results imply the interaction between systemic and bone marrow RAS.


   Introduction
Top
 Abstract
 Introduction
Patients and Procedures
 Method
 Results
 Discussion
 Conclusions
 References
 
In mouse experiments, the relationship between sodium [Na]n and potassium [K]n excretions in urine measured in 24-h samples and radiosensitivity was proved about 30 years ago. In interindividual comparison, the [Na]n/[K]n ratio changes recorded in 48- or 72-h intervals were proved to predict the leucocyte count changes and survival after whole-body irradiation. The [Na]n/[K]n ratio in urine was considered to be an indirect indicator of adrenal cortex reactivity not only in radiation syndrome [1] but also in other stress conditions, where a relationship between [Na]n/[K]n ratio fluctuations and leucocyte blood values was found [2]. Later, the above-mentioned method was modified to be used to follow healing in man. The oscillations revealing decreasing amplitude and slightly increasing periods that became stabilized at values not very different from seven days were recorded during the improving status [3]. On the contrary, decreasing amplitude and increasing the period indicated poor prognosis in patients treated with cytostatics [4]. These results are compatible with the findings that the rhythm of about a seven-day period (circaseptan) is involved in various physiological and pathophysiological processes in man. The circaseptan rhythm was proved to be of substantial importance in self healing and adaptation [5, 6], immunological response [7] and also in immunomodulation [8, 9]. Unfortunately, only periodic processes of constant frequencies were considered in these studies.

The cell differentiation in different populations in organs, representing compartments of cells revealing some characteristic features, could be necessary for the homeostasis [4]. This hypothesis supports the finding that the administration of large numbers of reconstituting cells that represent heterogeneous populations appears to be a cautionary procedure, since it should ensure polyclonal hemopoiesis after bone marrow transplantation (BMT) [10]. The cyclic processes of cell proliferation and differentiation are both stochastic on one or few cell levels and controlled on compartment and organ levels [11]. Hypothetically, this large population could represent unstable periodic multidimensional orbits of an oscillator. Each characteristic of a given cell population represents probably only one dimension of the orbit. Control by feedback makes accessible selected stabilized orbit, which can be chosen so as to optimize the system performance. A controlled chaotic system provides rich dynamic behavior, namely frequency selection in periodic processes. The selected frequency is likely to determine the system performance [12]. If bone marrow is a controlled oscillator, the feedback that enables this oscillator to control frequency exists.

The bone marrow renin-angiotensin system (RAS) role in negative proliferation regulation is discussed [13-19]. Considering the earlier results [2, 4], bone marrow RAS could be involved in both extracellular fluid volume and proliferation control representing part of a complex system that coordinates periodic processes of proliferation and extracellular volume changes.

This is why the purpose of this study was to learn whether the bone marrow recovery influences the oscillations of sodium and potassium excretions. As bone marrow recovery is conventionally followed by means of granulocyte (GR) count in peripheral blood after BMT or peripheral blood stem cell transplantation (PBSCT), the object of the study was to prove the relationship between changes of sodium and potassium excretions in urine and GR after autologous BMT and PBSCT.


   Patients and Procedures
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 Abstract
 Introduction
 Patients and Procedures
Method
 Results
 Discussion
 Conclusions
 References
 
Twelve patients of both sexes treated by autologous BMT and/or PBSCT entered the study. The patients' data are summarized in Table 1. The conditioning regimens were used as follows:

  1. BEAC: BCNU 300 mg/m2 i.v. day -8, Etoposide 200 mg/m2 i.v., Cytosinarabinosid 200 mg/m2 i.v., Cyclophosphamide 35 mg/kg days -7 to -2.

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              		Table 1. Patients' data
     
  2. BEAM: BCNU 300 mg/m2 i.v. day -7, Etoposide 200-400 mg/m2 i.v. days -6 to -3, Ara-C 400 mg/m2 i.v. days -6 to -3, Melfan 140 mg/m2 i.v. day -2.
  3. BuCy: Busulphan 4 mg/kg p.o. days -8 to -5, Cyclofosfamide 60 mg/kg i.v. days -4 to -3, Mesna 60 mg/kg i.v. days -4 to -2.
  4. CBV: Cyclofosfamide 1.5 g/m2 i.v. days -5 to -2, BCNU 300 mg/m2 i.v. day -6, Etoposide 400 mg/m2 i.v. days -5 to -2, Mesna 1.5 g/m2 i.v. days -5 to -1.
  5. HD-M: Melphan 200 mg/m2 i.v. day -1.
  6. ICE: Carboplatin 13 mg/kg i.v., Etoposide 13 mg/kg i.v., Isofosfamide 63 mg/kg i.v. days -6 to -4, G-CSF (Neupogen) 3.8 mg/kg s.c. days 1 to 12.
  7. ICE-EPI: Carboplatin 13 mg/kg i.v., Etoposide 10 kg/kg i.v, Isofosfamide 80 mg/kg i.v, Epirubicin 1.4 mg/kg i.v. days -7 to -5, Etoposide 4 mg/kg i.v. day -4, GM-CSF (Leucomax) 0.4 mg/kg s.c. days 4 to 10.

The hydration regimen had been started twelve hours before BuCy, CBV, ICE and ICE-EPI chemotherapies and continued during their administration: Dextrose of 5% concentration, 3 ml/kg/h; sterile saline (F 1/1), 2 ml/kg/h; potassium chloride of 7.5% concentration, 0.04 ml/kg/h and Mannitol of 15% concentration, 0.6 ml/kg/h. The solutions were administered simultaneously via a three-lumen catheter. The internal environment, namely sodium, potassium, and creatinin, and urea levels were maintained within reference ranges considering the balance and central venous pressure in all patients.

The bone marrow was harvested at the recovery time after previous chemotherapy according to widely used methods. The peripheral blood stem cell collection was performed by cell separator (Cobe Spectra; BCT, Inc., Colorado). Hemopoietic progenitor cells were cryopreserved in liquid nitrogen after addition of dimethylsulfoxide by computer-directed freezer according to routinely used scheme. The transplantation was successful in all patients except for patient No. 5, who revealed severe myelodysplastic syndrome with predominant thrombocytopenia and granulocytopenia immediately after the engraftment and died six weeks later of intracerebral hemorrhage. In patient No. 6 with successful engraftment, the non-Hodgkin's lymphoma (peripheral T-type) stage IV B with liver involvement progressed and the patient died six weeks after BMT of hepato-renal syndrome with pancytopenia, caused not only by the lymphoma but also by hepatitis virus, type nonAnonB. The autopsy proved bone marrow dysplasia, but no bone marrow infiltration by lymphoma. That is why the treatment was successful in ten cases only.


   Method
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 Abstract
 Introduction
 Patients and Procedures
 Method
Results
 Discussion
 Conclusions
 References
 
The sodium concentrations [Na]n and potassium concentrations [K]n were evaluated in urine collected during 24 h from 7 a.m. (dayn-1) to 7 a.m. (dayn). The amplitude Fourier spectra of the function Fn=d[Na]n/d[K]n were estimated; where: n=day number and d[Na]n=[Na]n-[Na]n-1, d[K]n=[K]n-[K]n-1 are the changes of sodium and potassium urine concentrations in 24-h intervals.

The Fourier transformation of an F function (FF) was performed over the 7-d intervals. The interval number indicated the middle of the analyzed interval, thus dayn-3 to dayn+3 were included in intervaln. The frequency corresponding to maximal amplitude—amplitude maximum (FFmax)—was found. The analogical method over 14-d intervals was used to confirm the existence of low frequency oscillations. The blood GR count was used as the marker of the bone marrow recovery and was plotted against FFmaxn-k , where k [day] was the hypothetical granulocyte-transit-time through non-proliferating compartment that caused the time-lag between FFmax change and GR response. It was estimated by means of maximal value of vector product FFmaxn-k* GRn, that was used to find the k for which the angle between the vectors was minimal. The correlation between corresponding values FFmaxn-k and GRn was calculated for each patient.


   Results
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 Abstract
 Introduction
 Patients and Procedures
 Method
 Results
Discussion
 Conclusions
 References
 
The urine sodium and potassium excretions were within the range from 36 to 938 and from 22 to 243 (mmol/d), respectively, in all patients and were not very different from normal values [20] ( Fig. 1).



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  		Figure 1. FFmax and GR in peripheral blood. Day 0 is the transplantation day. FFmax [day–1] is plotted against the day that indicates the middle of the sampled interval. FFmax is amplitude maximum of the Fourier transformed function F = d[Na]/d[K], where d[Na] and d[K] are sodium and potassium excretion changes in 24 h.

 
Remarkable consecutive changes of the F function amplitude spectrum were found in all patients: A) FFmax decreased from starting value to minimum. B) Another peak of higher frequency occurred. C) At this frequency FFmax with inversed phase was recorded. D) FFmax reached value not very different from the starting one ( Fig. 2).



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  		Figure 2. Amplitude spectrum of F function compared to GR counts.The figure consists of the above-mentioned substantial changes of spectra and corresponding GR counts. The amplitude of function F is plotted against Fourier frequency [day–1]. The day number refers to the middle of the sampled interval. The transplantation was performed on day 0. Granulocytes [106/l] are GR counts in peripheral blood. All values are plotted as medians and the range of amplitude maximum is indicated. Patient No. 5 is excluded; his spectra are drown by dotted line. The time intervals (day) are displayed as average ± SD, median, <range>, /patient's No. 5 value/.

 
Compared with day of engraftment ( Table 1) or granulocytopenia duration ( Fig. 1), the time interval between the last two above-mentioned changes (t4) revealed a low variability and also the preceding time interval (t3) was not very different in patients with successful engraftment. The large interindividual differences were found in t2, but it was not extreme in patient No. 5 with unsuccessful engraftment ( Fig. 2). The correlation between FFmaxn-k and GRn was proved in all patients. However, the correlation curves were interindividually very different ( Fig. 3). In patients with successful engraftment, the difference between t4 and k did not exceed 1 day. However, this difference was 7 days in patient No. 5. In patient No 6, t1, t2, t4, and k were not different from values obtained in successfully treated patients and also no difference between k and t4 was found (Table 2, Fig. 2). The latest FFmax values recorded in patients No. 5 and No. 6 were 0.08 and 0.10 (day -1), respectively. In surviving patients the FFmax values, estimated after engraftment, did not drop below 0.18 day -1 ( Fig. 2).



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  		Figure 3. The regression of GR on amplitude maximum FFmax.The granulocyte counts [106/l] recorded on day n are plotted against FFmax [day–1] estimated over interval the middle of which is day n-k.

 

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  		Table 2. The correlation between GR and corresponding FFmax GR(n) = f (a+b*FFmax(n-k))
 

   Discussion
Top
 Abstract
 Introduction
 Patients and Procedures
 Method
 Results
 Discussion
Conclusions
 References
 
Our results suggest the relationship between periodic sodium and potassium excretion changes and GR production (Table 2). However, the correlation alone does not imply causal relationship as also time relations between FFmax and GR must be considered. In patients with successful transplantation t4 equaled k, t4 and t3 ranged from 4 to 7 and 1 to 4 days, respectively, and revealed lower variability compared with t1 and t2 ( Fig. 2). Interestingly, t4 and t3 were in accordance with formerly reported myelocyte-to-blood transit time (the transit time through the nondividing maturation pool) and myelocyte compartment transit time. The former was reported to be from about 6 to 9 days, with the minimum value between 96 and 144 h, the latter 2.9 days [21]. The calculated time-lag (k) between FFmax and corresponding granulocyte changes also supports the causal relationship of the studied processes. The interindividual differences in granulocytopenia duration were above all due to broad t2 variability. The t1 and t2 meanings could probably be suggested as the time in which the bone marrow oscillator response to chemotherapy develops and the time in which the oscillator restored its structure, respectively. In patient No. 5 with unsuccessful engraftment, the t4 was clearly longer and FFmax lower in the time of engraftment compared with the other patients and the clear difference between k and t4 was found. These findings probably suggest that an abnormal granulopoiesis developed in this patient after transplantation.

Since predictive signification of FFmax values for granulocyte counts in peripheral blood was proved in all patients, and also in two patients (Nos. 1 and 2) with myelodysplastic syndrome, the presented method could be of importance in bone marrow dysfunction prediction.

The follow-up was probably not long enough to confirm the cyclical neutrophils' evolution found by Frederick Stohlman more than 20 years ago [22], but FFmax periodical changes were recorded at least in several patients.


   Conclusions
Top
 Abstract
 Introduction
 Patients and Procedures
 Method
 Results
 Discussion
 Conclusions
References
 
The bone marrow is involved not only as the hematopoietic organ, but it also influences sodium and potassium excretions in urine. The underlying hypothetical mechanism could be the bone marrow RAS interaction with systemic RAS, coordinating the periodic processes of cell proliferation in bone marrow with extracellular volume changes.


   Acknowledgments
 
Supported by grant No. VS96097 given by the Czech Ministry of Education.


   References
Top
 Abstract
 Introduction
 Patients and Procedures
 Method
 Results
 Discussion
 Conclusions
 References
 

  1. Pospisil M, Sikulova J, Sevcik F. The fluctuation of urine electrolyte excretion and its relation to mortality of multiple irradiated mice. Z Ges Exp Med 1965;139:112-121.

  2. Vacha J, Pospisil M. Individual differences in the stress response of mice and their relationship to the differences in radiation tolerance. Med Exp Int J Exp Med 1969;19:58-63.[Medline]

  3. Hajek D. The clinical use of Na/K oscillations in urine. In: Guttenbrunner G, Hildebrandt G, Moog R, eds. Chronobiology & Chronomedicine, Basic Research and Applications. Frankfurt am Main: Peter Lang, 1993:386-389.

  4. Hajek D, Simcikova B, Vorlicek J. Circaseptan rhythm restitution by means of timed high dose methylprednisolon—an improvement of cytostatic treatment response? J Interdiscipl Cycle Res 1993;24:342-344.

  5. Halberg F, Cornellissen G, Kopher R et al. Chronobiologic blood pressure and ECG assessment by computer in obstetric, neonatology, cardiology and family practice. In: Maedea K, Hogaki M, Nakano H, eds. Computers and Perinatal Medicine. Amsterdam: Excerpta Medica 1997:3-18.

  6. Hildebrandt G. Circaseptane Reaktionperiodic beim Menschen. Therapeuticon 1990;4:402-413.

  7. Halberg F. Chronobiology: methodological problems. Acta Med Rom 1980;18:399-440.

  8. Halberg E, Halberg F. Chronobiologic study design in everyday life, clinic and laboratory. Chronobiologia 1980;7:95-120.[Medline]

  9. Cavallini M, Halberg F, Cornelissen G et al. Modern drug administration devices for the chronobiologic optimalization of conventional treatment modes. In: Scheving LE, Halberg F, Ehret CF, eds. Chronobiotechnology and Chronobiological Engineering. Nijnhof: Dordreccht Martinus, 1987:47-49.

  10. Charbord P. Hemopoietic stem cells: analysis of some parameters critical for engraftment. STEM CELLS 1994;12:545-562.[Abstract]

  11. Gordon MY, Amos TA. Stochastic effects in hemopoiesis. STEM CELLS 1994;12:175-179.[Abstract]

  12. Lloyd AL, Lloyd D. Hypothesis: the central oscillator of the circadian clock is a controlled chaotic attractor. BioSystems 1993;29:77-85.[Medline]

  13. Grillon C, Bonnet D, Mary JY et al. The tetrapeptide AcSerAspLysPro (Seraspenide), a hematopoietic inhibitor, may reduce the in vitro toxicity of 3'-azido-3'-deoxythymidine to human hematopoietic progenitors. STEM CELLS 1993;11:455-464.[Abstract]

  14. Robinson S, Lenfant M, Wdzieczak-Bakala J et al. The molecular specificity of action of the tetrapeptide acetyl-N-Ser-Asp-Lys-Pro (AcSDKP) in the control of hematopoietic stem cell proliferation. STEM CELLS 1993;11:422-427.[Abstract]

  15. Rousseau-Plasse A, Lenfant M, Potier P. Catabolism of the hemoregulatory peptide N-Acetyl-Ser-Asp-Lys-Pro: a new insight into the physiological role of the angiotensin-I-converting enzyme N-active site. Bioorg Med Chem 1996;4:1113-1119.[Medline]

  16. Haznedaroglu IC, Tuncer S, Gursoy M. A local renin-angiotensin system in the bone marrow. Med Hypotheses 1996;46:507-510.[Medline]

  17. Haznedaroglu IC. Haematopoietic effects of ACE inhibitors and local bone marrow renin-angiotensin system: an hypothesis. Nephrol Dial Transplant 1996;11:2373.[Free Full Text]

  18. Chisi JE, Wdzieczak-Bakala J, Riches AC. Inhibitory action of the peptide AcSDKP on the proliferative state of hematopoietic stem cells in the presence of captopril but not lisinopril. STEM CELLS 1997;15:455-460.[Abstract/Free Full Text]

  19. Li J, Volkov L, Comte L et al. Production and consumption of the tetrapeptide AcSDKP, a negative regulator of hematopoietic stem cells, by hematopoietic microenvironmental cells. Exp Hematol 1997;25:140-146.[Medline]

  20. Lentner C, Lentner Ch, Wink A. Geigy Scientific Tables 1. Basel: Ciba-Geigy Limited, 1981:55-59.

  21. Athens JW. Granulocytes—neutrophils. In: Lee GR, Bithell TC, Foerster J et al., eds. Windrobe's Clinical Haematology. London: Lea & Febiger, 1993:223-266.

  22. Stohlman F, Quesenberry PJ, Tyler WS. The regulation of myelopoiesis as approached with in vivo and in vitro techniques. Prog Hematol 1973;8:259-297.[Medline]

accepted for publication December 11, 1998.



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